Exact solution for shear deformable model of free damped vibration of magnetorheological fluid sandwich beam

Abstract

Abstract An exact procedure is proposed to analyze vibration suppression of magnetorheological fluid (MRF) sandwich beams based on the Timoshenko shear deformable beam model. The equations of motion and corresponding boundary conditions are extracted using Hamilton’s principle. Then, by introducing four innovative functions, five highly coupled equations of motion are divided into three coupled equations and two independent equations. Employing a systematic procedure, the displacement fields and consequently frequency characteristic equation of the beam are exactly derived. High accuracy and stability of the exact natural frequencies and corresponding loss factors are shown in comparison with those available in literature.