91
Natural Frequencies and Damping Properties of Hybrid Polymeric Composite Material Reinforced with Nitinol Shape Memory Alloy Wires
Ibtihal A. Mahmood, Qasim A. Atiyah and Ali M. Jasim
Mechanical Engineering Department, University of Technology, Baghdad -Iraq [email protected]
Abstract.In this study, the damping ratio and the natural frequencies of the vibration modes were investigated. Hand lay-up technique was used to prepare the samples, which were formed by stacking the layers within the laminates, that containing epoxy as a matrix reinforced by layers of woven roving carbon fibers and smart shape memory alloy (Nitinol) wires, with different volume fractions.
Experimentally, the damping ratio was determined by using half-power bandwidth techniques. The natural frequencies of the vibration modes were calculated by using the equations of the cantilever beam and compared with the experimental results. ANSYS composite Prep-Post (ACP) integrated within ANSYS Workbench software was first used to determine the mode shape and find the natural frequencies of the vibration modes and then compared with the experimental results. The results showed that increasing the number of Nitinol wires leads to increase the values of the bending modulus, the damping ratio of the vibration modes and the natural frequencies of the vibration modes at room temperature (martensite phase). While at austenite phase (55°C), the values of the damping ratio of the vibration modes decreased, and the bending modulus and the natural frequencies increased (higher than martensite phase), this change in natural frequencies values is useful in order to avoid the resonance.
Keywords: Hybrid polymer matrix composite, Shape memory alloys, Damping ratio, Natural frequencies, Carbon fiber.
1. Introduction
To achieve the requirements of the industrial applications, materials with special mechanical properties are needed, depending on the application. Composite material can achieve these requirements. Composite materials hybridized with shape memory alloy are able to sense and respond to the external and the internal conditions. External conditions may include the applied loads, environment, and the shape of the composite materials. Internal conditions may include defect or damage of the composite materials. Embedding shape memory alloys wires can create smart hybrid composites (so-called adaptive or intelligent materials) able to control the mechanical properties of composites, such as damping characteristic, natural frequencies of the vibration modes and stiffness.
Composite materials with embedded shape memory alloys (SMA) become smart composite materials, which found wide applications in recent years. With suitable heat and stress/strain, shape memory alloy is able to change the physical properties of the composite materials. Because of its unique behavior, smart composite materials have a great attention in many studies. Some of these studies are reviewed here.
Chung [1] compared between materials (metals, polymers, cement) and their composites. The study showed that, because of their viscoelasticity, polymers and metals (including shape memory alloy) are better than cement in damping.
Turner et al. [2] studied the mechanical properties of a hybrid composite contained epoxy as a matrix reinforced by E-glass fibers
and SMA alloy type Nitinol in a ribbon form.
The experimental resulting tests provided the possibility of controlling stiffness behavior when pre-strained nitinol ribbon responded to a thermal excitation.
Schrooten et al. [3] evaluated the thermomechanical behavior and vibration response of smart composite materials having embedded pre-strain shape memory alloys (NiTiCu) wires and Aramid fibers. The result showed that the SMA composite is able to adapt its thermal behavior, shape and vibrational characteristics during service. The wire has a stable shape memory behavior, high damping ratios and generates high recover strain (up to 6%).
Stalmans [4] used the shape memory alloy as fibers reinforced polymer composites offering significant technologies, integrate sensing and actuating. Polymer composites having embedded shape memory alloy were able to control the stiffness, shape, damping and increased corrosion and fatigue resistance.
Boussu and Bailleul [5] investigated the damping characteristics of composite material made of epoxy reinforced by 32 ply carbon fibers and shape memory alloy (Nitinol) wires.
The result showed that the damping dissipation by internal friction for the nitinol wire is very good in the martensitic phase, but still more important in the transition zone (martensite- austenite). In the transition zone, damping to shock in nitinol wire is more efficient, whereas damping of continuous vibration in the martensitic zone is superior.
Tan et al. [6] investigated the control of vibration for a hybrid plate containing embedded shape memory alloy (SMA) wire with glass fiber as a reinforcement and epoxy as a matrix. The result showed that the activated shape memory alloy wires generated internal stress, which reduced and changed the position of the vibration amplitude.
3. Theoretical Consideration 3.1 Shape Memory Alloys
Shape memory alloys (SMAs) also known as (smart alloys, memory metals), are a group of alloys having unique ability to remember their original shape after deformed permanently (plastically) and recover the original shape when heated to an appropriate temperature. Shape memory alloy type Nitinol (nickel-titanium) is widely used in many applications, because of its excellent mechanical properties, large strains recovery (up to 8%), thermally stable, high corrosion resistance, and good electrical conductivity, in addition to their high mechanical damping depending on its phase transformation [7]. Nitinol has two unique properties, they are shape memory effect and super-elasticity.
