Modeling of a Magnetorheological Elastomer-Based Nanocomposite Higher-Order Beam: Tunable Dynamic and Damping Characteristics

Abstract

This study involves the comprehensive modeling of material properties and a numerical investigation of the free-damped vibrations exhibited by an innovative composite beam. The beam under consideration is a laminated magnetorheological (MR) elastomer, strategically reinforced with graphene platelets (GPLs). Initially, the mechanical properties of the MR matrix are meticulously calculated using a modified generalized Kelvin–Voigt viscoelastic model. To ensure the accuracy and credibility of the proposed model, nonlinear regression analysis based on the nonlinear least squares technique is employed. This modeling approach enables the tunability of the MR matrix’s storage and loss modulus, which depend on factors such as the magnetic field, iron particles, and excitation frequency. The proposed model is verified by comparing the results with experimental data from the literature, using analyses of root mean square error (RMSE) and correlation coefficients. Subsequently, the composite media, comprising the magnetorheological elastomer (MRE) matrix and GPL reinforcements, undergoes homogenization through the application of the Halpin–Tsai micromechanical procedure. Theoretical formulations, encompassing third-order beam theory, strains, linear elasticity, and viscoelasticity, are then utilized to derive the motion equations governing the dynamic behavior of the composite beam. Hamilton’s principle guides the derivation of these equations. To obtain the complex frequencies characterizing the system, the generalized differential quadrature (GDQ) method is implemented. In this study, particular emphasis is placed on investigating the performance achieved by adding GPL reinforcements to the MRE with different iron particle volume fractions under various magnetic fields.