Dynamic analysis of stepped functionally graded piezoelectric plate with general boundary conditions

A stepped functionally graded piezoelectric (FGPM) plate model is proposed for the first time, and its free and forced vibration are studied by using the domain energy decomposition method. The segmentation technique is used to discretize the structure along the length direction. At the structural boundary and piecewise interface, the weight parameters are introduced to satisfy the boundary conditions and the coordination conditions between the piecewise interfaces. On this basis, the boundary conditions of subdomains can be regarded as free boundary a constraint, which reduces the difficulty in constructing the displacement admissible function. Because all the structures of subdomains are the same, the displacement admissible functions of them are uniformly obtained by the two-dimensional Jacobian orthogonal polynomial expansion. The potential energy function of the plate is based on the first-order shear deformation theory. The displacement admissible function is substituted into the potential energy function, then the standard variational operation is used to obtain the solution equation of the dynamic characteristics of the FGPM plate. Through the numerical calculation, the superior calculation performance of the method is proved, and it is not limited to the boundary conditions. On this basis, the effects of geometric and material parameters on free and forced vibration of FGPM plate are also discussed.