Mechanical coupling and nonlinear vibrational characteristics of doubly-curved shells with orientation-tuned auxetic-hexagonal cores

Doubly-curved sandwich shells are widely used in offshore, marine, and aerospace structures due to their high strength-to-weight ratio. However, the role of lattice orientation in zero-Poisson’s-ratio (ZPR) metamaterial cores on nonlinear vibration has not been systematically investigated. This study examines doubly-curved sandwich shells with Aux-Hex cores, which combine auxetic and honeycomb architectures, to reveal orientation-dependent nonlinear behavior. The governing equations of the doubly-curved shell are derived based on Sanders shell theory, incorporating first-order shear deformation theory (FSDT) and von Kármán nonlinear kinematic assumptions. Subsequently, the coupled nonlinear equations are solved employing the Galerkin method and the Homotopy Perturbation method (HPM). Parametric analyses explore the effects of cell link angle (θ), lattice orientation (φ = 0–90°), geometric ratios, and core thickness on nonlinear frequency ratios. The results show that Aux-Hex cores outperform conventional positive- and negative-Poisson-ratio (NPR) cores in mitigating vibration decay and enhancing dynamic resilience. Maximum nonlinear frequency ratios occur at φ = 90° due to suppression of bending–twisting coupling (D16,D26), while θ = 5π/12 marks a critical geometric threshold. These findings provide a theoretical and practical basis for designing lightweight, vibration-resistant sandwich shells in marine and aerospace structures.