A SGM-IHB approach for nonlinear free and forced vibration analysis of FG-GPLRC beams rested on viscoelastic foundation

Abstract Combining the spectral geometry method and the incremental harmonic balance method (IHB), the nonlinear analytical model of functionally graded graphene platelet reinforced composite (FG-GPLRC) beams is developed in this paper. Nonlinear free and forced vibration characteristics are studied based on this model containing viscoelastic foundation and geometric nonlinear factors. Geometric nonlinear strain-displacement relationship and Lagrangian energy generalization for the FG-GPLRC beam structure are derived according to the Von-Kármán and Timoshenko theories. The IHB method is applied to track the nonlinear vibration response solution of the reduced-order model, which is constructed by introducing linear modal components into the overall nonlinear dynamic equation of the FG-GPLRC beam. Through comparison of the present solution with those from numerical method and literature, the correctness of the established nonlinear analytical model is evidenced. Further, the influence of material-, geometry-, foundation-related parameters and boundary constraints on the nonlinear frequency parameter and amplitude-frequency response of FG-GPLRC beams rested on viscoelastic foundation is analyzed, which can serve as a theoretical guide for designing and evaluating the dynamic environment adaptation of FG-GPLRC beams.