Free Vibration Analysis of Levy-Type Smart Hybrid Plates Using Three-Dimensional Extended Kantorovich Method

In this research work, three-dimensional (3D) piezoelasticity solution is developed to analyze the free vibration behaviour of rectangular hybrid piezo-laminated plate using three-dimensional extended Kantorovich method (3D EKM). The partial differential equations (PDEs) of a bivariate problem is converted into two sets of ordinary differential equations (ODEs) in the two directions, by approximating the solution as a series of products of two separable functions. Following an iterative process which converges fast the free vibration frequency and other state variables are computed. The accuracy of this method is extensively verified by comparing the present prediction with previous analytical results published in the literature and with the finite element solutions wherever analytical solutions are not available. Benchmark results are presented for bimorph and hybrid composite plates for different boundary conditions. Effect of electric circuit conditions and plate aspect ratios (b/a) on the natural frequency are also investigated. The present results can serve as benchmark to assess the two-dimensional and numerical solutions.