저작자표시-비영리-변경금지 2.0 대한민국 이용자는 ... - S-Space

저작자표시-비영리-변경금지 2.0 대한민국 이용자는 아래의 조건을 따르는 경우에 한하여 자유롭게 l. 이 저작물을 복제, 배포, 전송, 전시, 공연 및 방송할 수 있습니다.. 다음과 같은 조건을 따라야 합니다:. 저작자표시. 귀하는 원저작자를 표시하여야 합니다.. 비영리. 귀하는 이 저작물을 영리 목적으로 이용할 수 없습니다.. 변경금지. 귀하는 이 저작물을 개작, 변형 또는 가공할 수 없습니다.. l l. 귀하는, 이 저작물의 재이용이나 배포의 경우, 이 저작물에 적용된 이용허락조건 을 명확하게 나타내어야 합니다. 저작권자로부터 별도의 허가를 받으면 이러한 조건들은 적용되지 않습니다.. 저작권법에 따른 이용자의 권리는 위의 내용에 의하여 영향을 받지 않습니다. 이것은 이용허락규약(Legal Code)을 이해하기 쉽게 요약한 것입니다. Disclaimer. 공학석사 학위논문. Experimental and Numerical Studies on Floor Impact Sound Design of Residential Buildings 공동주택 바닥충격음 저감 설계를 위한 실험 및 해석 연구. 2016 년 2 월. 서울대학교 대학원 건축학과. 백 길 옥. Abstract. Experimental and Numerical Studies on Floor Impact Sound Design of Residential Buildings Baek, Gil-Ok Department of Architecture and Architectural Engineering College of Engineering Seoul National University In Korea, floor impact noise in apartment buildings frequently causes disputes between the residences, which rise as an important issue in the society. Main problem of the noise is heavy-weight floor impact sound which has low-frequency components below 200 Hz. It is induced by heavy-weight impact source such as children’s jumping or walking. According to Canada NRC research report (2010), heavy-weight floor impact sound is mainly influenced by structural system, floor plan type, thickness of slab, and boundary condition. It indicates that heavy-weight floor impact sound is a kind of structure-borne sound which is radiated by slab vibration. Thus, to fundamentally reduce floor impact sound, structural parameters related to slab vibration should be determined by designers first. Especially, numerical study for predicting floor impact vibration and sound is needed because experiments which investigate such parameters cost a lot of money and time in actual building design. And it should be considered at initial building design stage to prevent the plans which show poor floor impact sound insulation performance.. i. Analytical solution for structure-borne sound including heavy-weight floor impact sound can be proposed with high accuracy if vibration analysis model predicts the actual behavior well. This study focused on proposal of total floor impact sound analysis process for designers in the practical field. The process includes numerical modeling, analysis, prediction and verification of floor impact sound. And it proposed several design values and detail process of numerical analysis for designers who have to perform the analysis with limited information. For this purpose, floor impact sound and vibration test in a multi-story residential building was firstly performed. And, to investigate applicability of the numerical analysis process on actual floor impact sound design, the test results were compared with corresponding results of finite element model. Finally parametric study on actual building design factors was performed to investigate the correlation with floor impact sound. The result showed that the proposed process predicts the floor impact sound within suitable error level range when compared with experimental deviation. Also, parametric study found that axial stiffness of resilient materials and section plan design parameters have high correlation with floor impact sound. Concrete material properties and floor area, aspect ratio showed relatively low correlation with floor impact sound.. Keywords : floor impact sound; structural-borne sound; finite element analysis; residential building Student Number : 2014-20514. ii. Contents. Abstract ...................................................................... i Contents.................................................................... iii List of Tables ............................................................ vi List of Figures ........................................................ viii List of Symbols ....................................................... xii Chapter 1. Introduction ........................................... 1 1.1 Background of Research ............................................................... 1 1.2 Objective of Research................................................................... 3 1.3 Outline of Master’s Thesis............................................................ 4. Chapter 2. Review .................................................... 6 2.1 Code Review ................................................................................ 6 2.1.1 Provisions about Housing Construction Standard .......................... 7 2.1.2 Standard Floor Structure................................................................. 8 2.1.3 KS Code.......................................................................................... 9. 2.2 Literature Review ....................................................................... 11 2.2.1 Structure-borne Sound Theory ...................................................... 11 2.2.2 Research on Floor Impact Sound.................................................. 13. Chapter 3. Floor Impact Sound and Vibration Test in a Residential Building ............................... 18 iii. 3.1 Introduction ................................................................................ 18 3.2 Test Program ............................................................................... 20 3.2.1 Test site ......................................................................................... 20 3.2.2 Modal test plan ............................................................................. 25 3.2.3 Floor impact sound test plan ......................................................... 28. 3.3 Test Result .................................................................................. 31 3.3.1 Modal Test Result ......................................................................... 31 3.3.2 Vibration Response ....................................................................... 35 3.3.3 Acoustic Response ........................................................................ 37 3.3.4 Floor Impact Sound Level ............................................................ 38. 3.4 Discussions ................................................................................. 47. Chapter 4. Numerical Analysis of Floor Impact Sound ....................................................................... 48 4.1 Introduction ................................................................................ 48 4.2 Proposal of Numerical Analysis Process .................................... 49 4.2.1 Assumptions ................................................................................. 49 4.2.2 Proposal of Design Property ......................................................... 51 4.2.3 Numerical Analysis Process ......................................................... 53. 4.3 Analysis Plan .............................................................................. 55 4.3.1 Bare Concrete Slab ....................................................................... 55 4.3.2 Floating Floor ............................................................................... 57. 4.4 Analysis Result ........................................................................... 59 4.4.1 Modal analysis .............................................................................. 59 4.4.2 Vibration Analysis ........................................................................ 61 4.4.3 Floor Impact Sound Analysis ....................................................... 64 4.4.4 Numerical Verification ................................................................. 68. 4.5 Discussions ................................................................................. 76. Chapter 5. Parametric Study on Floor Impact Sound Design Factors ............................................ 77 5.1 Introduction ................................................................................ 77 iv. 5.2 Concrete Slab Design ................................................................. 78 5.2.1 Compressive Strength of Concrete ............................................... 78 5.2.2 Mass Density of Concrete............................................................. 80 5.2.3 Young’s Modulus of Concrete ...................................................... 82. 5.3 Resilient Materials Design.......................................................... 85 5.3.1 Dynamic Stiffness of Resilient Materials ..................................... 85 5.3.2 Thickness of Resilient Materials .................................................. 89 5.3.3 Axial Stiffness of Resilient Materials ........................................... 91. 5.4 Floor Plan Design ....................................................................... 96 5.4.1 Floor Area ..................................................................................... 96 5.4.2 Aspect Ratio................................................................................ 103. 5.5 Discussions ............................................................................... 106. Chapter 6. Conclusions ........................................ 108 References ............................................................. 110 Appendix A: Test Database ................................. 113 초. 록 .................................................................. 