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Transient Response Analysis for a Circular Sandwich Plate with an FGM Central Disk

Published online by Cambridge University Press:  11 August 2015

H.-L. Dai ,
T. Dai  and
S.-K. Cheng
H.-L. Dai*
Affiliation:
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University Changsha, China Key Laboratory of Manufacture and Test Techniques for Automobile Parts, Ministry of Education, Chongqing University of Technology Department of Engineering Mechanics College of Mechanical & Vehicle Engineering Hunan University Changsha, China
T. Dai
Affiliation:
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University Changsha, China Department of Engineering Mechanics, College of Mechanical & Vehicle Engineering, Hunan University, Changsha, China
S.-K. Cheng
Affiliation:
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University Changsha, China Department of Engineering Mechanics, College of Mechanical & Vehicle Engineering, Hunan University, Changsha, China
*
* Corresponding author ([email protected])
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Abstract

In this paper, transient response analysis of a circular sandwich plate with a functionally graded material (FGM) central disk and two piezoelectric layers is presented. Material properties of the FGM central disk for the circular sandwich plate are assumed to vary through the structural thickness according to a power law and the Poisson’s ratio is assumed as the same constant. Based on the first-order shear deformation theory and geometric nonlinear relationship, the nonlinear motion equations of the circular sandwich plate are formulated by using the Hamilton’s variational principle, then combining with the boundary and initial conditions, the whole problem is solved by adopting the finite difference method, Newmark method and iterative method. Numerical results are presented to illustrate that the volume fraction index, geometric parameters, mechanical and electrical loads have a great influence on transient response of the circular sandwich plate.

Keywords

Transient responseCircular sandwich plateFGM central diskPiezoelectric layer
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 4 , August 2015 , pp. 417 - 426
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2015 