There are many applications for Nitinol, such as robot, biomedical, toys, sensors and cell phone antennas.
3.2 The Behavior of Nitinol at Different Temperatures
Nitinol has three different crystal structures, which include twinned martensite (M ), de-twinned martensite (M ) and austenite (A). The transformation in these crystal structures induced by stress or thermal.
Because of the transitions in crystal structure associated with the change of temperature, there are four transition temperatures related with the phase transformation which, are martensite start temperature (M ), martensite finish temperature (M ), austenite start temperature (A ), and austenite finish temperature (A ), Fig. 1.
Figure 2 illustrates the behavior of Nitinol during [8].
1. Shape Memory Effect. At low temperatures, the Nitinol is 100% twinned martensite. When load is applied, Nitinol deforms with a residual strain, Nitinol starts
transforming to austenite at (A ) and completes transforming to austenite at (A ), heating above the temperature (A ) leads to complete shape recovery. During cooling, Nitinol starts transforming to martensite at (M ) and completes transforming to martensite at (M ).
2. Superelasticity. At high temperature (above A ), the Nitinol at austenite phase will behave elastically (like a rubber) and with the removal of stress, the deformations will be recovered (superelasticity).
3. Normal alloy. Nitinol behaves like normal alloy above the temperature (M ), if Nitinol deforms plastically, it will never complete shape recovery.
3.3 Natural Frequencies of the Cantilever Beam
The cantilever beam has an infinite degree of freedom, which is calculated from the following equation;
= ( ) (1) Where, E is the Young’s modulus of elasticity, L is the length of beam, I is the moment of
inertia of the beam cross section, is the density, is the cross-sectional area and ( = 1.875104, 4.69409, 7.85476, 10.99554, … etc.) is a dimensionless parameter having the value corresponding to the degree of freedom
[9].
ANSYS composite Prep-Post (ACP) integrated within ANSYS Workbench software (14.5) was used to determine the mode shape and find the natural frequencies of the vibration modes. The element type of the surface bodies is the quadrilateral dominant (8 nodes) and the sweep method is used for shape memory alloy wire. The element size for the surface bodies is 2 mm, while it is 0.25 mm for the shape memory alloy wire. The minimum number of the elements was 1150 and the maximum number was 4419. The minimum number of the nodes was 3701 and the maximum number was 43580.
Figures 3, 4 and 5 show the modal analysis response, and the mode shape for the vibration modes of the composite cantilever beam contains 6 shape memory alloy wires (Nitinol) + 4 layers of carbon fibers woven roving embedded into epoxy as a matrix.
Fig. 1. Shape memory effect.
Fig. 2. The behavior of Nitinol during changing the temperature on Stress–Strain Schematic.
Fig. 3. First mode shape.
Fig. 4. Second mode shape.
Fig. 5. Third mode shape.
3.4 Half-Power Bandwidth Method
Depending on frequency domain, the half-power points are used to estimate the resonant frequency and the damping ratio.
Frequencies points R and R called half power points falls on the response curve ( √ ). The bandwidth of the system is the difference of frequencies between the half power points R and R , this is denoted by
∆ , Fig. 6.
The damping ratio ( ) is defined as:
= (2) Where, ω = ω at R , ω = ω at R and is the resonant frequency.
For continuous systems (as a cantilever beam), the systems has a multi-degree of freedom. The previous method can extend to estimate the damping ratio for widely spaced resonances [10].
Figure 7 shows the acceleration- frequency response curve as an example, for sample contains epoxy as a matrix reinforced by 4 layers of carbon fibers. For the first mode, the maximum acceleration response at the peak ( ) = 3.7 (m/s2) corresponds to ω =
42 Hz which represents the natural frequency for the first mode, ( ) reduces to .
√ which represents half-power points (ω = 35 Hz at R and ω = 45.248 Hz at R ).
The damping ratio ( ) = = 0.122 for the first mode.
For the second mode, the maximum acceleration at ( ) = 10.2 (m/s2) corresponds to ω = 215 Hz, ω = 195 Hz at R , ω = 221.66 Hz at R and = 0.062, and so on for the third mode.