121. v. List of Tables Table 2.1 Floor impact sound insulation performance grade ................. 7 Table 3.1 Scope and objective of test ................................................... 18 Table 3.2 Material property of bare concrete slab ................................ 23 Table 3.3 Resilient material property of floating floor ......................... 23 Table 3.4 Vibration property of bare concrete slabs ............................. 33 Table 3.5 Mode shapes ......................................................................... 34 Table 3.6 Vibration acceleration level of bare concrete slabs .............. 36 Table 3.7 Floor impact sound level of bare concrete slabs ................... 39 Table 3.8 Heavy-weight floor impact sound reduction of floating floor .............................................................................................................. 41 Table 4.1 Design values for numerical modeling ................................. 52 Table 4.2 Requirements of floor impact sound analysis process .......... 54 Table 4.3 Numerical model plan........................................................... 56 Table 4.4 Input property of floating floor model .................................. 58 Table 4.5 Mode shapes by experiment and analysis ............................. 60 Table 4.6 Analytical result of 1/1 octave floor impact sound level ...... 64 Table 4.7 Floor impact sound level prediction error ............................ 71 Table 5.1 Floor impact sound design parameters ................................. 77 Table 5.2 Analysis of vibration property according to concrete strength .............................................................................................................. 79 Table 5.3 Analysis of floor impact sound according to concrete strength .............................................................................................................. 79 Table 5.4 Analysis of vibration property according to mass density .... 81 Table 5.5 Analysis of floor impact sound according to mass density... 81 Table 5.6 Analysis of vibration property according to Young’s modulus .............................................................................................................. 84 Table 5.7 Analysis of floor impact sound according to Young’s modulus .............................................................................................................. 84 vi. Table 5.8 Floor impact sound reduction level according to dynamic stiffness ................................................................................................. 88 Table 5.9 Floor impact sound reduction level according to unit axial stiffness ................................................................................................. 95 Table 5.10 Floor impact sound reduction level according to axial stiffness ................................................................................................. 95 Table 5.11 Analysis of floor impact vibration according to floor area . 97 Table 5.12 Analysis of floor impact sound according to floor area ...... 97 Table 5.13 Statistical result of floor impact sound level of bare concrete slabs .................................................................................................... 102 Table 5.14 Design property according to aspect ratio ........................ 103 Table 5.15 Floor impact vibration level by aspect ratio ..................... 104 Table 5.16 Floor impact sound level by aspect ratio .......................... 104 Table 5.17 Floor impact sound tendency ............................................ 106. vii. List of Figures Figure 1.1 Floor impact sound transmission mechanism ....................... 1 Figure 1.2 Outline of research ................................................................ 5 Figure 2.1 Section plan of typical standard floor ................................... 8 Figure 2.2 Inverse A curve (KS F 2863-2) ........................................... 10 Figure 2.3 Measurement system arrangement (Kim et al.) .................. 14 Figure 2.4 Mode shape of slab system (Hwang et al.) ......................... 15 Figure 2.5 Prediction of acceleration response and sound pressure by FRF (Mun et al.) ................................................................................... 17 Figure 3.1 Test site ................................................................................ 20 Figure 3.2 Floor plan of test site ........................................................... 21 Figure 3.3 Section plan of test site ....................................................... 22 Figure 3.4 Dynamic stiffness measurement set-up on resilient materials .............................................................................................................. 24 Figure 3.5 Dynamic stiffness measurement result of resilient materials .............................................................................................................. 24 Figure 3.6 Modal test plan .................................................................... 26 Figure 3.7 Test grid setup on floor slab ................................................ 27 Figure 3.8 Section plan of floor impact sound test room ..................... 29 Figure 3.9 Location of impact points and receiving points .................. 30 Figure 3.10 Receiving room ................................................................. 30 Figure 3.11 Acceleration FRF at P1 by impacting P1 .......................... 32 Figure 3.12 Acceleration FRF at P2 by impacting P2 .......................... 32 Figure 3.13 Acceleration level at P1 by impacting P1 ......................... 35 Figure 3.14 Acceleration response of bare slab and floating floor ....... 36 Figure 3.15 Correlation between acoustic FRF and acceleration FRF . 37 Figure 3.16 1/3 Octave floor impact sound level of bare concrete slabs .............................................................................................................. 38 Figure 3.17 1/1 Octave floor impact sound level of bare concrete slabs .............................................................................................................. 39 viii. Figure 3.18 Single number quantity ..................................................... 41 Figure 3.19 Heavy-weight floor impact sound according to dynamic stiffness ................................................................................................. 42 Figure 3.20 Heavy-weight floor impact sound according to thickness of resilient materials .................................................................................. 42 Figure 3.21 Floor impact sound level of floor structure A ................... 44 Figure 3.22 Floor impact sound level of floor structure B ................... 44 Figure 3.23 Floor impact sound level of floor structure C ................... 45 Figure 3.24 Floor impact sound level of floor structure D ................... 45 Figure 3.25 Floor impact sound level of floor structure E ................... 46 Figure 3.26 Floor impact sound level of floor structure F.................... 46 Figure 4.1 Structural FE model ............................................................ 50 Figure 4.2 Acoustic FE model .............................................................. 50 Figure 4.3 Numerical analysis process ................................................. 53 Figure 4.4 Floor plan of numerical model ............................................ 55 Figure 4.5 Concept of floating floor analysis model ............................ 58 Figure 4.6 Acceleration response at receiving point P1 by impact at P1 .............................................................................................................. 62 Figure 4.7 Acceleration response at receiving point P2 by impact at P1 .............................................................................................................. 62 Figure 4.8 Acceleration response at receiving point P3 by impact at P1 .............................................................................................................. 63 Figure 4.9 Acceleration response at receiving point P4 by impact at P1 .............................................................................................................. 63 Figure 4.10 Analytical and experimental result of floor impact sound by impact at P1 .......................................................................................... 65 Figure 4.11 Analytical and experimental result of floor impact sound by impact at P2 .......................................................................................... 65 Figure 4.12 Analytical and experimental result of floor impact sound by impact at P3 .......................................................................................... 66 Figure 4.13 Analytical and experimental result of floor impact sound by impact at P4 .......................................................................................... 66 Figure 4.14 Analytical and experimental result of floor impact sound by impact at P5 .......................................................................................... 67 ix. Figure 4.15 Analytical and experimental result of average floor impact sound..................................................................................................... 