Stochastic microvibration response analysis of a magnetorheological viscoelastomer based sandwich beam under localized magnetic fields

The microvibration of a horizontal magnetorheological viscoelastomer (MRVE) based sandwich beam with supported mass under random disturbances and localized magnetic fields is studied to verify its control effectiveness. The localized magnetic field covering incompletely the beam results in the MRVE properties varying in space. The effects of the localized magnetic field distribution on the microvibration are considered in the analysis. The vibration equations with spatial parametric variation and temporal randomness of the beam system under the localized magnetic field are derived, and solved by the modal transformation and frequency spectrum analysis. Then the expression of the root-mean-square velocity criterion for microvibration is given, where the non-homogeneous MRVE modulus is considered due to the localized magnetic field. The proposed analysis method can be extended to other random excited composite structures with viscoelastic cores. The stochastic microvibration control effectiveness of the beam system and the effects of the localized magnetic field intensity and placement on the microvibration response are verified by numerical results.