Coupled effects of porosity and orthotropic foundations on the fundamental frequency characteristics of orthotropic laminated doubly curved shallow shells

Porous laminated composite shells are increasingly critical for lightweight structural applications where achieving high stiffness-to-weight ratios is mandatory. This study comprehensively examines the coupled effects of porosity distribution, foundation orthotropy, shell curvature, lamination sequence, and material orthotropy on the fundamental frequency characteristics of orthotropic laminated doubly curved shallow shells. The governing motion equations are formulated using a higher-order shear deformation theory (HSDT) and solved via the Galerkin method, incorporating the interaction with an orthotropic Pasternak foundation. Numerical results reveal that the orthotropic foundation markedly enhances the fundamental frequency by up to 33% through directional shear coupling and lateral restraint. While porosity generally reduces frequencies, surface-stiff (NUDP3) and uniform (UDP) patterns interact most effectively with the foundation to mitigate stiffness loss. Notably, the orthotropic support reduces the frequency discrepancy between spherical and hyperbolic shells by nearly 25%. However, increasing the in-plane orthotropy ratio diminishes the influence of the Pasternak layer by 25–33%. These findings highlight that the integrated optimization of porosity distribution, lamination configuration, and foundation anisotropy is essential for maximizing the dynamic performance of next-generation composite shell structures.