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References

1.Koizumi, M., “Concept of FGM,” Ceramic Transactions, 34, pp. 3–10 (1993).Google Scholar
2.Chen, L. and Hirai, T., “Recent and Prospective Development of Functionally Graded Materials in Japan,” Materials Science Forum, pp. 308–311 and pp. 509–514 (1999).Google Scholar
3.Hirai, T., “Functionally Gradient Materials and Nanocomposites,” American Ceramic Society, 34, pp. 11–20 (1993).Google Scholar
4.Paulino, G. H., Jin, Z. H. and Dodds, J. R. H., Failure of Functionally Graded Materials, Elsevier Science, New York (2003).Google Scholar
5.Zhang, W., Yang, J. and Hao, Y. X., “Chaotic Vibrations of an Orthotropic FGM Rectangular Plate Based on Third Shear Deformation Theory,” Nonlinear Dynamics, 59, pp. 619–660 (2010).Google Scholar
6.Yang, J., Hao, Y. X., Zhang, W. and Kitipornchai, S., “Nonlinear Dynamic Response of a Functionally Graded Plate with a Through-Width Surface Crack,” Nonlinear Dynamics, 59, pp. 207–219 (2010).CrossRefGoogle Scholar
7.Ma, L. S. and Wang, T. J., “Relationships Between Axisymmetric Bending and Buckling Solutions of FGM Circular Plates Based on Third-Order Plate Theory and Classical Plate Theory,” International Journal of Solids and Structures, 41, pp. 85–101 (2004).CrossRefGoogle Scholar
8.Li, S. R., Zhang, J. H. and Zhao, Y. G., “Nonlinear Thermomechanical Post-Buckling of Circular FGM Plate with Geometric Imperfection,” Thin-Walled Structures, 45, pp. 528–536 (2007).Google Scholar
9.Saidi, A. R., Rasouli, A. and Sahraee, S., “Axisymmetric Bending and Buckling Analysis of Thick Functionally Graded Circular Plates Using Unconstrained Third-Order Shear Deformation Plate Theory,” Composite Structures, 89, pp. 110–119 (2009).Google Scholar
10.Hosseini-Hashemi, S. H., Fadaee, M. and Eshaghi, M., “A Novel Approach for In-Plane/Out-Of-Plane Frequency Analysis of Functionally Graded Circular/Annular Plates,” International Journal of Mechanical Sciences, 52, pp. 1025–1035 (2010).Google Scholar
11.Alijani, F., Bakhtiari-Nejad, F. and Amabili, M., “Nonliear Vibrations of FGM Rectangular Plates in Thermal Environments,” Nonlinear Dynamics, 66, pp. 251–270 (2011).Google Scholar
12.Hu, Y. D. and Zhang, Z. Q., “The Bifurcation Analysis on the Circular Functionally Graded Plate with Combination Resonances,” Nonlinear Dynamics, 67, pp. 1779–1790 (2012).CrossRefGoogle Scholar
13.Dai, H. L. and Zhen, H. Y., “Creep Buckling and Post-Buckling Analyses of a Viscoelastic FGM Cylindrical Shell with Initial Deflection Subjected to a Uniform In-Plane Load,” Journal of Mechanics, 28, pp. 391–399 (2012).Google Scholar
14.Xie, H., Dai, H. L. and Rao, Y. N., “Thermoelastic Dynamic Behaviors of a FGM Hollow Cylinder Under Non-Axisymmetric Thermo-Mechanical Loads,” Journal of Mechanics, 29, pp. 109–120 (2013).Google Scholar
15.Dai, H. L., Yang, X. and Yang, L., “Nonlinear Dynamic Analysis for FGM Circular Plates,” Journal of Mechanics, 29, pp. 287–296 (2013).Google Scholar
16.Golmakani, M. E. and Kadkhodayan, M., “An Investigation Into the Thermoelastic Analysis of Circular and Annular Functionally Graded Material Plates,” Mechanics of Advanced Materials and Sructures, 21, pp. 1–13 (2014).Google Scholar
17.Zhong, Z. and Shang, E. T., “Exact Analysis of Simply Supported Functionally Graded Piezother-moelectric Plates,” Journal of Intelligent Material Systems and Structures, 16, pp. 643–651 (2005).CrossRefGoogle Scholar
18.Li, X. Y., Ding, H. J. and Chen, W. Q., “Three-Dimensional Analytical Solution for a Transversely Isotropic Functionally Graded Piezoelectric Circular Plate Subject to a Uniform Electric Potential Difference,” Science in China Series G: Physics, Mechanics and Astronomy, 51, pp. 1116–1125 (2008).Google Scholar
19.Birschetto, S. and Carrera, E., “Refined 2D Models for the Analysis of Functionally Graded Piezoelectric Plates,” Journal of Intelligent Material Systems and Structures, 20, pp. 1783–1797 (2009).Google Scholar
20.Wang, Y., Xu, R. Q. and Ding, H. J., “Analytical Solutions of Functionally Graded Piezoelectric Circular Plates Subjected to Axisymmetric Loads,” Acta Mechanica, 215, pp. 287–305 (2010).Google Scholar
21.Alibeigloo, A., “Thermo-Elasticity Solution of Functionally Graded Plates Integrated with Piezoelectric Sensor and Actuator Layers,” Journal of Thermal Stresses, 33, 754–774 (2010).Google Scholar
22.Mao, Y. Q., Fu, Y. M. and Dai, H. L., “Creep Buckling and Post-Buckling Analysis of the Laminated Piezoelectric Viscoelastic Functionally Graded Plates,” European Journal of Mechanics-A/Solids, 30, pp. 547–558 (2011).Google Scholar
23.Li, X. Y., Wu, J., Ding, H. J. and Chen, W. Q., “3D Analytical Solution for a Functionally Graded Transversely Isotropic Piezoelectric Circular Plate Under Tension and Bending,” International Journal of Engineering Science, 49, pp. 664–676 (2011).CrossRefGoogle Scholar
24.Javanbakht, M., Shakeri, M., Sadeghi, S. N. and Daneshmehr, A. R., “The Analysis of Functionally Graded Shallow and Non-Shallow Shell Panels with Piezoelectric Layers Under Dynamic Load and Electrostatic Excitation Based on Elasticity,” European Journal of Mechanics-A/Solids, 30, pp. 983–991 (2011).Google Scholar
25.Birman, V., “Examples of Advanced Applications: Plates with Piezoelectric Sensors and Actuators and Functionally Graded Plates,” Plate Structures, Springer Netherlands, 178, pp. 257–293 (2011).Google Scholar
26.Khorshidvand, A. R., Jabbari, M. and Eslami, M. R., “Thermoelastic Buckling Analysis of Functionally Graded Circular Plates Integrated with Piezoelectric Layers,” Journal of Thermal Stresses, 35, pp. 695–717 (2012).Google Scholar
27.Sladek, J., Sladek, V., Stanak, P., Zhang, C. Z. and Wünsche, M., “Analysis of the Bending of Circular Piezoelectric Plates with Functionally Graded Material Properties by a MLPG Method,” Engineering Structures, 47, pp. 81–89 (2013).CrossRefGoogle Scholar
28.Woo, J. and Meguid, S., “Nonlinear Analysis of Functionally Graded Plates and Shallow Shells,” International Journal of Solids and Structures, 38, pp. 7409–7421 (2001).CrossRefGoogle Scholar
29.Ebrahimi, F., Rastgoo, A. and Kargarnovin, M., “Analytical Investigation on Axisymmetric Free Vibrations of Moderately Thick Circular Functionally Graded Plate Integrated with Piezoelectric Layers,” Journal of Mechanical Science and Technology, 22, pp. 1058–1072 (2008).Google Scholar
30.Najafizadeh, M. M. and Eslami, M. R., “Buckling Analysis of Circular Plates of Functionally Graded Materials Under Uniform Radial Compression,” International Journal of Mechanical Sciences, 44, pp. 2479–2493 (2002).Google Scholar
31.Timoshenko, S. and Goodier, J. N., Theory of Elasticity, McGraw-Hill, New York (1951).Google Scholar
32.Timoshenko, S. and Woinowsky-Krieger, S., Theory of Plates and Shells, McGraw-Hill, New York (1959).Google Scholar
33.Reddy, J. N. and Huang, C. L., “Nonlinear Axisymmetric Bending of Annular Plates with Varying Thickness,” International Journal of Solids and Structures, 17, pp. 811–825 (1981).Google Scholar
34.Reddy, J. N., Wang, C. M. and Kitipornchai, S., “Axisymmertric Bending of Functionally Graded Circular and Annular Platesm,” European Journal of Mechanics-A/Solids, 18, pp. 185–199 (1999).Google Scholar
35.Sahraee, S. and Saidi, A. R., “Axisymmertric Bending Analysis of Thick Functionally Graded Circular Plates Using Fourth-Order Shear Deformation Theory,” European Journal of Mechanics-A/Solids, 28, pp. 974–984 (2009).Google Scholar
36.Allahverdizadeh, A., Naei, M. and Nikkhah, B. M., “Vibration Amplitude and Thermal Effects on the Nonlinear Behavior of Thin Circular Functionally Graded Plates,” International Journal of Mechanical Sciences, 50, pp. 445–454 (2008).Google Scholar
37.Gautschi, W., Numerical Analysis, Springer, New York (2011).Google Scholar
38.Bodaghi, M., Damanpack, A. R., Aghdam, M. M. and Shakeri, M., “Non-Linear Active Control of FG Beams in Thermal Enviroments Subjected to Blast Loads with Integrated FGP Sensor/Actuator Layers,” Composite Structures, 94, pp. 3612–3623 (2012).Google Scholar