Stochastic micro-vibration suppression of a sandwich plate using a magneto-rheological visco-elastomer core

Magneto-rheological visco-elastomer (MRVE) is used to construct sandwich plates for micro-vibration control. The micro-vibration response of a sandwich plate with an MRVE core under stochastic support motion excitation is studied to evaluate the vibration suppression capability. The dynamic behavior of MRVE in micro-vibration is characterized by a non-homogeneous complex modulus dependent on the vibration frequency and controllable by an applied magnetic field, in which the effect of the localized magnetic field distribution is considered. The partial differential equations for the coupled transverse and longitudinal motions of the sandwich plate are derived from the dynamic equilibrium, constitutive and geometric relations. A frequency-domain solution method for the stochastic micro-vibration response of sandwich plates is developed based on the Galerkin method and random vibration theory. The partial differential equations are first converted into ordinary differential equations according to the Galerkin method. Then the expressions for the frequency-response function, response power spectral density and root-mean-square velocity spectrum in terms of the one-third octave frequency band for micro-vibration are obtained. Finally, numerical results are given to illustrate the high response reduction capacity of the MRVE sandwich plate under stochastic support motion excitation, and the influence of the MRVE parameters and localized magnetic field placement on the micro-vibration response.