4. Experimental Details
Hand lay-up technique was used to prepare the samples, which are the simplest method formed by stacking the layers within the laminates. The infrastructural requirements is minimal. In this work, a glass with thickness 4 mm was used to prepare the molds, to ensure getting a smooth surface of the sample, with dimensions (300 x 120 x 4) mm, The preparation of specimens include:
1. Epoxy reinforced by carbon (woven roving) fibers with (1, 2, 3, and 4) layers.
2. Epoxy reinforced by shape memory alloy (2, 4, and 6) wires having 0.5 mm diameter.
3. Hybrid composite including epoxy reinforced by 4 layers of carbon (woven roving) fibers and shape memory alloy (2, 4, and 6) wires, Fig. 8.
4.1 Vibration System
The instruments used to measure the vibration characteristic include:
1. Automatic Voltage Regulator (stabilizer). At unstable voltage, an automatic circuit adjusts the output voltage to obtain a steady rate voltage value, Fig. 9-1.
2. Function generator type (FG2003) provides the frequency and the type of signal to the Power amplifier, Fig. 9 -2.
3. Power amplifier type (B&K 2712).
Driving the vibration exciter has a permanent magnetic field by providing sufficient power to obtain the frequency response. The excitation type and frequency are taken from a function generator, Fig. 9-3.
4. Electro- dynamic shaker (Vibration Exciter B&K 4808). Coil moves in a permanent magnetic field same as a loud- speaker. In this study, a sinusoidal excitation at the edge of beam was produced. The power was taken from a power amplifier, Fig. 9-4.
5. Accelerometer type (ADXL330), which is a sensing device, small size, lightweight, thin, low energy consumption (the supply voltage is 5V DC), working at temperature range between (−25°C to +70°C), measuring acceleration at three-axis with analog voltage outputs (proportional to acceleration). It measures the acceleration with a minimum full-scale range of ±3 g. It can measure the acceleration caused by vibration, shock and motion (linear or centrifugal acceleration), as well as static acceleration (G- value or gravity), Fig. 9-5 [11].
6. Arduino Uno (microcontroller), a small computer having memory and processor,
which controls many functions of devices.
Arduino Uno has been designed to connect the computer by USB cable for programming, which is saved in the memory. It works independent to control the input and output by the code. It has 6 analog input pins (A0-A5), the operating voltage is 5V DC, Fig. 9-6 [12] .
7. Electronic Digital Temperature Controller thermostat (type STC-200). It switches off the heater when reaching to the temperature required inside the box (on and off Power), Fig. 9-7.
4.2 The Test Procedure
1. The samples have dimensions (4 x 20 x 250) mm, the length was decreased 20 mm for fixation. The samples were fixed from one end on the shaker and free from the other end (as a cantilever beam), this mounting of the beam on the shaker is according to [13].
2. The accelerometer was fixed at a predetermined position on each sample beam to avoid the nodes matching at vibration modes.
3. A connection was made between the accelerometer and the Arduino Uno, then the Arduino Uno was connected to the laptop to obtain the acceleration (forced vibration response) at different frequencies.
4. The experiment begins when the function generator gives the signal to the shaker and lets the beam to vibrate.
5. The results obtained from mat-lab program were recorded.
6. Excel sheet was used to plot the acceleration versus frequency, then from frequency- acceleration response plot, the damping ratio and the natural frequency at the vibration modes were determined by using half power bandwidth techniques.
7. The test procedure was repeated to the same sample for checking, then the whole test procedure for all samples was repeated.
8. For the samples that contain SMA wires, the test procedure was conducted at room temperature and 55°C.
The tests of damping and vibration characteristic include:
1. Acceleration- frequency response curve.
2. Natural frequencies.
3. Damping ratios.
4. Mode shapes.
Fig. 6. Frequency response curve. Half-power bandwidth method.
Fig. 7. Acceleration- frequency response curve for composite material containing epoxy reinforced by 4 layers of carbon fiber.
a b
Fig. 8.Preparation of samples. a. SMA wires b. carbon fiber.
Fig. 9. Vibration Testing System.
5. Results and Discussion
The Tables 1-5 show the results, which include the bending modulus, the density, the experimental, theoretical and numerical results of the natural frequency of the vibration modes, comparison between the experimental and theoretical results of the natural frequency, comparison between the experimental and numerical results of the natural frequency of the vibration modes, and the results of the damping ratio.
The comparison between the experimental and (theoretical, numerical) results of the natural frequency showed error percentage, which is lower at the high frequencies and increases at the low frequencies because of the noise.
The damping ratio results were obtained experimentally for all the samples by using the half-power bandwidth techniques.
