Multi-frequency excitation of magnetorheological elastomer-based sandwich beam with conductive skins

The present work deals with the dynamic stability of a symmetric sandwich beam with magnetorheological elastomer (MRE) embedded viscoelastic core and conductive skins subjected to time varying axial force and magnetic field. The conductive skins induce magnetic loads and moments under the application of magnetic field during vibration. The MRE part works in shear mode and hence the dynamic properties of the sandwich beam can be controlled by magnetic fields due to the field dependent shear modulus of MRE material. Considering the core to be incompressible in transverse direction, classical sandwich beam theory has been used along with extended Hamilton's principle and Galarkin's method to derive the governing equation of motion. The resulting equation reduces to that of a multi-frequency parametrically excited system. Second order method of multiple scales has been used to study the stability of the system for simply supported and clamped free sandwich beams. Here the experimentally obtained properties of magnetorheological elastomers based on natural rubber have been considered in the numerical simulation. The results suggest that the stability of the MRE embedded sandwich beam can be improved by using magnetic field.

Dynamics of MRE embedded sandwich beam under dynamic magnetic field is carried out.
► Equation of motion is that of a multi-frequency parametrically excited system.
► Method of multiple scales is used to get the expressions for instability regions.
► Parametric studies have been carried out for three different resonance conditions.
► The study will find applications for designing smart sandwich structures.