Generalized Kelvin-Voigt viscoelastic modeling and numerical study of Free-Damped vibrations in MR elastomer reinforced with graphene platelets

•Development of a generalized Kelvin-Voigt model for the modeling of functionally graded (FG) graphene platelets (GPL) reinforced magnetorheological elastomers (MREs)•Implementation of a nonlinear least-square approach to fit the model with experimental data, thus ensuring accuracy and reliability.•Utilization of correlation coefficient analysis (R) and root mean square error (RMSE) tools to assess the model's accuracy and to validate its effectiveness.•Utilization of higher-order plate theory to approximate the displacement field of the plate, thereby improving the model's precision and robustness in predicting the mechanical behavior of FG-GPL-reinforced MREs. This study focuses on the modeling and numerical analysis of a novel composite plate, which consists of a laminated magnetorheological elastomer (MRE) reinforced with graphene platelets (GPLs). The investigation begins with the determination of the mechanical properties of the MRE, utilizing a modified generalized Kelvin-Voigt viscoelastic model. Through nonlinear regression analysis and the nonlinear least squares technique, the dependencies of the storage and loss modulus of the magnetorheological (MR) matrix are evaluated, considering factors such as the magnetic field, iron particles, and excitation frequency. The proposed model is validated by comparing the obtained results with existing experimental data from the literature, employing root mean square error and correlation coefficients as metrics of consistency. Next, the homogenization process is applied to the composite media, which involves integrating the MR elastomer matrix and GPL reinforcements using the Halpin-Tsai micromechanical approach. This procedure enables the extraction of effective material properties governing the behavior of the composite structure. The theoretical framework, encompassing third-order plate theory, linear elasticity, and viscoelasticity, is then employed to derive the dynamic equations of the composite plate, employing Hamilton's principle as a guiding principle. To solve the dynamic problem and obtain the complex frequencies characterizing the system, the generalized differential quadrature (GDQ) method is implemented. This numerical technique offers a robust and accurate solution approach, providing comprehensive insights into the vibrational behavior of the composite plate. The study conducts a thorough investigation, exploring the performance achieved by incorporating GPL reinforcements within the MRE ma