The significant sources of damping in polymeric composites are due to viscoelastic nature of the polymer and during the interface slipping between the reinforcement and the matrix. The damping characteristic of polymeric composites affected by the matrix type, fiber type, the orientation of the fiber, the volume fraction of the reinforcement, fabric type (mat chopped, unidirectional, woven, etc.), layers number, the values of the applied load frequency and the environmental influence.
Figure 10 illustrates the results for composites contained epoxy reinforced by (1, 2, 3, and 4 layers) carbon fibers, the damping ratio increased by 22.54%, 22.99% and 14.02% respectively, as the layers number increased from 1 to 2, from 2 to 3 and from 3 to 4 layers.
Figure 11 manifested the results of composites contained epoxy reinforced by (2, 4, and 6) shape memory alloy wires at
martensite phase, the damping ratio increased by 6.45% and 7.58%, respectively, as the wires number increased from 2 to 4 and from 4 to 6 wires.
Figure 12 depicts the results of composites contained epoxy reinforced by (2, 4, and 6) shape memory alloy wires at austenite phase.
Comparison the values of the damping ratio between the martensite and austenite phases showed that the damping ratio of composites contained epoxy reinforced by (2, 4, and 6) shape memory alloy wires decreased by by -4.35%, -5.45% and -9.01%, respectively, at the phase transformation from martensite to austenite.
While, the natural frequencies increased during activating the nitinol wires by an electrical heater. Nitinol has two phases with different crystal structures and different modulus, both phases Austenite and Martensite are stable. The transition between phases is due to the change of temperatures.
These transformations between phases have given Nitinol the unique characteristics.
Activating and deactivating the nitinol wires changed the bending modulus value, which changed the natural frequencies of the vibration modes, this process is useful to avoid the resonance, which is related to the possibility of the failure.
Figure 13 shows the effect of phase transformation from martensite to austenite on the acceleration- frequency response curve, for composites contained epoxy reinforced by 6 shape memory alloy wires.
Nitinol at martensite phase is easily deform, soft and has good damping characteristics, while it is super-elastic and rigid at austenite phase, this finding is in agreement with the reference (Nitinol has an ability to be vibration-attenuating and highly
damping below austenite start temperature (A )).
Figure 14 illustrates the results of hybrid composites contained epoxy reinforced by 4 carbon fiber layers with (2, 4 and 6) shape memory alloy wires at martensite phase. The damping ratio increased by 7.38% and 5.73%, respectively, as the wires number increased from 2 to 4 and from 4 to 6 wires.
Figure 15 indicates the results of the hybrid composites contained epoxy reinforced by 4 carbon fiber layers with (2, 4 and 6) shape memory alloy wires at austenite phase.
At the phase transformation from martensite to austenite, for the hybrid composites contained epoxy reinforced by 4 carbon fiber layers with (2, 4 and 6) shape memory alloy wires, the damping ratio decreased by -0.82%, -3.05% and -5.42%, respectively.
Figure 16 shows the effect of phase transformation from martensite to austenite on the acceleration- frequency response curve, for hybrid composites contained epoxy reinforced by 4 carbon fiber layers with 6 shape memory alloy wires.
Table 1. Composites material containing epoxy reinforced by (1, 2, 3, and 4) carbon fiber layers.
Table 2. Composites material containing epoxy reinforced by (2, 4, and 6) wires at martensite phase.
Mode 1 21 16.85 16.95 24.629 23.894 0.071
Mode 2 115 105.598 106.08 8.904 8.409 0.041
Mode 3 301 295.633 296.66 1.815 1.463 0.021
Mode 1 25.2 24.039 24.064 4.830 4.721 0.087
Mode 2 138.5 150.648 150.33 8.064 7.869 0.050
Mode 3 370 421.755 418.93 12.271 11.680 0.027
Mode 1 33 30.4688 30.466 8.308 8.317 0.107
Mode 2 172 190.938 190.08 9.918 9.512 0.054
Mode 3 455 534.551 528.54 14.882 13.914 0.03
Mode 1 42 36.033 36.012 16.560 16.628 0.122
Mode 2 215 225.807 224.43 4.786 4.202 0.062
Mode 3 564 632.1697 622.95 10.783 9.463 0.0348
Ep+
3carbon 6985.399 1.12265
Ep+
4carbon 9835.387 1.1302 Ep+
2carbon 4319.194 1.1151
Damping ratio (ζ)
Experimental
Results Theoretical Results
ANSYS Results
Errors%
with Theor
Errors%
with Num.
