Nonlinear primary resonance of doubly curved laminated nanocomposite shells within shear deformation theory

Abstract Accurate prediction of nonlinear resonance in lightweight doubly curved composite structures is essential for ensuring their dynamic reliability under external excitations. This study develops a unified analytical framework for investigating the geometrically nonlinear forced vibration response of laminated functionally graded nanocomposite (FG-NC) shells with spherical and hyperbolic paraboloidal geometries supported by a Winkler elastic foundation (WEF). The structural formulation is established within shear deformation theory, while the nonlinear strain–displacement relations associated with the non-zero Gaussian curvature are explicitly retained to capture the curvature-induced nonlinear coupling mechanisms. The model simultaneously accounts for the through-thickness distribution and stacking sequence of the FG-NC layers, foundation–structure interaction, viscous damping, and harmonic excitation. The coupled nonlinear partial differential equations governing shell dynamics are transformed into a reduced-order nonlinear modal equation using the Galerkin procedure. The method of multiple time scales is subsequently employed to derive the modulation equations and closed-form amplitude–frequency response relations governing the primary resonance regime. The resulting analytical model provides an efficient means of identifying amplitude-dependent resonance shifts and quantifying the combined effects of geometric curvature, shear deformation, elastic foundation stiffness, excitation intensity, material distribution pattern, and laminate configuration on the nonlinear dynamic response. Extensive parametric investigations reveal the physical mechanisms through which these parameters alter the resonance characteristics and vibration amplitudes of spherical and hyperbolic paraboloidal FG-NC shells. The proposed framework therefore provides a computationally efficient reduced-order tool for the dynamic assessment and resonance-oriented design of advanced curved nanocomposite structures.