Dynamic stability of magnetorheological elastomer based adaptive sandwich beam with conductive skins using FEM and the harmonic balance method

• Equation of motion of a MRE embedded sandwich beam has been derived using FEM.
• Effect of length and location of the MRE patch on natural frequency has been studied.
• Parametric instability regions have been obtained for eight different configurations.
• Effects of magnetic field and static load on dynamic instability regions have been studied.
• The work will find extensive application for active and passive vibration attenuation.

The dynamic stability of a partially treated magnetorheological elastomer (MRE) cored sandwich beam with conductive skins subjected to time varying axial load has been studied. The finite element method (FEM) and Guyan reduction method are used to derive the governing equation of motion which is similar to that of Mathieu's equation. The instability regions of the sandwich beam for the principal parametric resonance case are calculated by using the harmonic balance method. Effects of applied magnetic field, static load, dynamic load, the length and the location of the MRE patch on the stability of the sandwich beam are investigated. The results suggest that the stability of the MRE embedded sandwich beams are strongly influenced by the strength of the applied magnetic field, static load, dynamic load, the location and the length of the MRE patch.