Density
(g/cm^3) Modes
Natural frequency (HZ)
Ep+
1carbon 2107.842 1.10755 (Epoxy +
layers no.)Ebending
(Mpa)
Mode 1 20 18.507 19.628 8.067 1.895 0.062
Mode 2 105 115.979 115.98 9.466 9.467 0.028
Mode 3 290 324.696 321 10.686 9.657 0.017
Mode 1 21.5 19.697 21.665 9.154 0.762 0.066
Mode 2 113 123.44 123.42 8.458 8.443 0.032
Mode 3 295 345.584 338.94 14.637 12.964 0.018
Mode 1 21.5 20.484 22.667 4.960 5.148 0.071
Mode 2 114 128.367 128.29 11.192 11.139 0.036
Mode 3 312 359.377 351.56 13.183 11.253 0.021
Ep+6wires 3315.48 1.1789 Ep+2wires 2585.7 1.1263
Ep+4wires 2997.21 1.1525
Damping ratio (ζ)
Experimental
Results Theoretical Results
ANSYS Results
Errors%
with Theor
Errors%
with Num.
(Epoxy +
wires no.) Ebending
(Mpa)
Density
(g/cm^3) Modes
Natural frequency (HZ)
Table 3. Composites material containing epoxy reinforced by (2, 4, and 6) wires at austenite phase.
Table 4. Composites material containing epoxy reinforced by 4 layers carbon fiber + (2, 4, and 6) wires at martensite phase.
Table 5. Composites material containing epoxy reinforced by 4 layers carbon fiber + (2, 4, and 6) wires at austenite phase.
Mode 1 20.05 20.284 21.286 1.154 5.807 0.0593 Mode 2 110.5 127.11 127.03 13.067 13.013 0.027 Mode 3 314.5 355.862 350.98 11.623 10.394 0.015
Mode 1 22.5 22.297 24.011 0.910 6.293 0.0624
Mode 2 124 139.733 139.66 11.259 11.213 0.028 Mode 3 337.2 391.197 383.79 13.803 12.139 0.0166
Mode 1 23.2 23.436 25.309 1.007 8.333 0.0646
Mode 2 132.4 146.865 146.82 9.849 9.822 0.031 Mode 3 365.5 411.1644 402.83 11.106 9.267 0.0174 Ep+6 wires 4339.87 1.1789
Ep+4 wires 3840.623 1.1525
Damping ratio (ζ)
Experimental
Results Theoretical Results
ANSYS Results
Errors%
with Theor
Errors%
with Num.
(Epoxy +
wires no.)
E
bending(Mpa)
Density
(g/cm^3) Modes
Natural frequency (HZ)
Ep+2 wires 3105.9 1.1263
Mode 1 43.1 36.266 36.961 18.844 16.609 0.122
Mode 2 216 227.27 226.88 4.959 4.795 0.063
Mode 3 569 636.266 628.32 10.572 9.441 0.0366 Mode 1 43.5 36.562 37.813 18.976 15.040 0.131 Mode 2 216.5 229.125 228.93 5.510 5.430 0.069 Mode 3 573 641.456 632.09 10.672 9.348 0.0391
Mode 1 43.8 36.752 38.2 19.177 14.660 0.1385
Mode 2 218 230.315 230.22 5.347 5.308 0.071
Mode 3 580 644.789 634.74 10.048 8.624 0.042 Ep+
4carbon+
2wires
10195.1 1.1565 Ep+
4carbon+
4 wires
10596.88 1.1827
Damping ratio (ζ)
Experimental
Results Theoretical Results
ANSYS Results
Errors%
with Theor
Errors%
with Num.
Ep+
4carbon+
6wires
10945.35 1.209 Ep +
layers+
wires no.
E
bending(Mpa)
Density
(g/cm^3) Modes
Natural frequency (HZ)
Mode 1 43.5 37.315 38.041 16.575 14.350 0.121 Mode 2 221.5 233.844 233.67 5.279 5.208 0.061 Mode 3 581 654.669 646.26 11.253 10.098 0.032 Mode 1 44.25 38.515 39.755 14.890 11.307 0.127 Mode 2 227.3 241.362 241.34 5.826 5.818 0.064 Mode 3 591 675.718 665.04 12.537 11.133 0.036
Mode 1 44.4 39.432 40.801 12.599 8.821 0.131
Mode 2 231 247.107 246.98 6.518 6.470 0.068
Mode 3 607 691.802 679.04 12.258 10.609 0.038
E
bending(Mpa)
Density
(g/cm^3) Modes
Ep+
4carbon+
wires
12599.64 1.209 Ep+
4carbon+
2wires
10793.39 1.1565 Ep+
4carbon+
4 wires
11759.1 1.1827
Natural frequency (HZ)
Damping ratio (ζ)
Experimental
Results Theoretical Results
ANSYS Results
Errors%
with Theor
Errors%
with Num.
