Soft magnetorheological elastomer (s-MRE) is a kind of smart material which often fabricated by embedding magnetic particles into an elastomer matrix. Under a magnetic field, a pronounced magnetostriction and modulus magnetic stiffening effect is exhibited for MRE, offering a wide application prospects in soft robotics, vibration control and tactile displays. Recently, much of the existing work of MRE has focused on its quasi-static behavior while the effect of inertia is neglected. However, in some applications, MRE may deform dynamically and undergo nonlinear oscillations. The research to analyze the influence of inertia on its dynamic behavior is still an open topic. In this work, the magneto-mechanical coupling behavior of isotropic s-MRE is characterized and a full-filed nonlinear dynamic model of isotropic s-MRE is proposed. Following, the corresponding two-dimensional finite element implementation framework is developed. Afterwards, the dynamic behavior of an isotropic s-MRE-based bilayer beam is studied to explore the simulation capacity of the FME model. The influence of inertia and viscoelasticity on the magneto-induced deflection along with the super-harmonic, sub-harmonic and jump resonance of the isotropic s-MRE-based bilayer beam are all investigated. Based on the simulation results, magnetic field control algorithms to tune the oscillation frequency and reduce harmonic distortion are proposed. This work can promote the application of MRE in magnetic actuation areas, such as magnetic-based loudspeakers, frequency tuning and magneto-controllable devices in micro-electro-mechanical systems (MEMS).

Isotropic soft magnetorheological elastomer, inertia effect, nonlinear vibration, constitutive modelling