Mehmet Mert Serveren

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.

This paper focuses on the geometrically nonlinear dynamic analyses of a three-layered curved sandwich beam with isotropic face layers and a time-dependent viscoelastic core. The boundary conditions and equations of motion governing the forced vibration are derived by using Hamilton’s principle. The first-order shear deformation theory is used to obtain kinematic relations. The spatial discretization of the equations is achieved using the generalized differential quadrature method (GDQM), and the Newmark-Beta algorithm is used to solve the time variation of the equations. The Newton–Raphson method is used to transform nonlinear equations into linear equations. The validation of the proposed model and the GDQM solution’s reliability are provided via comparison with the results that already exist in the literature and finite element method (FEM) analyses using ANSYS. Then, a series of parametric studies are carried out for a curved sandwich beam with aluminum face layers and a time-dependent viscoelastic core. The resonance and cancellation phenomena for the nonlinear moving-load problem of curved sandwich beams with a time-dependent viscoelastic core are performed using the GDQM for the first time, to the best of the authors’ knowledge.