Free vibration and forced harmonic response of an electrorheological fluid-filled sandwich plate

A dynamic model for the electric field-dependent steady-state vibrational response of a rectangular sandwich plate with a tunable electrorheological fluid (ERF) interlayer, subjected to a general harmonic transverse excitation, is developed. Hamilton's principle and the classical thin plate theory are applied to derive a set of fully coupled dynamic equations of motion along with the associated general boundary conditions. Assuming simply-supported edge conditions, the displacement components of the ERF-based sandwich plate are postulated by means of generalized double Fourier series with frequency-dependent coefficients. The natural frequencies and modal loss factors are subsequently determined by solving a complex eigenvalue problem. Analytical solutions are also obtained for the forced vibration characteristics of the adaptive structure under different external transverse excitations of varying frequency (0–300 Hz) and applied electric field strength (0–3.5 kV mm−1). Primary attention is focused on the effects of electric field magnitude, geometric aspect ratio, loading type, and ER core layer thickness on the dynamic characteristics of the sandwich plate. In addition, an effort is made to find the optimal electric field which yields minimized vibration amplitude for each excitation frequency. Limiting cases are considered and good agreements with the numerical solutions available in the literature are obtained