free vibrations analysis of a sandwich rectangular plate with electrorheological fluid core

in this paper, a rectangular sandwich plate with a constrained layer and an electrorheological (er) fluid core is investigated. the rectangular plate is covered an er fluid core and a constraining layer to improve the stability of the system. the two outer layers of the sandwich structure are elastic. the viscoelastic materials express the middle layer behavior under electric field and small strain. rheological property of an er material, such as viscosity, plasticity, and elasticity, may be changed when applying an electric field. the er core is found to have a significant effect on the stability of the sandwich plate. in this paper, based on the displacement field of each layer, the kinetic energy and strain energy are separately obtained for each layer. transverse displacement of the second layer changes linearly between the transverse displacement of the first and third layers. the loss energy of the second layer consisting of the er fluid is also calculated and, with the replacement of total kinetic energy, total strain energy, and energy dissipation in the lagrange's equation, the structural motion equation is obtained. natural frequencies and loss factor for the electric fields as well as the ratio of different thicknesses calculated are by navier analytical method. as the applied electric field increases, the natural frequency of the sandwich plate increases and the modal loss factor decreases. with increasing the thickness of the er layer, the natural frequencies of the sandwich plate are decreased. thickness of the constrained layer also affects the stability of the sandwich plate.