Ep + layers+
wires no.
Fig. 10. Experimental damping ratio against natural frequency of EP + c (1, 2, 3 and 4 layers).
Fig. 11. Experimental damping ratio against natural frequency of EP + (2, 4 and 6) SMA wires at martensite phase.
Fig. 12. Experimental damping ratio against natural frequency of EP + (2, 4 and 6) SMA wires at austenite phase.
Fig. 13.Experimentalthe acceleration- frequency response curvesof EP + 6 SMA wires atmartensite and austenite phases.
Fig. 14. Experimental damping ratio against natural frequency of EP + 4 c layers + (2, 4 and 6) SMA wires at martensite phase.
Fig. 15. Experimental damping ratio against natural frequency of EP + 4 c layers + (2, 4 and 6) SMA wires at austenite phase.
Fig. 16. Experimental the acceleration- frequency response curves of EP + 4 c layers + 6 SMA wires at martensite and austenite phases.
6. Conclusion
The aim of this work is to study the damping characteristics and the natural frequencies of laminated hybrid composite reinforced with shape memory alloy wires.
The following conclusions are drawn:
1. For all the samples, increasing the natural frequency (mode orders) leads to decrease the damping ratio.
2. Increasing the number of layers of carbon fibers leads to increase the values of the bending modulus, the damping ratio and the natural frequencies of the vibration modes.
3. At room temperature (martensite phase), increasing the number of shape memory alloy wires leads to improve the damping characteristics (which increased by 7.38% and 5.73%, respectively, as the wires number increased from 2 to 4 and from 4 to 6 wires for the hybrid composites contained epoxy reinforced by 4 carbon fiber layers with) and increase the values of the bending modulus and the natural frequencies of the vibration modes.
4. At increasing the temperature to 55°C (the shape memory alloy wires transformed to
austenite phase), the damping ratio of the vibration modes decreased, while the values of bending modulus and natural frequencies increased (higher than martensite phase). This operation is useful to avoid the resonance by controlling the values of the natural frequencies of the vibration modes.
References
[1] Chung , D. L., "Review materials for vibration damping", Journal of Materials Science, 36: 5733-5737 (2001).
[2] Turner, T. L., Lach, C. L. and Cano, R. J., "Fabrication and characterization of SMA hybrid composites", NASA Langley Research Center, SPIE 4333-60, March (2001).
[3] Schrootenl, J., Michaud, V., Parthenios, J., Psarras, G.
C., Galiotis, C., Gotthardt, R. and Minson, J. A.,
"Progress on Composites with Embedded Shape Memory Alloy wires", Materials Transactions, 43 (5): 1-13 (2002).
[4] Stalmans, R., "Adaptive hybrid composites with a focus on the integration of shape memory elements", Advances in Science and Technology, 25: 1 – 12(1999).
[5] Boussu, F. and Bailleul, G., "Development of shape memory alloy fabrics for composite structures", AUTEX Research Journal, 2 (1): 1 – 7, March (2002).
[6] Tan, W.C., Murni, A., Ghazali, M.I. and Jamian, S.,
"Shape memory alloy hybrid composite plate for vibration control ", International Conference on Composite and nano-Structures, Shah Alam, April, 2006. PP: 25 – 29.
[7] Lagoudas, D. C. (ed.), "Shape Memory Alloys", In:
Modeling and Engineering Applications. Springer, 1st edition, (2008).
[8] Auricchio, F. and Zanaboni, E., "One Way and Two Way–Shape Memory Effect: Thermo–Mechanical Characterization of Ni–Ti wires", Master Thesis, degli Studi di Pavia University (2008).
[9] Rao, S. S., "Mechanical Vibrations", 5th Ed., Prentice- Hall, (2011).
[10] De Silva, C.W. "Vibration Damping Control and Design", Taylor and Francis, 2007.
[11] iMEMS Accelerometer ADXL330, (2006), online available (http://www.analog.com/static/imported-files/data_sheets/
ADXL330.pdf), 2006.
[12] Kimmo, K. and Karvinen, T., "Make: Arduino Bots and Gadgets, Learning by Discovery", O'Reilly Media/Make Cambridge (2011).
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ﺺﻠﺨﺘﺴﻤﻟﺍ .
