Electro-mechanical vibration characteristics of functionally graded piezoelectric plates with general boundary conditions

This paper describes a unified approach for free vibration and transient response of functionally graded piezoelectric plates with different boundary conditions on the basis of first order shear deformation theory. Both effective electrical and mechanical properties of the plate are estimated by the Voigt model combined with a simple power law distribution. The formulation is derived by variational principle in conjunction with penalty function method which relaxes the requirement of admissible functions to explicitly satisfy geometrical boundary conditions. A modified Fourier series is adopted to express the displacements and electric potential, which is capable of representing any continuous function by adjusting auxiliary functions. Numerical comparisons with available results are made to show that the analysis model and obtained algorithm have good accuracy and stability as well as possess versatility in handling general boundary conditions. In addition, the effects of the gradient index, boundary conditions and applied voltage on the dynamic characteristic of functionally graded piezoelectric plates are investigated. (C) 2018 Elsevier Ltd. All rights reserved.