Micro-vibration response of a stochastically excited sandwich beam with a magnetorheological elastomer core and mass

Magnetorheological (MR) elastomers are used to construct a smart sandwich beam for micro-vibration control. The micro-vibration response of a clamped-free sandwich beam with an MR elastomer core and a supplemental mass under stochastic support micro-motion excitation is studied. The dynamic behavior of MR elastomer as a smart viscoelastic material is described by a complex modulus which is controllable by external magnetic field. The sixth-order partial differential equation of motion of the sandwich beam is derived from the dynamic equilibrium, constitutive and geometric relations. A frequency-domain solution method for the stochastic micro-vibration response of the sandwich beam is developed by using the frequency-response function, power spectral density function and spatial eigensolution. The root-mean-square velocity response in terms of the one-third octave frequency band is calculated, and then the response reduction capacity through optimizing the complex modulus of the core is analyzed. Numerical results illustrate the influences of the MR elastomer core parameters on the root-mean-square velocity response and the high response reduction capacity of the sandwich beam. The developed analysis method is applicable to sandwich beams with arbitrary cores described by complex shear moduli under arbitrary stochastic excitations described by power spectral density functions.