Transverse vibration responses of the in-plane-wise functionally graded piezoelectric composite plates

Abstract

Aided by the scaled boundary finite element method (SBFEM), analytical precise integration solutions to the transverse free vibration responses of functionally graded piezoelectric composite plates are provided for the first time. Distributions of the functionally graded piezoelectric materials follow arbitrary mathematical formulae as concerns the in-plane unidirectional or bidirectional coordinates. The vibration behaviors of piezoelectric composite plates with various geometrical shapes, multifarious boundary constraints and any number of laminae can be explored by the introduced technique. Additionally, the shear correction factors and assumptions on the changing patterns of mechanical and electrical variables are not needed to be offered in the employed methodology. The proposed approach regards only four quantities containing three elastic displacement components and the electric potential as the primary unknowns, which can be denoted as an analytical matrix exponent in terms of the thickness coordinate. Only two-dimensional high-order spectral elements are adopted to discretize the in-plane surface of the plate with less nodes and degree of freedoms, which promotes to lowering the calculative expense and advancing the computational efficiency. The introduced scaled boundary coordinate system and the dual vector technology are helpful to simplify the basic partial differential equations of piezoelectric materials into the first order ordinary differential SBFEM governing equation, from which the highly accurate global stiffness matrix are constructed by dine of the precise integration technique (PIT). With the aid of the kinetic energy scheme and compatibility conditions between neighboring layers, the whole mass matrix for the laminated piezoelectric plates can be built. According to solving the eigenvalue equation, the precise integration solutions to free vibration frequencies can be acquired. Finally, numerical experiments are afforded to elucidate the high precision and fast convergence of the present method. Moreover, the effect of different boundary constraints, gradation parameters and aspect ratios on the transverse vibration responses of in-plane-wise functionally graded piezoelectric composite plates is revealed.