67 Figure 4.16 Analytical result of floor impact sound of test model ....... 68 Figure 4.17 Analytical result of floor impact sound in 59-type household .............................................................................................. 69 Figure 4.18 Analytical result of floor impact sound in 74-type household .............................................................................................. 69 Figure 4.19 Analytical result of floor impact sound in 84-type household .............................................................................................. 70 Figure 4.20 Analytical result of floor impact sound in 114-type household .............................................................................................. 70 Figure 4.21 Analytical result of floor impact sound in floating floor structure A ............................................................................................ 73 Figure 4.22 Analytical result of floor impact sound in floating floor structure B ............................................................................................ 73 Figure 4.23 Analytical result of floor impact sound in floating floor structure C ............................................................................................ 74 Figure 4.24 Analytical result of floor impact sound in floating floor structure D ............................................................................................ 74 Figure 4.25 Analytical result of floor impact sound in floating floor structure E ............................................................................................. 75 Figure 4.26 Analytical result of floor impact sound in floating floor structure F ............................................................................................. 75 Figure 5.1 Flexural stiffness measurement of concrete specimen ........ 83 Figure 5.2 Dynamic stiffness according to concrete aging .................. 83 Figure 5.3 Heavy-weight floor impact sound according to dynamic stiffness by bang machine excitation .................................................... 86 Figure 5.4 Heavy-weight floor impact sound according to dynamic stiffness by impact ball excitation ........................................................ 86 Figure 5.5 Heavy-weight floor impact sound reduction according to dynamic stiffness by bang machine excitation ..................................... 87 Figure 5.6 Heavy-weight floor impact sound reduction according to dynamic stiffness by impact ball excitation ......................................... 87 Figure 5.7 Heavy-weight floor impact sound according to resilient material thickness of test site ................................................................ 90 Figure 5.8 Heavy-weight floor impact sound according to resilient x. material thickness of site A ................................................................... 90 Figure 5.9 Heavy-weight floor impact sound according to unit axial stiffness by bang machine excitation .................................................... 92 Figure 5.10 Heavy-weight floor impact sound according to unit axial stiffness by impact ball excitation ........................................................ 92 Figure 5.11 Heavy-weight floor impact sound reduction according to unit axial stiffness by bang machine excitation .................................... 93 Figure 5.12 Heavy-weight floor impact sound reduction according to unit axial stiffness by bang machine excitation .................................... 93 Figure 5.13 Heavy-weight floor impact sound reduction according to axial stiffness by bang machine excitation ........................................... 94 Figure 5.14 Heavy-weight floor impact sound reduction according to axial stiffness by impact ball excitation ............................................... 94 Figure 5.15 Heavy-weight floor impact sound level according to floor area by bang machine excitation .......................................................... 99 Figure 5.16 Heavy-weight floor impact sound level according to floor area by impact ball excitation ............................................................... 99 Figure 5.17 1/1 Octave floor impact sound level according to floor area ............................................................................................................ 102 Figure 5.18 Heavy-weight floor impact sound according to aspect ratio ............................................................................................................ 105. xi. List of Symbols A. floor area, m2. c. velocity of sound, m/s. Ec. static modulus of elasticity of concrete, GPa. Ed. dynamic stiffness of resilient materials, MN//m3. fc. design concrete strength, MPa. fn. natural frequency, Hz. k. axial stiffness, MN//m2. k/A. unit axial stiffness per floor area, MN//m4. LFmax. maximum sound pressure level measured by sound level meter with ‘F’ time calibration, dB. LFmax,k. maximum sound pressure level at k-th impact point measured by sound level meter with ‘F’ time calibration, dB. Li,Fmax. average value of maximum impact sound level at each frequency measured by sound level meter with ‘F’ time calibration, dB. Li,Fmax,AW. inverse A-weighted value of Li,Fmax assessed by inverse A curve, dB. Ln,AW. inverse A-weighted value of Ln assessed by inverse A curve, dB xii. p. sound pressure, Pa. R. reflection coefficient of material. SNQ. single-number quantity of floor impact sound, dB. SPL. sound pressure level, dB. VAL. vibration acceleration level, dB(ref. 1x10-6 m2/s). t. resilient material thickness, mm. vn. surface normal velocity of structure, m/s. Z. acoustic panel impedance, kg/m2/s. . sound absorption coefficient of material. . angular frequency, rad/s. n. damping ratio of n-th normal vibration mode. ρ. mass density, kg/m3. ρ·c. acoustic characteristic impedance, kg/m2/s. xiii. Chapter 1. Introduction 1.1 Background of Research In Korea, floor impact noise often causes disputes between the residences, which rise as an important issue in the society. Generally, the structure of residential buildings in Korea is mainly bearing wall-slab structure, where walls replace columns and a room is enclosed by the walls and slab. As shown in Figure 1.1, floor impact noise is transmitted to the lower household through walls and slab by various paths. The main problem of floor impact noise is heavy-weight floor impact sound, which is induced by low-frequency vibration of heavy and soft impact source. The typical example of the heavy and soft impact source is children’s jumping or walking.. Figure 1.1 Floor impact sound transmission mechanism. 1. In 2010, Canada NRC research report [1] announced that heavyweight floor impact sound is mainly influenced by structural parameters. The parameters are structure system type, slab thickness, floor area, and boundary condition of buildings. It indicates that heavy-weight floor impact sound is a kind of structure-borne sound, which is radiated by slab vibration. The majority of previous researches have focused on investigating performance of resilient materials on the reduction of floor impact noise. A large number of resilient materials were randomly investigated by experimental method. The result showed that they have good insulation performance on light-weight floor impact noise but not on heavy-weight floor impact noise. It is difficult to reduce the heavyweight floor impact noise only by using resilient materials because they cannot reduce slab vibration itself. Thus, to fundamentally reduce floor impact sound, structural parameters should be significantly considered and determined at initial design stage by building designers. For the purpose, studies on floor impact sound prediction are needed to prevent the plans which show poor floor impact sound insulation performance. Numerical study should be especially developed because experiments which investigate such parameters cost a lot of money and time in actual building design. Analytical solution for structure-borne sound including heavy-weight floor impact sound can be proposed with high accuracy if vibration analysis model predicts the actual behavior well.. 2. 1.2 Objective of Research The objective of this research is to propose total floor impact sound analysis process to such designers in the practical field. Required performance of the process is that any designer can perform the floor impact sound analysis if FEA software and building structure plan is given. Because they have to perform the analysis with limited information, practical applicability was considered the most. The prediction accuracy of numerical analysis was targeted that floor impact sound error is within the range of experimental deviation database. For the above purposes, it firstly focused on finding proper design values which is needed for floor impact sound analysis. Several preceding tests were performed in a residential building to derive vibration properties and average floor impact sound data from them. And it secondly focused on proposing numerical analysis process for predicting floor impact sound of residential buildings. To evaluate prediction accuracy of the process, various buildings including the test site were analyzed and compared with experimental result. Finally, parametric studies on actual building design factors were performed to investigate correlation with floor impact sound.. 