Dynamic Characteristics and Dynamic Instability of Magnetorheological Material-based Adaptive Beams

Abstract

The theoretical model of a simply supported magnetorheological material-based adaptive beam under an axial harmonic load is modified based on the DiTaranto sandwich beam theory for a symmetric three-layer beam. A differential equation for extensional motion of a freely vibrating beam is derived. This study considers an axially forced vibration of asymmetric magnetorheological material-based beam and derives a sixth-order equation for transverse motion. The derived governing equation of motion is then simplified using Galerkin’s method to yield the Mathieu equation. The formulae for buckling load, natural frequency, and loss factor of a simply supported adaptive beam are developed. Numerical results demonstrated from the formulae are highly consistent with the published results. The incremental harmonic balance (IHB) method is utilized to study the regions of dynamic instability, which are demonstrated graphically. The dynamic responses of the adaptive beam are assessed via the fourth-order Runge-Kutta method. The effects of magnetic field, core thickness ratio and beam length on the buckling load, natural frequency, loss factor, and dynamic instability are also presented. The influence of the static load parameter factor on natural frequency, loss factor, and dynamic instability is considered.