Linear and Nonlinear free vibration of a Functionally Graded Magneto-electro-elastic Rectangular Plate Based on the Third Order Shear Deformation Theory

Document Type : Research Article

Authors

Mechanical Engineering Department, Bu-Ali Sina University, Hamedan, Iran

Abstract

In this paper, linear and nonlinear free vibration of one functionally graded magnetoelectro-
elastic rectangular plate is studied. The boundary conditions in all side of plate have been
considered as simply supported. Also the equations of motions have been derived calculation the
kinetic energy and potential energy based on the third order shear deformation theory using Hamilton
principle. Considering the top surface of the plate as an pizeomagnetic material and the bottom surface
as a piezoelectric material, the bottom and upper surfaces of the plate are subjected to electric and
magnetic potentials. The electric and magnetic behaviors of the plate are modeled by using Gauss’s laws.
Then, the equations of motions have been transformed from partial differential equations to ordinary
differential equations by using Galerkin Method. Then, Using Lindeshtot- Poincare method a closed
form expression for linear and nonlinear natural frequency has been obtained. for validation of the
proposed model, some numerical examples have been presented and comparisons between the obtained
results with the results in literature have been down. It is shown that good agreement exist between
obtained results and previous works. Then, to study the effects of several parameters on the nonlinear
vibration response of functionally graded magneto-electro-elastic rectangular plates

Keywords

Main Subjects

References

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Amirkabir Journal of Mechanical Engineering
Volume 49, Issue 4
March 2018
Pages 743-758

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