Development of a novel fractional magneto-viscoelastic dynamic model for an adaptive beam featuring functional composite magnetoactive elastomers: Simulations and experimental studies

Abstract

Recently, the rapid emergence of functional composite magnetoactive elastomers with integrated hard magnetic particles (known as hard magnetoactive elastomers) has attracted significant interest in fields such as soft robotics and material science. It is of paramount importance to develop an efficient model that can accurately predict the nonlinear dynamic behavior of adaptive structures for their practical application and the synthesis of effective control strategies. In this study, a novel nonlinear fractional magneto-viscoelastic model of an adaptive cantilevered beam featuring hard magnetoactive elastomers has been developed. This model effectively characterizes the beam’s nonlinear and rate-dependent response behavior under magnetic stimuli of varying frequencies and magnitudes. Considering the fractional Kelvin-Voigt energy dissipation model and large deformation nonlinearity, the governing equations for the cantilevered hard-magnetic soft beam were derived using the Hamilton principle. The finite difference method, combined with the Galerkin modal decomposition scheme, was subsequently utilized to discretize the time and space domains, respectively. A hardware-in-the-loop experimental framework was finally designed to experimentally investigate the beam’s nonlinear response behavior and validate the simulation results. The simulated nonlinear quasi-static responses of the beam, subjected to magnetic loading up to 30 mT, exhibited excellent agreement with the experimental data collected. Moreover, the simulated dynamic responses of the beam, subjected to various amplitudes of the applied magnetic field and magnetic frequencies up to 2 Hz, were thoroughly investigated. These included time-histories, phase-plane, and hysteretic responses, all demonstrating strong alignment with the experimental observations.