Large-Amplitude free vibration of magneto-electro-elastic curved panels

Abstract

In this study, the large-Amplitude free vibration of magneto-electro-elastic curved panels was investigated. The panel was considered to be simply supported on all edges and the magneto-electro-elastic body was subjected to the electric and magnetic fields along z direction. To obtain the governing equations of motion, the Donnell shell theory and the Gauss's laws for electrostatics and magnetostatics were used. The first mode of vibration of these smart panels was studied in this paper. To this end, the nonlinear partial differential equations of motion were reduced to a nonlinear ordinary differential equation by introducing trial functions for displacements and rotations and then by applying the single-mode Galerkin method on the obtained equation. The resulting equation was solved by multiple timescales perturbation method. Some numerical examples were presented to validate the study and to investigate the effects of several parameters such as geometry of the panel and the magneto-electric boundary conditions on the vibration behavior of these smart panels.