An original analytical vibration analysis of clamped composite, regular, and auxetic honeycomb shells using the boundary continuous method

In this work, a robust analytical methodology is developed to investigate the free vibration response of fully clamped doubly-curved sandwich shells reinforced with hexagonal, rectangular, and auxetic reentrant honeycomb (HC) cores, which is quite scarce in the scientific literature. Several higher-order equivalent single-layer models are constructed within the versatile Carrera unified formulation. To further enhance the accuracy, particularly for sandwich shells with varying cell geometries and slenderness ratios, Murakami’s zig-zag function is incorporated into the displacement field. The enhanced Tornabene’s homogenization model is employed to compute the effective properties of the HC core. The dynamic governing equations are derived using the principle of virtual displacements. Novel analytical strong-form solutions are derived by solving the governing equations using the boundary continuous method, a technique that has been only sparsely explored in the scientific literature. Then, a detailed convergence analysis and several comparative studies against two- and three-dimensional FEM solutions available in the literature confirm the robustness and precision of the proposed methodology. Given their analytical nature, the results presented here can serve as benchmarks for future comparisons with approximate solutions, such as Galerkin, Ritz, Finite Element Method (FEM), or analytically trained IA models.