Tooth deflection under cyclic loading
6.3 Damping and Forced Vibration Characteristics of Sandwich Panels
is due to the plastic deformation of the material, although in the present study, the effect is neglected considering the low amplitude force excitation. The specimens (130mm13mm3.5mm) are shown in the Figure 6.11(a)-(c). Schematic and the corresponding experimental setup for the forced transverse vibration analysis of composite beams are shown in the Figure 6.12(a)-(b).
(a)
(b)
Chapter 6 Evaluation of Vibration and Mechanical Properties … (c)
Figure 6.11 Forced vibration samples (a) composite beam (b) Aluminum skinned sandwich beams and (c) GI skinned sandwich beams
Specimen
Force transducer
Exciter
Data Acquisition
System Laser point
Laser Vibrometer Accelerometer
Fixed clamp
(a)
TH-1430_09610309
Laser point Laser vibrometer
Sandwich specimen Force transducer
Exciter
(b)
Figure 6.12 Forced vibration accessories (a) Schematic diagram of experimental setup for forced vibration and (b) actual experimental setup
The test specimen is clamped at one end, a force transducer (Endevco type 2311- force transducer) equipped with a Modal Exciter Type 4824 (maker: Bruel Kjaer) is fixed at the middle position of the samples as shown in the schematic diagram Figure 6.12(a). A LASER assisted vibrometer (maker: Bruel Kjaer) is used to acquire the vibration response data through laser beam, pointed at the end of the specimen as depicted schematically. The exciter is vibrated with sinusoidal exciting frequency maintained at 40 Hz for all the specimens.
Using LABSHOP- Pulse 7700 software, the experimental data are analyzed. The phase difference (φ) is calculated using the relation (Subramanian et al, 2011) as:
3600
T
(6.4)
where, T denotes the time period for one cycle and τ refers the time (s) difference between exciting force and the LASER acquisition response. Phase difference is the time by which the response lags behind the exciting force and the material response and this gives measure of the damping. Further, for a material, phase difference is directly proportional to the damping (Aberg and Widell, 2004) where, damping factor for forced vibration is calculated using the relationship (Genta, 1999) as:
Chapter 6 Evaluation of Vibration and Mechanical Properties …
n 2n
tan
2 f f 1 f
f
(6.5)
where, φ denotes the mean phase difference in degree, f denotes the forced frequency (maintained 40 Hz for all the cases) and fn is the natural frequency; obtained from the free vibration FFT analysis while, forced excitation frequency is taken 80 Hz for sandwich beam experimentation.
6.3.1 Results and Discussions
The phase difference obtained experimentally taking into account of all the composite samples under forced vibration responses are shown in the Figure 6.13. Mean phase difference and damping ratio of all the composite specimens are illustrated in the Figure 6.14(a) and (b) along with pure polypropylene respectively. Mean phase difference of 0%, 5%, 10% and 15% cement reinforced composite materials are found to be 30.15º, 18.77º, 19.28º and 16.9º respectively. It is observed that addition of cement fillers into the pure polypropylene matrix significantly limits elastic deformation of the material and results in falling of phase difference between the excitation force and the corresponding material response captured by the Laser vibrometer.
-0.1 -0.05 0 0.05 0.1
-0.13 -0.08 -0.03 0.02 0.07 0.12
100 110 120 130 140 150 160 170 180 190 200
Amplitude (mV)
Force (N)
Time (ms)
Force signal Laser signal
(a)
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-0.1 -0.05 0 0.05 0.1
-0.1 -0.05 0 0.05 0.1
100 110 120 130 140 150 160 170 180 190 200
Amplitude (mV)
Force (N)
Time (ms)
Force signal Laser signal
(b)
-0.1 -0.05 0 0.05 0.1
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
100 110 120 130 140 150 160 170 180 190 200
Amplitude (mV)
Force (N)
Time (ms)
Force signal Laser signal
(c)
Chapter 6 Evaluation of Vibration and Mechanical Properties …
-0.25 -0.15 -0.05 0.05 0.15 0.25
-0.25 -0.15 -0.05 0.05 0.15 0.25
100 110 120 130 140 150 160 170 180 190 200
Amplitude (mV)
Force (N)
Time (ms)
Force signal Laser signal
(d)
Figure 6.13 Forced vibration response of (a) 0%, (b) 5%, (c) 10% and (d) 15% cement reinforced polypropylene
Among the other cement reinforced composite materials, 15% cement reinforced composite depicts lower phase difference compared to 10% and 5% cement reinforced composites owing to filler matrix interface, which, eventually, caused delayed response of the specimens.
Experimentally obtained forced vibration data are taken into consideration and the damping ratio of the composite materials (0%, 5%, 10% and 15% fillers) are obtained as, 0.031, 0.034, 0.036 and 0.036 respectively. It is observed that as the filler loading increases, results in minute increase of loss factors of the composites.
0 10 20 30 40
0 5 10 15
Phase angle (φ)
Cement content (wt%)
(a) TH-1430_09610309
0 0.01 0.02 0.03 0.04
0 5 10 15
Damping ratio (ξ)
Cement content (wt%) (b)
Figure 6.14 Forced vibration response results of composite specimens (a) mean phase angle (φ) and (b) damping ratio (ξ)
Similar results have also been obtained for Aluminum (Al) and Galvanized iron (GI) skinned sandwich panel with cement reinforced composite as core material. The forced vibration response of Al and GI skinned sandwich composite beams are illustrated in the Figure 6.15 and Figure 6.17 respectively. Figure 6.16 and Figure 6.18 show the variation of phase difference and damping ratio of Al and GI skinned sandwich composite panels respectively.
As expected, high stiffness metal skin for sandwich composite panels, significantly limits the materials elastic deformation and decrease the phase angle (φ) between the excitation force and the corresponding material response captured by LASER vibrometer. The damping ratio for aluminum skinned sandwich panels are obtained as 0.061, 0.069, 0.074 and 0.080 with pure polypropylene, 5%, 10% and 15% cement reinforced composite materials as core materials. Similarly, for GI skinned sandwich panels, the damping ratio obtained from the forced vibration test are 0.082, 0.086, 0.091 and 0.093 respectively. It is observed that 10%
cement reinforced composite core material with both aluminum and galvanized iron skinned sandwich panels give optimal damping ratio compared to other sandwich panels. It is anticipated that incorporation of cement materials aided the resistance to mobility of the materials and subsequently results in fall in elastic deformation. However, it is observed that 15% cement reinforced composite materials offer more resistance to mobility and elastic deformation although enhances the brittle characteristics simultaneously as compared to other core materials.