Three-dimensional free vibration analysis of multi-directional functionally graded piezoelectric annular plates on elastic foundations via state space based differential quadrature method

doi:10.1007/s10483-015-1923-9

摘要/Abstract

摘要：

The three-dimensional free vibration analysis of a multi-directional functionally graded piezoelectric (FGP) annular plate resting on two parameter (Pasternak) elastic foundations is investigated under different boundary conditions. The material properties are assumed to vary continuously along the radial and thickness directions and have exponent-law distribution. A semi-analytical approach named the state space based differential quadrature method (SSDQM) is used to provide an analytical solution along the thickness using the state space method (SSM) and an approximate solution along the radial direction using the one-dimensional differential quadrature method (DQM). The influence of the Winkler and shear stiffness of the foundation, the material property graded variations, and the circumferential wave number on the non-dimensional natural frequency of multi-directional FGP annular plates is studied.

关键词: free vibration, piezoelectric, annular plate, multi-directional functionally graded

Abstract:

Key words: multi-directional functionally graded, annular plate, piezoelectric, free vibration

中图分类号:

O327
O302

M. H. YAS;N. MOLOUDI. Three-dimensional free vibration analysis of multi-directional functionally graded piezoelectric annular plates on elastic foundations via state space based differential quadrature method[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(4): 439-464.

