Exact solutions of axisymmetric free vibration of transversely isotropic magnetoelectroelastic laminated circular plates

Jiangying Chen, Rongqiao Xu, Xusheng Huang and Haojiang Ding

Abstract

The axisymmetric free vibrations of transversely isotropic magnetoelectroelastic laminated circular plates are studied. Based on the three-dimensional governing equations of magnetoelectroelastic medium, the state space equations of laminated circular plates are obtained. By using the finite Hankel transform and rendering the free terms left by the transform in terms of the boundary quantities, the solutions of the state space equations are given for two kinds of boundary conditions. The frequency equations of the free vibration are derived using the propagator matrix method and the boundary conditions at top and bottom surfaces. By virtue of the inverse Hankel transform, the mode shapes are also determined. Since the solutions strictly satisfy the governing equations in the region and the boundary conditions at the edges, they are the three-dimensionally exact. Finally, the natural frequencies of such plates are tabulated and compared with those of the piezoelectric and elastic plates in the numerical example.

Key Words

magnetoelectroelastic medium; laminated circular plates; free vibration; state space method.

Address

Jiangying Chen; Faculty of Engineering, Ningbo<br />University, Ningbo 315211, China (Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China)<br />Rongqiao Xu; Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China<br />Xusheng Huang; Faculty of Engineering, Ningbo University, Ningbo 315211, China<br />Haojiang Ding; Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China

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