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

Abstract

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.

Magnetic Particle Filled Elastomeric Hybrid Composites and Their Magnetorheological Response

“…Nayak et al [ 143 ] performed a dynamical analysis of the three-layer symmetrical sandwich beams with the MR elastomer embedded core and conductive layers, subjected to a periodic axial load under various boundary conditions. Ying et al [ 144 ] examined a micro-vibration response of a clamped–free sandwich beam using an MR elastomer core and a supplemental mass under stochastic supporting micro-motional excitation. Furthermore, MR elastomers have been recently adopted for manufacturing plane electric capacitors to measure electrical capacitance [ 145 , 146 ].…”

Experimental investigation of 3D-printed polymer-based MR sandwich beam under discretized magnetic field

“…Sixth-order differential equation of sandwich beam was developed by dynamic equilibrium, constitutive, and geometric relations. Also, for minimizing the velocity response of the sandwich beam, the optimizing problem of the complex shear modulus of MR elastomer was constricted [42]. Umanath reported frequency and strain dependency of MRE with dynamic loading condition.…”

Vibration Characteristic Analysis of Polar Orthotropic Sandwich Annular Plate with Tunable MR Elastomer Treatment

“…Sun et al [6] used Hamilton's principle to obtain analytical model for sandwich beam structure with MR core layer based and calculated the numerical results with simply-supported boundary condition. Ying and Ni [7] calculated the micro-vibration response of a stochastically excited sandwich beam with a MR elastomer core. In recently, the dynamic characteristics analysis of MR elastomer-based sandwich beam with conductive skins for various boundary conditions was calculated and discussed by Nayak et al [8].…”