Dynamic Stability of a Sandwich Beam with Magnetorheological Core

Abstract

Abstract This study investigated the dynamic stability of a simply supported sandwich beam with a magnetorheological core under an axial harmonic and parametric load. The complex modulus of the magnetorheological material is a function of the applied magnetic field. The governing equation of motion is theoretically derived using the Mead and Markus sandwich beam model, and also by applying Galerkin's method to simplify the governing equation of motion into a complex Mathieu equation with the coefficient function of the external magnetic field. The natural frequency and structural loss factor of the sandwich beam function of the applied magnetic field are conveniently computed from these coefficients. The influence of the magnetic field strength on the natural frequency and loss factor is also studied. Moreover, the boundaries of dynamic stability are analytically determined by applying the complex incremental harmonic balance (CIHB) method. Finally, the effects of the magnetic field strength, core thickness ratio, beam width, beam length, and static load parameter factor on the instability regions are also investigated.