ﺕﺎﻨﻴﻌﻟﺍ ﻊﻴﻨﺼﺗ ﻢﺗ .ﺔﻨﻴﺠﻫ ﺔﻴﻘﺋﺎﺒﻁ ﺔﺒﻛﺮﻣ ﺩﺍﻮﻤﻟ ﺔﻴﺟﻮﻤﻟﺍ ﺭﺍﻮﻁﻸﻟ ﺮﺤﻟﺍ ﺩﺩﺮﺘﻟﺍﻭ ﺪﻴﻤﺨﺘﻟﺍ ﺹﺍﻮﺧ ﺔﺳﺍﺭﺩ ﺚﺤﺒﻟﺍ ﺍﺬﻫ ﻲﻓ ﻢﺗ
،ﺔﻤﻈﺘﻨﻤﻟﺍ ﺓﺮﻴﺼﺤﻟﺍ ﺕﺍﺫ ،ﻥﻮﺑﺭﺎﻜﻟﺍ ﻑﺎﻴﻟﺃ ﻦﻣ ﺕﺎﻘﺒﻄﺑ ﻢًﻋﺪُﻣ ﺱﺎﺳﺃ ﻩﺩﺎﻤﻛ ،ﻲﺴﻛﻮﺒﻳﻹﺍ ﺞــﻨﺗﺍﺭ ﻦﻣ ﺔﻧﻮﻜﺘﻤﻟﺍﻭ ﺔﻳﻭﺪﻴﻟﺍ ﺔﺒﻟﻮﻘﻟﺍ ﺔﻘﻳﺮﻄﺑ ﻴﺘﻧ ﻉﻮﻧ ﻞﻜﺸﻠﻟ ﺓﺮﻛﺬﺘﻣ ﻙﻼﺳﺃﻭ ﻞﻜﻴﻧ) ﻝﻮﻨ
- ﺎﻴﻠﻤﻋ .ﺔﻔﻠﺘﺨﻣ ﺔﻴﻤﺠﺣ ﺭﻮﺴﻜﺑ (ﻡﻮﻴﻧﺎﺘﻴﺗ
، ﻡﺍﺪﺨﺘﺳﺎﺑ ﺪﻴﻤﺨﺘﻟﺍ ﺔﺒﺴﻧ ﺏﺎﺴﺣﻭ ﺮﺤﻟﺍ ﺩﺩﺮﺘﻟﺍ ﺱﺎﻴﻗ ﻢﺗ
"ﺔﻘﻳﺮﻁ
Half-power bandwidth
ﺎﻬﺘﻧﺭﺎﻘﻣﻭ ﺔﻴﻟﻮﺑﺎﻜﻟﺍ ﺔﺒﺘﻌﻠﻟ ﺕﻻﺩﺎﻌﻤﻟﺍ ﻡﺍﺪﺨﺘﺳﺎﺑ ﺎﻳﺮﻈﻧ ﺔﻴﺟﻮﻤﻟﺍ ﺭﺍﻮﻁﻸﻟ ﺮﺤﻟﺍ ﺩﺩﺮﺘﻟﺍ ﻢﻴﻗ ﺏﺎﺴﺣ ﻢﺗ ﺎﻤﻛ . "
ﺑ .ﺔﻴﻠﻤﻌﻟﺍ ﺞﺋﺎﺘﻨﻟﺍ ﻊﻣ ﺎ
ﺞﻣﺎﻧﺮﺑ ﻡﺍﺪﺨﺘﺳ
"
)
ANSYS composite Prep-Post (ACP
ﺞﻣﺎﻧﺮﺑ ﻊﻣ ﻞﻣﺎﻜﺘﻟﺎﺑﻭ "
"
ANSYS Workbench
"
ﻢﺗ