3. 1.3 Outline of Master’s Thesis In Chapter 2, domestic laws and codes about floor impact sound in residential buildings were reviewed. And sound radiation theory of vibrating structures was briefly introduced to explain the principle of floor impact sound occurrence. Preceding experimental and numerical studies about floor impact sound were reviewed. In Chapter 3, experimental study was conducted about investigating floor impact sound and vibration characteristics of a building. Modal test was performed to measure vibration properties of the building. And floor impact sound test according to building construction stage was performed at the same site. The standard floor impact vibration and sound data was derived from the tests and compared with analytical results in Chapter 4. It found the deviation of floor impact sound level in bare concrete slabs of identical plan. Also, floor impact sound insulation performance of floating floors was investigated according to various test parameters. In Chapter 4, it was proposed floor impact sound prediction process by finite element method. Modal analysis, steady-state dynamics analysis, and acoustic harmonic FEM analysis were performed. Each analytical result was compared with the corresponding test result in Chapter 3. Several design values about structural and acoustic properties of general residential buildings were proposed for practical usage. The result showed that floor impact sound prediction error is 1-2 dB on average, which is smaller than deviation level of the test result. Thus, it seemed that the numerical method in this study is able to be utilized for designers who perform the floor impact sound analysis with limited information. In Chapter 5, parametric study on floor impact sound was performed by both numerical and experimental method. Actual building design factors such as material property, floor plan, and section plan were set as. 4. parameters. And correlation with floor impact sound was investigated for each parameter. Finally, conclusion of this study is summarized in Chapter 6. The outline of this research is shown in Figure 1.2. Figure 1.2 Outline of research. 5. Chapter 2. Review 2.1 Code Review Before the revision of Korean housing laws, there was no specific regulation or design guide about floor impact noise in residential buildings. However, as floor impact noise problem occurred as an important social issue in Korea, Ministry of Land, Infrastructure and Transport established the laws which comment the specific criterion for floor impact sound insulation performance. The criterion is commented in ‘Provisions about Housing Construction Standard-Clause 3, Article 14’ [2]. In the provision by 2013, it is commented that residential buildings should satisfy two criteria about floor impact sound. The first one is floor impact sound insulation performance criteria and the second one is construction specification of standard floor structure. But the standard floor structure was abolished in 2014 and two criteria were integrated into one criterion. The explanation about them is introduced in chapter 2.1.1 and 2.1.2. Also, measurement and assessment code of floor impact sound in residential building is briefly reviewed in chapter 2.1.3. Currently, KS (Korean Industrial Standard) codes regulate the standard floor impact sound test method in Korea. KS F 2810-2 [3] is about field measurement of heavy-weight floor impact sound and KS F 2863-2 [4] is about assessment of heavy-weight floor impact sound.. 6. 2.1.1 Provisions about Housing Construction Standard According to ‘Provisions about Housing Construction Standard’, rating of floor impact sound insulation performance is provided as shown in Table 2.1. Floor impact sound insulation performance grade is classified from Grade 1 to Grade 4. It is recommended that floor impact sound level in residential buildings is lower than 50 dB1 for standard heavy-weight floor impact sound ( L 'i ,F max, AW ) and 58 dB for standard light-weight floor impact sound ( L 'n , AW ). But most of standard floor systems satisfying the criteria have grade 1 in light-weight floor impact sound but they only have grade 3 or 4 in heavy-weight floor impact sound. It indicates that present floor system has structural limits for heavy-weight floor impact sound insulation performance.. Table 2.1 Floor impact sound insulation performance grade Grade. 1. L 'n, AW. Grade. L'i,Fmax,AW. 1. L 'n, AW  43. 1. L'i,Fmax,AW  40. 2. 43  L 'n, AW  48. 2. 40 < L'i,Fmax,AW  43. 3. 48  L 'n, AW  53. 3. 43 < L'i,Fmax,AW  47. 4. 53  L 'n, AW  58. 4. 47 < L'i,Fmax,AW  50. Sound pressure reference : 20x10-5 Pa. 7. 2.1.2 Standard Floor Structure Standard floor structure is a floor structure which is recommended in ‘Korea Construction Standards, Article 14, section 3’. The representative section plan of standard floor structure is shown in Figure 2.1.. Floor coverings Finishing mortar (40mm) Autoclaved Lightweight Concrete (40mm) Resilient Material (20mm) Resilient Material. Concrete Slab (210mm). Figure 2.1 Section plan of typical standard floor. It is composed of concrete slab, resilient material, autoclaved lightweight concrete (ALC), finishing mortar, and floor coverings. Minimum thickness of concrete slab is 210 mm for buildings with bearing wall-slab structure. It is generally called as ‘floating floor’ because it physically separates the concrete slab from the finishing mortar by placing resilient materials between them. Most of residential buildings after revision of Korean housing laws were constructed by the specification of standard floor. In 2014, the law about stand floor structure specification was abolished. Instead of this, standard floor was integrated with the floor structures which satisfy constant sound insulation performance criteria regardless of slab thickness. But this study focused on residential buildings which were constructed as standard floor structure.. 8. 2.1.3 KS Code In Korea, there is no specific design code for floor impact sound in residential buildings. Instead, measurement and assessment criterion for floor impact sound is specified in KS (Korean Industrial Standard) codes. Field measurement of floor impact sound insulation of buildings is prescribed in KS F 2810 codes. The contents are based on ISO 140-6 code. KS F 2810-1 states the method using standard light impact sources and KS F 2810-2 states the method using standard heavy impact sources. KS F 2810-2 is briefly introduced among them because this study focused on heavy-weight floor impact sound. Primary terms defined in the code are as follows. LF max is maximum sound pressure level measured by sound level meter with ‘F’ time calibration. Especially,. Li ,F max is maximum impact sound level at each frequency. Calculation of Li ,F max is stated as follows.. LF max,k , which is LF max at the k-th impact point, is calculated by energy average value of maximum sound pressure level measured at all receiving points like equation (2.1).. 1 m L  LF max,k  10log10  10 F max, j /10   m j 1 . (2.1). In equation (2.1), LFmax,j is maximum sound pressure level measured at j-th receiving point. m is the number of receiving points. Then Li ,F max is calculated by the linear average of LF max,k as shown in equation (2.2).. Li ,F max. 1 n   LF max,k n k 1. (2.2). Assessment of heavy-weight floor impact sound follows KS F 2863-2, which is based on ISO 717-2 [5]. The code defines the assessment method of single-number quantity by Li ,F max, AW , which is inverse Aweighted value of maximum sound pressure level. It is calculated by. 9. using inverse A curve as shown in Figure 2.2. The measured 1/1 octave floor impact sound level curve is translated until the summation of difference between reference value and the measured value is less than 8.0 dB. Then, sound pressure level at 500 Hz in the translated curve is defined as Li ,F max, AW .. Figure 2.2 Inverse A curve (KS F 2863-2). 10. 2.2 Literature Review 2.2.1 Structure-borne Sound Theory This chapter briefly introduces about the structural-borne sound radiation theory, stated by Fahy and Gardonio [6]. It is the basis theory of floor impact sound radiation which this study focuses on. The definition of sound is small variation of an acoustic medium around a state of equilibrium. It is classified into air-borne sound and structure-borne sound according to acoustic source pathway. Structureborne sound, including floor impact sound, is mainly caused by vibration of solid structures. Sound pressure wave equation in the time domain t is like equation (2.3).. 2 p( r,t)-. 1  2 p( r,t) =0 c 2 t 2. (2.3). In equation (2.3), p(r , t ) is sound pressure at position vector r , c is sound velocity. If simple harmonic excitation is assumed, time variable can be removed by Fourier transform equation (2.4)..  . p r, t . 1 2. .  p  r,    e.  jt. dt. . (2.4). By substituting equation (2.4) to (2.3), it can lead to Helmholtz equation (2.5) which represents wave equation in the frequency domain.. 2 p( r, )+ k 2 p( r, )= 0. (2.5). p(r ,  ) is sound pressure variation at position r with angular frequency ω. k is wave number which is defined as. c . ω. In Helmholtz equation, p(r ,  ) , which is vector component, can be expressed by using velocity potential  which is scalar component as shown in equation (2.6).. 