Transient Vibration of a MRE Based Sandwich Beam

Dynamic response (transient vibration) of a magnetorheological elastomer (MRE) based simply supported sandwich beam under various transient loads is investigated. The MRE is modeled as a Kelvin-Voigt viscoelastic material. Hamilton’s principle in conjunction with the classical Euler-Bernoulli beam equations and linearized compatibility relations of sandwich beams with transversely flexible cores is used to derive the equations of motion and pertaining boundary conditions. Fourier series and Durbin’s algorithm for the inversion of Laplace transform are used to solve the equations of motion for different transient loads (i. e. impulse، moving load، and uniformly distributed harmonic load) in different magnetic fields. Limiting cases are compared with the data in the classic literature as verification.