ﺓﺩﺎﻳﺯ ﻥﺃ ﺕﺎﻨﻴﻌﻟﺍ ﻊﻴﻤﺠﻟ ﺞﺋﺎﺘﻨﻟﺍ ﺕﺮﻬﻅﺃ .ﺔﻴﻠﻤﻌﻟﺍ ﺞﺋﺎﺘﻨﻟﺍ ﻊﻣ ﺎﻬﺘﻧﺭﺎﻘﻣﻭ ﺔﻴﺟﻮﻤﻟﺍ ﺭﺍﻮﻁﻸﻟ ﺮﺤﻟﺍ ﺩﺩﺮﺘﻟﺍ ﻢﻴﻗ ﺩﺎﺠﻳﺇﻭ ﻲﺟﻮﻤﻟﺍ ﻞﻜﺸﻟﺍ ﺪﻳﺪﺤﺗ ﺎﻳﺯﻭ .ﺪﻴﻤﺨﺘﻟﺍ ﺔﺒﺴﻧ ﻥﺎﺼﻘﻧ ﻰﻟﺇ ﻱﺩﺆﺗ (ﺭﻮﻄﻟﺍ ﺔﺒﺗﺮﻣ) ﺩﺩﺮﺘﻟﺍ ﻞﻣﺎﻌﻣ ﻢﻴﻗ ﺓﺩﺎﻳﺯ ﻰﻟﺇ ﻱﺩﺆﺗ ﻲﺴﻛﻮﺒﻳﻹﺍ ﻊﻣ ﻥﻮﺑﺮﻜﻟﺍ ﺓﺮﻴﺼﺣ ﺕﺎﻘﺒﻁ ﺩﺪﻋ ﺓﺩ
ﻴﻤﺨﺘﻟﺍ ﺔﺒﺴﻧﻭ ,ﺔﻳﺎﻨﺤﻠﻟ ﺔﻧﻭﺮﻤﻟﺍ ﻞﻣﺎﻌﻣ ﻢﻴﻗ ﺩﺍﺩﺰﺗﻭ .ﺔﻴﺟﻮﻤﻟﺍ ﺭﺍﻮﻁﻸﻟ ﺮﺤﻟﺍ ﺩﺩﺮﺘﻟﺍﻭ ﺪﻴﻤﺨﺘﻟﺍ ﺔﺒﺴﻧ ﺓﺩﺎﻳﺯ ﻰﻟﺇ ﻱﺩﺆﺗ ﺎﻤﻛ ،ﺔﻳﺎﻨﺤﻠﻟ ﺔﻧﻭﺮﻤﻟﺍ ،ﺪ
ﺍ ﺓﺭﺍﺮﺣ ﺔﺟﺭﺩ ﻲﻓ ﻙﻼﺳﻷﺍ ﺩﺪﻋ ﺓﺩﺎﻳﺰﺑ ﺔﻴﺟﻮﻤﻟﺍ ﺭﺍﻮﻁﻸﻟ ﺮﺤﻟﺍ ﺩﺩﺮﺘﻟﺍﻭ (ﺖﻳﺎﺴﻨﺗﺭﺎﻤﻟﺍ ﺭﻮﻁ) ﺔﻓﺮﻐﻟ
، ﻰﻟﺇ ﺓﺭﺍﺮﺤﻟﺍ ﺔﺟﺭﺩ ﺓﺩﺎﻳﺯ ﺪﻨﻋ ﺎﻤﻨﻴﺑ
٥٥
° ﻡ ﺔﻴﺟﻮﻤﻟﺍ ﺭﺍﻮﻁﻷﺍ ﻲﻓ ﺪﻴﻤﺨﺘﻟﺍ ﺔﺒﺴﻧ ﻞﻘﺗﻭ ،ﻰﻠﻋﺃ ﺮﺤﻟﺍ ﺩﺩﺮﺘﻟﺍﻭ ﺔﻳﺎﻨﺤﻠﻟ ﺔﻧﻭﺮﻤﻟﺍ ﻞﻣﺎﻌﻣ ﻢﻴﻗ ﻥﻮﻜﺘﻓ (ﺖﻳﺎﻨﺘﺳﻭﻻﺍ ﺭﻮﻁ) ﻥﻮﻜﺘﻳ
، ﺍﺬﻫ
ﻦﻴﻧﺮﻟﺍ ﺐﻨﺠﺘﻟ ﻚﻟﺫﻭ ،ﺪﻴﻔﻣ ﺮﺤﻟﺍ ﺩﺩﺮﺘﻟﺍ ﻢﻴﻗ ﻲﻓ ﺮﻴﻴﻐﺘﻟﺍ .
ﺔﻴﺣﺎﺘﻔﻣ ﺕﺎﻤﻠﻛ :
ﺕﺍﺫ ﺔﻨﻴﻨﻴﺠﻬﻟﺍ ﺕﺎﺒﻛﺍﺮﺘﻤﻟﺍ ﺃ
ﻥﻮﺑﺮﻜﻟﺍ ﻑﺎﻴﻟﺃ ،ﺮﺤﻟﺍ ﺩﺩﺮﺘﻟﺍ ،ﺪﻴﻤﺨﺘﻟﺍ ﻝﺪﻌﻣ ،ﺓﺮﻛﺍﺬﻠﻟ ﺔﻈﻓﺎﺤﻟﺍ ﻚﺋﺎﺒﺴﻟﺍ ،ﺮﻤﻴﻟﻮﺑ ﺱﺎﺳ .