11. v  . (2.6). The term v in (2.6) is substituted to Euler’s equation (2.7) which states conservation of momentum of fluid. Then equation (2.8) and (2.9) is derived from it as a result.. 0. v  p  0 t.  0. (2.7).   p  0 t. (2.8).   const. t. (2.9). p  0. In equation (2.9),.  can be expressed as t. p  0 j. j . (2.10). Finally, wave equation of velocity potential  can be derived by substituting equation (2.11) to equation (2.5).. (2  k 2 )  0. (2.11). (2  k 2 )  q. (2.12). Equation (2.11) and (2.12) show the relationship between sound pressure and velocity of acoustic medium. These equations are the basis for acoustic FEM analysis.. 12. 2.2.2 Research on Floor Impact Sound Previous researchers had been studying about characteristics of floor impact sound by experimental and numerical method. And most of research results found that floor impact sound is a kind of a structureborne sound. It indicates that floor impact sound prediction is possible if structural vibration is analyzed with high accuracy. The primary researches are reviewed as follows. In 1896, Rayleigh et al. [7] proposed the sound radiation equation that calculates sound pressure at any position through surface normal velocity of vibrating structure.. p( r ) . j 0 2. s. vn ( rs )e  jkR R. dS (2.13). In equation (2.13),  is angular frequency of acoustic source,  0 is mass density of acoustic medium, vn is surface normal velocity of vibrating structure, r is position vector of acoustic field, R is distance between acoustic field point and vibrating surface. On the basis of this equation, sound pressure at any specific measurement points can be calculated by using surface normal velocity of floor slab. This equation had been applied to both experimental and analytical researches on floor impact sound prediction field.. 13. In 2003, Kim et al. [8] studied the prediction of floor impact sound by measuring the vibration responses on the interior structure in residential buildings. It focused on the applicability of the sound radiation theory, which shows correlation between floor impact sound and vibration. In the study, the vibration acceleration levels on the interior structures were measured. Figure 2.3 shows the measurement system arrangement.. Figure 2.3 Measurement system arrangement (Kim et al.). Then, the sound pressure level was predicted by substituting the measured vibration acceleration levels to equation (2.14). And it was compared with the measured sound pressure level. SPL  VAL  10log   10log( S A)  20log f m  36. (2.14). The equation (2.14) is generally used in estimating the sound pressure level of structural-borne sound by sound radiation theory. SPL is average interior sound pressure level, VAL is vibration acceleration level (dB, ref. 6. 2. 1  10 m s ), A is interior total sound absorption (m ), and 2. f m is. center frequency (Hz). The result showed that the predicted values were in good agreement with the measured values within 5~10 % in error rate. In conclusion, it proved that floor impact sound is greatly related with slab vibration. It also indicates that if numerical model predicts the actual vibration response with high accuracy, floor impact sound can be predicted from them as well. In 2009, Hwang et al. [9] performed finite element analysis to. 14. investigate the sound radiation characteristics according to building structural system type. The sound pressure of floor impact noise radiated by slab vibration at any point r can be expressed by following equation.. P( r )  . ik  c G( r | rs )V ( rs )ds( rs ) 4 s. (2.15). Three kinds of structural system such as wall-slab, ramen, and flat slab system were compared. The vibration mode of three structural system is shown in Figure 2.4. The result showed that heavy-weight floor impact noise of wall-slab system is larger than that of the other system and the sound radiation from the wall have great effect on total floor impact sound. It indicates that floor impact sound radiation can be controlled by structural parameter design.. Figure 2.4 Mode shape of slab system (Hwang et al.). 15. In 2014, Mun et al. [10] proposed a prediction method of concrete slab acceleration and floor impact sound by using frequency response function. FRF (Frequency Response Function) is a transfer function defined as unit response per applied force. Because FRF is one of inherit dynamic characteristics of a linear system, prediction of dynamic response is possible if FRF is given. As shown in equation (2.16), the relationship between input signal. X.  f  and output signal. related with frequency response function Y  f   H  f  X  f. Hf. Yf.  is. .. . (2.16). To investigate the applicability of FRF to floor impact sound prediction, actual test was conducted. The acceleration response of concrete slab and the floor impact sound in the living room were measured by bang machine and impact ball excitation. And the test results were compared with the predicted results which is based on FRF and impact force spectrum. The predicted result of acceleration response is Figure 2.5 (a) and the floor impact sound level is Figure 2.5 (b). The predicted values were generally in good agreement with the measured values. The result showed that the floor impact sound could be predicted according to various input forces. Also, calculation time can be effectively reduced by applying FRF to numerical analysis on floor impact sound.. 16. (a) Acceleraion response by bang machine excitation. (b) Acoustic pressure response by bang machine excitation Figure 2.5 Prediction of acceleration response and sound pressure by FRF (Mun et al.). 17. Chapter 3. Floor Impact Sound and Vibration Test in a Residential Building 3.1 Introduction Floor impact sound and vibration tests were conducted in a multistory residential building. Modal test was firstly performed on bare concrete slab. And floor impact sound measurements were performed three times according to building construction stage. The scope and objective of each test is shown in Table 3.1.. Table 3.1 Scope and objective of test Test. Scope. Purpose. Modal test. bare concrete slab. Measurement of vibration properties such as natural frequency, mode shape, and damping. Floor impact sound test. bare concrete slab. Acquisition of average floor impact sound level for comparison with numerical model. Floor impact sound test. floating floor. Investigation of floor impact sound insulation performance according to resilient material type. Floor impact sound test. floating floor with ceiling. Investigation of influence of ceilings on floor impact sound insulation performance. The purpose of modal test is to get intrinsic vibration properties of concrete slab such as natural frequency, mode shape, and damping ratio. Correlation between floor impact sound and vibration can be investigated through this test. And the measured properties are utilized to numerical analysis in the next chapter. They become the basis of design values proposed for floor impact sound prediction process. The purpose of floor impact sound test is to get standard sound. 18. pressure level data which can be compared with the corresponding data of numerical model. The sound pressure level deviation was investigated for the households of identical floor plan. Then average value was derived from the results. Measurement of heavy-weight floor impact sound followed KS F 2810-2 and assessment of floor impact sound followed KS F 2863-2. Impact ball, or rubber ball, was used as a standard heavy-weight impact source. Additionally, to investigate correlation between floor impact sound and vibration, floor impact vibration was measured together when the floor impact sound test was conducted. Because there is no specific code for floor impact vibration measurement, the test setup was planned as same as floor impact sound test.. 19. 3.2 Test Program 3.2.1 Test site Floor impact sound and vibration test was conducted in an actual apartment building. The test site is a 27-story building under construction, which is located at Chunan-si, Korea. The main structural system is bearing wall-slab system, which is generally used for Korean apartment houses. Total six households which have identical floor plans were selected from 8th story to 13th story. The floor structure at each story was named as floor structure A, B, C, D, E and F. Figure 3.1 shows test site and interior test room of the household.. Figure 3.1 Test site. The test was performed three times according to floor structure construction stage. In the test site, the floor structure was constructed by three steps – bare concrete slab, floating floor, and floating floor with ceiling. The first step is bare concrete slab without any resilient materials. In the step, all six households have identical section plan. The thickness of floor slab is 210 mm. The second step is floating floor. The components are concrete slab of 210 mm, resilient materials of 20-60 mm, autoclaved lightweight concrete (ALC) of 40 mm, and finishing mortar of 40 mm. All households have identical floating floor design. 