A new semi-analytical solution method for free vibration analysis of composite rectangular plates with general edge constraints coupled with single piezoelectric layer

Abstract

In this article, a new approach is presented to study the free vibrations of rectangular composite plates coupled with single piezoelectric layer. The laminated plate with general stacking sequences is subjected to the elastic edge restraints. Based on the first-order shear deformation theory and Hamilton’s principle, the equations of the motion along with boundary conditions of the problem are deduced. To solve the problem, generalized displacements as well as general electric potentials are expanded using the Legendre polynomial series as the base functions. Then, the kinetic and potential energies of the problem are obtained. Afterwards, by means of Lagrange multipliers all the boundary conditions have been added to the energies to form the functional. This energy functional is extremised to get the natural frequencies and mode shapes of the problem through generalized eigenvalue problem. Credibility of the proposed method is verified by comparing the obtained results with those achieved by other theories and finite element method.

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

“…Also, the maximum frequency values were obtained by subjecting the plate to SCSC BCs. Furthermore, Baghaee et al [456] explored the FV of rectangular LCPs (PVDF-Gr/Ep) that contain a single PE layer (PZT-4) and based on EF. The EOM and the BCs were defined by HP combined with the FSDT which was solved further by generating a base function based on the general electrical potential and the generalized displacements which were expanded by applying the Legendre polynomial series.…”