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Dynamic analysis of multi-directional functionally graded annular plates. (English) Zbl 1185.74047

Summary: Dynamic analysis of multi-directional functionally graded annular plates is achieved in this paper using a semi-analytical numerical method entitled the state space-based differential quadrature method. Based on the three-dimensional elastic theory and assuming the material properties having an exponent-law variation along the thickness, radial direction or both directions, the frequency equations of free vibration of multi-directional functionally graded annular plates are derived under various boundary conditions. Numerical examples are presented to validate the approach and the superiority of this method is also demonstrated. Then free vibration of functionally graded annular plates is studied for different variations of material properties along the thickness, radial direction and both directions, respectively. And the influences of the material property graded variations on the dynamic behavior are also investigated. The multi-directional graded material can likely be designed according to the actual requirement and it is a potential alternative to the unidirectional functionally graded material.

MSC:

74K20 Plates
74A40 Random materials and composite materials
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
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[1] Reddy, J.N.; Cheng, Zhen-Qiang, Frequency correspondence between membranes and functionally graded spherical shallow shells of polygonal planform, International journal of mechanical sciences, 44, 967-985, (2002) · Zbl 1115.74328
[2] Kitipornchai, S.; Yang, J.; Liew, K.M., Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections, International journal of solids and structures, 41, 2235-2257, (2004) · Zbl 1154.74344
[3] Vel, Senthil S.; Batra, R.C., Three-dimensional exact solution for the vibration of functionally graded rectangular plates, Journal of sound and vibration, 272, 703-730, (2004)
[4] Chen, W.Q.; Lee, Kang Yong; Ding, H.J., On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates, Journal of sound and vibration, 279, 237-251, (2005)
[5] Fung, Chin-Ping; Chen, Chun-Sheng, Imperfection sensitivity in the nonlinear vibration of functionally graded plates, European journal of mechanics A: solids, 25, 425-436, (2006) · Zbl 1111.74020
[6] Ferreira, A.J.M.; Batra, R.C.; Roque, C.M.C.; Qian, L.F.; Jorge, R.M.N., Natural frequencies of functionally graded plates by a meshless method, Composite structures, 75, 593-600, (2006)
[7] Woo, J.; Meguid, S.A.; Ong, L.S., Nonlinear free vibration behavior of functionally graded plates, Journal of sound and vibration, 289, 595-611, (2006)
[8] Huang, Xiao-Lin; Shen, Hui-Shen, Vibration and dynamic response of functionally graded plates with piezoelectric actuators in thermal environments, Journal of sound and vibration, 289, 25-53, (2006)
[9] Prakash, T.; Ganapathi, M., Asymmetric flexural vibration and thermoelastic stability of FGM circular plates using finite element method, Composites: part B, 37, 642-649, (2006)
[10] Bhangale, Rajesh K.; Ganesan, N., Free vibration of simply supported functionally graded and layered magneto-electro-elastic plates by finite element method, Journal of sound and vibration, 294, 1016-1038, (2006) · Zbl 1120.74597
[11] Chen, Chun-Sheng; Tan, An-Hung, Imperfection sensitivity in the nonlinear vibration of initially stresses functionally graded plates, Composite structures, 78, 529-536, (2007)
[12] Efraim, E.; Eisenberger, M., Exact vibration analysis of variable thickness thick annular isotropic and FGM plates, Journal of sound and vibration, 299, 720-738, (2007)
[13] Wu, Lanhe; Wang, Hongjun; Wang, Daobin, Dynamic stability analysis of FGM plates by the moving least squares differential quadrature method, Composite structures, 77, 383-394, (2007)
[14] Matsunaga, Hiroyuki, Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory, Composite structures, 82, 499-512, (2008)
[15] Bert, C.W.; Malik, M., The differential quadrature method in computational mechanics: a review, Applied mechanical review, 49, 1-28, (1996)
[16] F.R. Gantmacher, The Theory of Matrix, Chelsea, New York, 1960. · Zbl 0088.25103
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