20. plan except resilient materials. And the third step is floating floor with ceiling. Identical ceiling structure was added to the floating floor of previous step. The height of space between floating floor and ceiling frame is 170 mm. Figure 3.2 is floor plan and Figure 3.3 is section plan of floor structure in the test site.. Figure 3.2 Floor plan of test site. 21. Concrete Slab (210mm). (a) Bare concrete slab Finishing mortar (40mm) Autoclaved Lightweight Concrete (40mm) Resilient Material (20-60mm) Concrete Slab (210mm). (b) Floating floor Finishing mortar (40mm) Autoclaved Lightweight Concrete (40mm) Resilient Material (20-60mm) Concrete Slab (210mm). 170 mm Ceiling Frame. (c) Floating floor with ceiling Figure 3.3 Section plan of test site. 22. Specimen properties are as follows. Table 3.2 shows the material property of bare concrete slab. Design compressive strength (. ) of. concrete was 24 MPa for all households. Actual 28-day strength (f28) was ranged from 29.3 MPa to 41.9 MPa. And Table 3.3 shows the floating floor properties. All floating floors were designed with different resilient materials. Primary test parameters are resilient material type, thickness, dynamic stiffness (Ed) of resilient materials. Table 3.2 Material property of bare concrete slab Floor structure. Test date (YY-MM-DD). fc’ (MPa). f28 (MPa). A. 15-01-06. 24.0. 41.9. B. 15-01-17. 24.0. 40.1. C. 15-01-23. 24.0. 38.9. D. 15-02-03. 24.0. 33.7. E. 15-02-10. 24.0. 29.3. F. 15-02-17. 24.0. 41.5. Table 3.3 Resilient material property of floating floor Floor structure. 2 3 4. Resilient material type 2. 3. t (mm). Ed (MN/m3). A. PET 30 mm + EVA 20 mm + EVA 10 mm. 60. 6.1. B. EVA. 30. 10.6. C. EVA. 30. 4.8. D. 4. EPS. 30. 5.8. E. EPS. 30. 7.1. F. EVA. 30. 3.3. Polyethylene terephthalate Ethylene-vinyl acetate Expanded polystyrene. 23. In floating floor, dynamic stiffness measurement of resilient materials is provided in KS F 2868 [11]. Figure 3.4 shows the measurement setup by resonance method. To investigate actual deviation of dynamic stiffness, it was measured for all resilient materials placed in the test site. The measured result is shown in Figure 3.5.. Figure 3.4 Dynamic stiffness measurement set-up on resilient materials. Figure 3.5 Dynamic stiffness measurement result of resilient materials. 24. 3.2.2 Modal test plan Modal test was conducted at bare concrete slab of the test site. Modal test is mainly conducted test in the field of structural dynamics to measure intrinsic vibration properties of structures such as natural frequency, mode shape, and damping. In this study, vibration properties of bare concrete floor slab were measured for comparisons with numerical model in the next chapter. Natural frequency, damping ratio and mode shape can be measured from the test. Also, measured damping ratio is used for input property of vibration analysis model. Because damping only can be measured by actual testing, it is important to investigate the characteristic of damping from modal test before performing numerical analysis. The modal test plan is like Figure 3.6. Test grid was set on the floor slab with identical transverse interval of 570 mm and horizontal interval of 1250 mm. Total forty-five number of points were set and each point on the test grid was impacted by impact hammer. Impact hammer can hit the floor slabs with impact force over the frequency range of 1000 Hz. For measurements of floor impact vibration, two set of accelerometers were placed on the center and the edge of floor slab which corresponds to living room. The location of accelerometers was determined considering main mode shapes.. 25. 2,270 11,040. 3365 570 x 1250. 3905. Acc.2. 1,500. Acc.1. 4,120. 4,720 12,415. Figure 3.6 Modal test plan. 26. 3,575. Figure 3.7 Test grid setup on floor slab. 27. 3.2.3 Floor impact sound test plan Floor impact sound test was performed three times according to floor construction stage of the building. Measurement of floor impact sound followed KS F 2810-2 and assessment of floor impact sound followed KS F 2863-2. The section plan of test site and test setup is shown in Figure 3.8. All floor structures have identical setup plan. In Figure 3.8, source room is defined as living room of the household that causes floor impact sound by impact source. Tester dropped impact ball at the height of 1000 mm in the source room. And receiving room is defined as living room of the lower household that floor impact sound is radiated. Accelerometers and microphones are set for floor impact vibration and sound measurement in the receiving room. Figure 3.9 shows the location of impact points and receiving points in the floor plan. Impact points were set from P1 to P5 in a source room, and receiving points were set from P1 to P4 in a receiving room. It followed ‘Criteria on floor impact sound insulation structure in residential buildings [12]’ by Ministry of Land, Infrastructure and Transport. The center point P1 is located at the center of living room. The edge points from P2 from P5 are located at position separated about 750 mm from the walls. Impact ball was used for heavy impact source. In a receiving room, total four receiving points from P1 to P4 are set at microphones. The height of microphone is 1200 mm from the floor slab. Also, five accelerometers were set at the bottom of floor slab, which is located below the impact points. When impact ball hits the floor slab, sound pressure and acceleration response were measured at the same time by microphone and accelerometer. Figure 3.10 shows the receiving room with test setup.. 28. 2600. Source Room. 210. 1000. Impact Ball. Acc.3,4. Acc.1. Acc.2,5. 750 Mic.3,4. 1200. 750 Mic.1. Mic.2. Figure 3.8 Section plan of floor impact sound test room. 29. 2600. Receiving Room. 2,270 3365. 750. 11,040. 750. 750. P4. P5 750. 4,120. P3. P2 750. 750. 750 4,720. 1,500. 750. 3905. P1. 3,575. 12,415. Figure 3.9 Location of impact points and receiving points. Figure 3.10 Receiving room. 30. 3.3 Test Result 3.3.1 Modal Test Result Intrinsic vibration properties of concrete slabs in the building were derived from the modal test. Total 90 number of acceleration FRFs were measured by two set of accelerometers at each floor structure. Primary results are as follows. The measurement result of representative acceleration FRFs are plotted in Figure 3.11 and Figure 3.12. Figure 3.11 is the acceleration FRFs measured by accelerometer no.1 when impact hammer hit the center of floor slab. The floor slab of six specimens showed similar acceleration FRFs and vibration properties. The acceleration response of the first and the second vibration mode was clearly measured. But the third vibration mode was not clearly measured because nodal line is located at the center of floor slab. And Figure 3.12 shows the acceleration FRFs measured by accelerometer no.2 when impact hammer hit the edge of floor slab. The acceleration FRF level was differently measured because of impact location, the result of natural frequency was coincident with the result of Figure 3.11. Also, the accelerometer no.2 could measure the response of the third vibration mode, which was not clearly measured by accelerometer no.1.. 31. Figure 3.11 Acceleration FRF at P1 by impacting P1. Figure 3.12 Acceleration FRF at P2 by impacting P2. 32. The measured vibration property of each floor structure is summarized at Table 3.4. Although they have identical floor plan, the first natural frequency was ranged from 26 Hz to 32 Hz, which showed about 6 Hz difference. The natural frequency showed larger difference at the higher modes. And the natural frequency at the lower building story tended to be greater except floor structure D. It would be reason that aging of concrete slab is different according to building story. Modal damping coefficient was calculated by half-power bandwidth method. The average damping coefficient of first normal mode was 2.47 % and deviation of damping coefficient in six specimens was not very large.. Table 3.4 Vibration property of bare concrete slabs Floor structure. (Hz). f1. A. 32. 0.0260. 45. 0.0197. 53. 0.0301. B. 30. 0.0238. 43. 0.0200. 50. 00282. C. 30. 0.0211. 43. 0.0231. 46. 0.0305. D. 26. 0.0268. 38. 0.0266. 52. 0.0341. E. 28. 0.0241. 42. 0.0254. 54. 0.0314. F. 28. 0.0266. 43. 0.0279. 55. 0.0325. Average. 29. 0.0247. 42. 0.0238. 52. 0.0311. Deviation. 6. 0.0057. 7. 0.0082. 9. 0.0059. 1. f2 (Hz). 2. f3 (Hz). 3. And the measured mode shapes are plotted in Table 3.5. The result was derived from imaginary part of acceleration FRF at each measurement point. Mode shapes in the space between the measurement points were plotted by linear interpolation.. 33. Table 3.5 Mode shapes Frequency (Hz). Measurement result Mode shape. Location. 29. 43. 52. 74. 85. 34. 3.3.2 Vibration Response Floor impact vibration was measured together when floor impact sound test was conducted. Primary results according to construction stage are as follows. Firstly, vibration acceleration level of bare concrete slab was measured at six households. Time-history acceleration response signals were directly measured by accelerometers. Then the recorded signals were converted to frequency response spectrum through Fast Fourier transform. Figure 3.13 is the vibration acceleration response measured at receiving point P1 when impact ball hit the impact point P1. It showed relatively high vibration acceleration level at low frequency domain. It is influence of heavy impact source. The acceleration level at 1st mode is 90-100 dB5 and it would lead to amplification of heavy-weight floor impact sound. The measured level is shown in Table 3.6. The level was averaged for five impact points and four receiving points. Also, acceleration level deviation was investigated of six households.. Figure 3.13 Acceleration level at P1 by impacting P1. 