参考文献

[1] Gandhi, M. V. and Thompson, B. S. Smart Materials and Structures, Chapman and Hall, London (1992)
[2] Rao, S. S. and Sunar, M. Piezoelectricity and its use in disturbance sensing and control of flexible structures. Applied Mechanics Reviews, 47(4), 113-123 (1994)
[3] Branco, P. J. and Dente, J. A. On the electromechanics of a piezoelectric transducer using a bimorph cantilever undergoing asymmetric sensing and actuation. Smart Materials and Structures, 13(4), 631-642 (2004)
[4] Kruusing, A. Analysis and optimization of loaded cantilever beam microactuators. Smart Materials and Structures, 9(2), 186-196 (2000)
[5] Zhu, X. H. and Meng, Z. Y. Operational principle fabrication and displacement characteristic of a functionally gradient piezoelectric ceramic actuature. Sensors and Actuators, 48(3), 169-176 (1995)
[6] Wu, C. C., Kahn, M., and Moy, W. Piezoelectric ceramics with functional gradients: a new application in material design. Journal of the American Ceramic Society, 79(3), 809-812 (1996)
[7] Zhong, Z. and Shang, R. T. Three-dimensional exact analysis of simply supported functionally gradiant piezoelectric plate. International Journal of Solids and Structures, 40(20), 5335-5352 (2003)
[8] Lu, P., Lee, H. P., and Lu, C. Exact solutions for simply supported functionally graded piezoelectric laminates by Stroh-like formalism. Composite Structures, 72(3), 352-363 (2006)
[9] Lee, J. S. and Jiang, L. Z. Exact electroelastic analysis of piezoelectric laminae via state-space approach. International Journal of Solids and Structures, 33(7), 977-990 (1996)
[10] Bert, C. W. and Malik, M. Differential quadrature: a powerful new technique for analysis of composite structures. Composite Structures, 39(3-4), 179-189 (1997)
[11] Chen, W. Q. and Ding, H. J. Bending of functionally graded piezoelectric rectangular plates. Acta Mechanica Solida Sinica, 13(4), 312-319 (2000)
[12] Chen, W. Q. and Ding, H. J. On free vibration of a functionally graded piezoelectric rectangular plate. Acta Mechanica, 153(3-4), 207-216 (2002)
[13] Lim, C. W. and He, L. H. Exact solution of a compositionally graded piezoelectric layer under uniform stretch bending and twisting. International Journal of Mechanical Sciences, 43(11), 2479- 2492 (2001)
[14] Reddy, J. N. and Cheng, Z. Q. Three-dimensional solutions of smart functionally graded plates. Journal of Applied Mechanics, 68(2), 234-241 (2001)
[15] Lu, P., Lee, H. P., and Lu, C. An exact solution for simply supported functionally graded piezoelectric laminates in cylindrical bending. International Journal of Mechanical Sciences, 47(3), 437-458 (2005)
[16] 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(8), 1116-1125 (2008)
[17] Xiang, H. J. and Shi, Z. F. Static analysis for functinoally graded piezoelectric actuators or sinsors under a combined electro-thermnl load. European Journal of Mechanics-A/Solids, 28(2), 338-346 (2009)
[18] Li, Y. and Shi, Z. F. Free vibration of functionally graded piezoelectric beam via state-space based differential quadrature. Composite Structures, 87(3), 257-264 (2009)
[19] Alibeigloo, A. and Nouri, V. Static analysis of functionally graded cylindrical shell with piezoelectric layers using differential quadrature method. Composite Structures, 92(8), 1775-1785 (2010)
[20] Jam, J. E. and Nia, N. G. Semi-analytical solution for 3-D vibration of FGPM annular plates. International Journal of Emerging Trends in Engineering and Development, 3, 149-166 (2011)
[21] Nie, G. J. and Zhong, Z. Dynamic analysis of multi-directional functionally graded annular plates. Applied Mathematical Modelling, 34(3), 608-616 (2010)
[22] Qian, L. F. and Batra, R. C. Design of bidirectional funcaionally graded plate for optimal natural frequencies. Journal of Sound and Vibration, 280(1-2), 415-424 (2005)
[23] Qian, L. F. and Ching, H. K. Static and dynamic analysis of 2-D functionally graded elasticity by using meshless local Petrov-Galerkin method. Journal of the Chinese Institute of Engineers, 27(4), 491-503 (2004)
[24] Lü, C. F., Lim, C. W., and Chen, W. Q. Semi-analytical analysis for multi-directional functionally graded plates: 3-D elasticity solutions. International Journal for Numerical Methods in Engineering, 79(1), 25-44 (2009)
[25] Gupta, U. S., Ansari, A. H., and Sharma, S. Buckling and vibration of polar orthotropic circular plate resting on Winkler foundation. Journal of Sound and Vibration, 297(3-5), 457-476 (2006)
[26] Hosseini-Hashemi, S., Rokni Damavandi Taher, H., and Omidi, M. 3-D free vibration analysis of annular plates on Pasternak elastic foundation via p-Rite method. Journal of Sound and Vibration, 311(3-5), 1114-1140 (2008)
[27] Hosseini-Hashemi, S., Omidi, M., and Rokni Damavandi Taher, H. The validity range of CPT and Mindlin plate theory in comparison with 3-D vibrational analysis of circular plateson the elastic foundation. European Journal of Mechanics-A/Solids, 28(2), 289-304 (2009)
[28] Malekzadeh, P., Afsari, A., Zahedinejad, P., and Bahadori, R. Three-dimensional layerwise-finite element free vibrition analysis of thick laminated annular plates on elastic foundation. Applied Mathematical Modelling, 34(3), 776-790 (2010)
[29] Malekzadeh, P. Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations. Composite Structures, 89(3), 367-373 (2009)
[30] Amini, M. H., Soleimani, M., and Rastgoo, A. Three-dimensional free vibration analysis of functionally graded material plates resting on an elastic foundataon. Smart Materials and Structures, 18(8), 085015 (2009)
[31] Hosseini-Hashemi, S., Akhavan, H., Rokni Damavandi Taher, H., Daemi, N., and Alibeigloo, A. Differential quadrature analysis of functionally grared circular and annular sector plates on elastic foundation. Materials and Design, 31(4), 1871-1880 (2010)
[32] Hosseini-Hashemi, S., Rokni Damavandi Taher, H., and Akhavan, H. Vibration analysis of radially FGM sectorial plates of variable thickness on elastic foundations. Composite Structures, 92(7), 1734-1743 (2010)
[33] Yas, M. H. and Tahouneh, V. 3-D free vibration analysis of thick functionally graded annular platrs on Pasternak elastic foundation via differential quadrature method (DQM). Acta Mechanica, 223(9), 43-62 (2012)
[34] Yas, M. H., Jodaei, A., Irandoust, S., and Nasiri-Aghhdam, M. Three-dimensional free vibration of functionally graded piezoelectric annular plates on elastic foundations. Meccanica, 47(6), 1401- 1423 (2012)
[35] Chen, W. Q., Lv, C. F., and Bian, Z. G. Elasticity solution for free vibration of laminated beams. Composite Structures, 62(1), 75-82 (2003)
[36] Chen, W. Q., Lv, C. F., and Bian, Z. G. Free vibration of generally laminated beams via statespace based differential quadrature. Composite Structures, 63(3-4), 417-425 (2004)
[37] Chen, W. Q. and Lü, C. F. 3D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported. Composite Structures, 69(1), 77-87 (2005)
[38] Lü, C. F., Chen, W. Q., Xu, R. Q., and Lim, C. W. Semi-analytical elasticity solutions for bi-directional functionally graded beams. International Journal of Solids and Structures, 45(1), 258-275 (2008)
[39] Lee, J. S. and Jiang, L. Z. Exact electroelastic analysis of piezoelectric laminae via state space approach. International Journal of Solids and Structures, 33(7), 977-990 (1996)
[40] Zhong, Z. and Shang, E. T. Three-dimensional exact analysis of a simply supported functionally graded piezoelectric plate. International Journal of Solids and Structures, 40(20), 5335-5352 (2003)
[41] Bert, C. W. and Malik, M. The differential quadrature method in computational mechanics. Applied Mechanics Reviews, 49(1), 1-28 (1996)
[42] Karami, G. and Malekzadeh, P. A new differential quadrature methodology for beam analysis and the associated differential quadrature element method. Computer Methods in Applied Mechanics and Engineering, 191(32), 3509-3526 (2002)
[43] Malekzadeh, P. Differential quadrature large amplitude free vibration analysis of laminated skew plates based on FSDT. Composite Structures, 83(2), 189-200 (2008)
[44] Malekzadeh, P., Setoodeh, A. R., and Barmshouri, E. A hybrid layerwise and differential quadrature method for in-plane free vibration of laminated thick circular arches. Journal of Sound and Vibration, 315(1-2), 215-225 (2008)
[45] Wang, X. W. and Wang, Y. L. Free vibration analyses of thin sector plates by the new version of differential quadrature method. Computer Methods in Applied Mechanics and Engineering, 193(36-38), 3957-3971 (2004)
[46] Nie, G. J. and Zhong, Z. Semi-analytical solution for three-dimensional vibration of functionally graded circular plates. Computer Methods in Applied Mechanics and Engineering, 196(49-52), 4901-4910 (2007)
[47] Shu, C. and Richards, B. E. Application of generalized differential quadrature to solve twodimensional incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluid, 15, 791-798 (2012)