Nonlinear vibration analysis of viscoelastic sandwich beams by the generalized differential quadrature method and harmonic balance method

Abstract

This study investigates the nonlinear forced vibration of three-layered curved sandwich beams with a viscoelastic core and elastic face sheets. By using Hamilton's principle and First-order Shear Deformation Theory (FSDT), the governing equations are derived to account for large-deflection geometric nonlinearities. The core's frequency-dependent behaviour is modeled via fractional-order viscoelasticity. A novel, computationally efficient framework is developed by integrating the Harmonic Balance Method (HBM) with the Generalized Differential Quadrature Method (GDQM). The nonlinear equations are linearized using the Newton-Raphson method and discretized into algebraic form. To the best of the authors' knowledge, this represents the first application of a combined GDQM-HBM framework to curved sandwich structures under fractional Zener modelling. Validation against existing literature confirms the model's accuracy and precision. The results show that viscoelastic core thickness primarily enhances damping, while increased beam curvature significantly intensifies membrane-induced axial forces and triggers a transition from hardening to softening behaviour. Furthermore, load positioning fundamentally alters the nonlinear response even under identical geometric conditions. These findings provide a practical benchmark for the precise design and stability analysis of viscoelastic curved structures in large-deflection regimes.