5. Vibration acceleration reference: 1·10-6 m/s2. 35. Table 3.6 Vibration acceleration level of bare concrete slabs VAL (dB). Floor structure. (1,1) mode. (2,1) mode. (3,1) mode. A. 75.6. 63.1. 46.8. B. 75.8. 65.7. 55.2. C. 81.2. 66.1. 60.2. D. 77.4. 67.4. 57.2. E. 79.5. 72.9. 55.9. F. 74.9. 70.4. 58.6. Average. 77.4. 67.6. 55.7. Deviation. 5.6. 9.8. 13.2. Secondly, vibration response of floating floor was measured in the same way. Figure 3.14 shows the acceleration response of floating floor structure B, which is compared with the response of bare slab. The other floor structures showed the similar results. The acceleration level below 100 Hz was amplified in floating floor because secondary resonance between mortar and concrete slab occurred.. Figure 3.14 Acceleration response of bare slab and floating floor. 36. 3.3.3 Acoustic Response The acoustic FRF (i.e. sound pressure level per unit impact force) and acceleration FRF corresponding to impact point P1 were compared in Figure 3.15. It is FRFs measured at floor structure C and the other floor structures showed the similar results. The main peak acoustic responses occurred at 16 Hz, 26 Hz, 35 Hz, 38 Hz, 52 Hz, 65 Hz, and so on. Part of them are coincident with the peak vibration frequencies at 26 Hz, 38 Hz and 52 Hz of acceleration FRF. Thus it was shown that the first, second and third vibration mode makes the amplification of sound pressure level. The result proved that the vibration response directly influences the acoustic responses. The other peak acoustic responses are related with the acoustic modes which make stationary waves (i.e. waves in a medium in which each point on the axis of the wave has an associated constant amplitude in a closed space.) in a closed space.. Figure 3.15 Correlation between acoustic FRF and acceleration FRF. 37. 3.3.4 Floor Impact Sound Level The floor impact sound level were derived from 1/1 octave band and 1/3 octave band transform of acoustic FRFs. And inverse-A weighted floor impact sound level which is single-number quantity of each floor structure, Li,Fmax,AW, was assessed by KS F 2863-2. The results are as follows. The 1/3 octave and 1/1 octave floor impact sound level of bare concrete slabs are plotted in Figure 3.16 and Figure 3.17. To derive reliable test data, the maximum, minimum, average, and deviation of floor impact sound level was investigated as shown in Table 3.7. Although all households have an identical floor plan, the deviation clearly occurred at each 1/1 octave floor impact sound level about 2-4 dB. The maximum deviation of single-number quantity was 2 dB. It indicates that construction error or actual material properties such as concrete strength, mass density or Young’s modulus can significantly affect the floor impact sound level.. Figure 3.16 1/3 Octave floor impact sound level of bare concrete slabs. 38. Figure 3.17 1/1 Octave floor impact sound level of bare concrete slabs. Table 3.7 Floor impact sound level of bare concrete slabs Frequency (Hz). Maximum level (dB). Minimum level (dB). Average level (dB). Deviation (dB). 31.5. 80. 76. 78. 4. 63. 69. 67. 68. 2. 125. 69. 66. 67. 3. 250. 63. 61. 62. 2. 500. 54. 49. 50. 2. Li,Fmax,AW. 53. 51. 52. 2. 39. Floor impact sound insulation performance of floating floor was investigated. Figure 3.18 shows single-number quantity level of each floor structure according to building construction stage. All floor structures had different floor impact sound insulation performance at each construction stage. The difference level was relatively large at the construction stage of floating floor. Table 3.8 shows the final singlenumber quantity and single-number quantity reduction level of each floor structure. Floor impact sound level of floating floor according to various test parameters was analyzed. As shown in Figure 3.19 and Figure 3.20, floor impact sound tendency is clearly shown according to thickness and dynamic stiffness of resilient materials. Firstly, the floating floor with relatively low dynamic stiffness of resilient materials showed good floor impact sound insulation performance as respect to single-number quantity. It is clearly seen at the results of floor structure C and F. Dynamic stiffness of resilient materials in floor structure C is 4.8 MN/m3 and it showed floor impact sound reduction performance about 9 dB in single-number quantity. Floor structure F also has low dynamic stiffness of 3.3 MN/m3 and it showed 9-dB reduction in single-number quantity. On the other hand, floor structure B which has the highest dynamic stiffness of 10.6 MN/m3 showed only 5-dB reduction in single-number quantity. Secondly, the floating floor with relatively thick resilient materials had better floor impact sound insulation performance than others. Floor structure A, which has resilient material thickness of 60 mm, showed the best performance with reducing 10 dB in single-number quantity.. 40. Figure 3.18 Single number quantity. Table 3.8 Heavy-weight floor impact sound reduction of floating floor Floor structure. Ed (MN/. ). t (mm). Li,Fmax,AW (dB). △Li,Fmax,AW (dB). A. 6.1. 60. 42. 10. B. 10.6. 30. 46. 5. C. 4.8. 30. 43. 9. D. 5.8. 30. 45. 7. E. 7.1. 30. 46. 7. F. 3.3. 30. 43. 9. 41. Figure 3.19 Heavy-weight floor impact sound according to dynamic stiffness. Figure 3.20 Heavy-weight floor impact sound according to thickness of resilient materials. 42. And the 1/3 octave floor impact sound level was investigated according to construction stage. Because single-number quantity itself does not show the frequency-dependent characteristics of floor impact sound, it is necessary to analyze the same result by 1/3 octave floor impact sound. The results of six households are plotted from Figure 3.21 to Figure 3.26. Compared with bare concrete slab, floor impact sound level of floating floor was generally amplified at low-frequency domain under 80-100 Hz and reduced at high-frequency domain. It is estimated that vibration resonance between resilient materials and finishing mortar of floating floor because the floor impact vibration level at the same frequency domain was amplified as shown in Figure 3.15. Also, floating floors with ceilings showed different performance from floating floors without ceilings. Except floor structure D, ceiling structures amplified the floor impact sound level at low frequencies below 100 Hz. It led to increase of single-number quantity level at floor structure F. On the other hand, the level at high-frequency domain was generally reduced by ceilings. As a result, ceilings reduced singlenumber quantity level except floor structure F but did not have a good effect on heavy-weight floor impact noise reduction.. 43. Figure 3.21 Floor impact sound level of floor structure A. Figure 3.22 Floor impact sound level of floor structure B. 44. Figure 3.23 Floor impact sound level of floor structure C. Figure 3.24 Floor impact sound level of floor structure D. 45. Figure 3.25 Floor impact sound level of floor structure E. Figure 3.26 Floor impact sound level of floor structure F. 46. 3.4 Discussions Modal test and floor impact sound test were performed in an actual residential building. The primary test results are summarized as follows. 1) As an extension of preceding research, floor impact sound was directly influenced by main vibration modes, which proves that it is a structural-borne sound. 2) All bare concrete slabs showed different floor impact sound and vibration level although they have an identical floor plan, which indicates that construction error or material property can be influence factor on floor impact sound. 3) The experimental deviation of 1/1 octave floor impact sound level was about 2-4 dB at bare concrete slabs, which is not very significant that the average value of the test data can be used for verifying numerical model. 4) The floor impact sound insulation performance of floating floor was largely different according to resilient material parameters such as thickness and dynamic stiffness. 5) Ceilings of floating floor generally reduced overall single-number quantity level but it amplified the floor impact sound level at lowfrequency domain.. 47. Chapter 4. Numerical Analysis of Floor Impact Sound 4.1 Introduction When designers perform floor impact sound analysis on residential buildings, only limited information is given. It is generally floor plan, section plan and concrete strength data of the building. Thus, this chapter focused on proposal of numerical analysis process for designers who have to predict floor impact sound the above information. Total floor impact sound analysis process was proposed by finite element method. General dynamics analysis method which is included in common FEA software was used for applicability to the practical field. The object is bare concrete slab of residential building. Chapter 4.2 introduces the finite element modeling process for floor impact sound analysis. Several assumptions were presented in chapter 4.2.1. Structural and acoustic properties of residential buildings were proposed in chapter 4.2.2. And details about each analysis steps were stated in chapter 4.2.3. Chapter 4.3 shows numerical analysis plan. Various residential building models were designed to compare the prediction accuracy. And the verification of numerical model was conducted with the test result in Chapter 4.4. Finally, the discussion is summarized in Chapter 4.5.. 