Vibration Suppression of an Elastic Plate by Use of an Electrorheological Patch and Constraining Layer

Electrorheological materials are a class of smart materials which exhibit dramatic changes in mechanical properties (like shear modulus) due to strong applied external electric fields. In this paper forced harmonic vibration of a simply supported rectangular elastic plate with a rectangular ER patch with arbitrary size and location on the plate and a constraining layer on the patch is investigated. A dynamic model for the electric field-dependent frequency response of a rectangular plate and the ER patch and its constraining layer 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. The frequency response functions and the modal loss factors are subsequently determined. The effects of electric field intensity, patch size and patch location on the frequency response functions and modal loss factors are investigated in numerical results. This work represents a rigorous analytical solution for the problem of the ER patch which seems to be absent in the previous works