48. 4.2 Proposal of Numerical Analysis Process 4.2.1 Assumptions In this study, finite element analysis on floor impact sound was performed with several assumptions as follows. Element type was determined for numerical modeling. In case of structural model, floors and walls can be assumed as thin plates because thickness-width ratio of the slabs is less than 0.05-0.1. Shell element was used for them. In case of acoustic model, solid element was used for modeling the air as an acoustic medium and shell element was used for modeling the acoustic field. In order to reduce calculation time, fluid-structure interaction effect was excluded by assuming that influence of air to concrete is ignorable. Mesh size was determined considering the main target frequency range. Behavior of vibration wave can be modeled with minimum six elements as shown in equation (4.1). 6  ElementSize  min . c f max. (4.1). It means that numerical model can analyze the vibration wave within the range of wavelength with six times mesh size. If linear element with mesh size of 0.15 m was used, the frequency response under 381Hz can be exactly calculated. It is sufficient to analyze the heavy-weight floor impact noise which is main interest in this study. Modeling range for numerical model is as follows. In structural model, unit household model without exterior slab was compared with the model including exterior slab. Because floor slab is continuous for households in the same building story, the effect of modeling exterior slab was investigated. And acoustic model was made in the range of living room and kitchen, which corresponds to receiving room which sound pressure level is measured. It was assumed that the other rooms. 49. have little influence to floor impact sound level of receiving room. Figure 4.1 shows the example of structural finite element model and Figure 4.2 shows the acoustic finite element model. Various models were made according to design plan and verified with test results.. Figure 4.1 Structural FE model. Figure 4.2 Acoustic FE model. 50. 4.2.2 Proposal of Design Property When designers perform numerical analysis of floor impact sound, they only have limited information such as building floor plan. Most of structural and acoustic properties of buildings should be derived from experimental results. But it is not efficient to perform experiments all the time at every building construction sites. Thus, this study proposed design properties which can predict floor impact sound level within suitable error range. The prediction error was targeted for maximum 3 dB based on deviation of test results. The proposed structural and acoustic properties are shown in Table 4.1. For structural properties, mass density and elastic modulus of the concrete were assumed to be 2400 kg/. and 23 GPa on the basis of. design material property data. And modal damping ratio of main vibration modes was assumed to be 2-5% on the basis of preceding modal test results. The thickness of floor and wall was applied 210 mm and 200 mm according to building plan. For acoustic properties, acoustic panel impedance (Z) was applied to concrete slabs and walls. It is the ratio of sound pressure (P) and sound speed (U) as shown in equation (4.2). It indicates how large sound pressure occurs by air vibration at specific frequency domain, which represents the acoustic absorption characteristics of room.. Z. P U. (4.2). The actual value at the test site is difficult to be measured, because it only considers vertical incidence of plane wave. Thus it was theoretically calculated from equation (4.3)..   1 R. 2. (4.3). α is absorption coefficient of material at frequency domain. Absorption coefficient (α) of concrete at 250 Hz is 0.02. R is reflection. 51. coefficient of concrete and it is related with acoustic panel impedance Z like equation (4.4).. R. Z  c Z  c. (4.4). In equation (4.4), c is acoustic characteristic impedance which has value of 413 kg/m2/s at 20°C. From equation (4.3) and (4.4), value of Z could be calculated as 80000 kg/m2/s.. Table 4.1 Design values for numerical modeling Structural property. Value. Acoustic property. Value. Concrete strength. 24 MPa. Sound speed. 340 m/s. Young’s modulus of concrete. 23 GPa. Young’s modulus of air. 0.14 MPa. Mass density. 2400 kg/m3. Mass density. 1.23 kg/m3. Poisson’s ratio. 0.167. Modal damping ratio. 0.03 for 1st - 3rd mode 0.05 for other modes. Acoustic impedance. 80000 kg/m2/s for concrete slabs and walls. Boundary condition. Fixed support. Boundary condition. Surface velocity of slab. 52. 4.2.3 Numerical Analysis Process Floor impact sound analysis was performed as following process. Modal analysis, steady-state dynamics analysis and acoustic harmonic FEM analysis were done. Total process is shown in Figure 4.3.. Figure 4.3 Numerical analysis process. The first step is modal analysis. It was analyzed for structural model. Design properties of mass density, Young’s modulus, damping ratio were applied. Boundary condition that floor slabs contact walls was assumed to be fixed. The response was calculated from 1st mode to 1000th mode, which includes the target frequency range of heavy-weight floor impact sound. From this step, natural frequencies and mode shapes of structural model were derived and compared with the test results. The second step is steady-state dynamics analysis. It was also performed for structural model. In this step, impact force by impact ball, first, was assumed as harmonic excitation. The force response in the time domain was converted to frequency spectrum by Fourier Transform. Then, modal based steady-state dynamic analysis was conducted to calculate the linear response of a floor slab to harmonic excitation. This analysis method is based on modal superposition which the natural frequencies and modes were extracted by modal analysis. As a result, the acceleration response of floor slab could be calculated. And the third step is acoustic harmonic FEM analysis. In this step,. 53. acceleration response from the previous step is firstly converted to velocity response. Then, the surface normal velocity of slab is derived from it and transferred to acoustic field velocity. It is applied for boundary condition of sound pressure. The acoustic frequency response could be calculated and it was finally converted to 1/3 octave floor impact sound level. Table 4.2 Requirements of floor impact sound analysis process Process. Requirements. Results. Initial step. Floor plan Section plan. Building information. Structural material property. Density of concrete Compressive strength Poisson’s ratio. Structural FE model. Acoustic fluid property. Density of air Sound speed. Acoustic FE model. Modal analysis. Structural model property. Mass density Young’s modulus Modal damping ratio Boundary condition. Dynamic properties. Steady-state dynamics analysis. Impact force spectrum. Impact ball spectrum Bang machine spectrum. Surface normal velocity of slab. Acoustic harmonic FEM analysis. Acoustic panel impedance. Floor impact sound analysis. Octave band frequency band filters. FE modeling. 1/1 octave band filters 1/3 octave band filters. 54. Acoustic response Floor impact sound level. 4.3 Analysis Plan 4.3.1 Bare Concrete Slab Floor impact sound analysis model was designed by the finite element analysis process proposed in chapter 4.2. Bare concrete slab model was analyzed as the first step. To compare the prediction error of heavyweight floor impact sound level, two types of structural model were proposed in this chapter. The first one is unit household model without including any slab of exterior household. But actual buildings have continuous floor slab system regardless of division of household. It can change entire flexural stiffness of floor slab that affects the heavy-weight floor impact sound level in the building. Thus, the second model was designed including floor slab of exterior to the unit household model. Figure 4.4 shows the comparisons of two numerical models. In the model plan, Figure 4.4(a) shows FEM-1 model which is the unit household model without any exterior slabs. On the other hands, Figure 4.4(b) shows FEM-2 model which is modified to include part of floor slab in the exterior household. The boundary condition of exterior floor slab is fixed condition which indicates that floor slab is continuous. Exterior walls were excluded in the modeling. The other conditions of FEM-1 and FEM-2 are identically designed.. (a) Unit household. (b) Unit household with exterior slab. Figure 4.4 Floor plan of numerical model. 55. And, to investigate the influence of exterior slab on floor impact sound more clearly, various residential building models were additionally analyzed. Table 4.3 shows the numerical model plan which analysis was performed in the same way. The proposed numerical method and design values were identically applied to the models. Total four types of plans with various floor area were additionally selected. Table 4.3 Numerical model plan Floor area (m2). FEM-1 model. FEM-2 model. 59. 74. 84. 114. 56.