Influence of orthotropic Pasternak foundations on the nonlinear free vibration of higher-order shear deformable porous orthotropic laminated beams

This study examines the nonlinear free vibration of higher-order shear deformable porous orthotropic laminated beams resting on orthotropic Pasternak foundations. A unified analytical model is developed by combining higher-order shear deformation theory with von Kármán geometric nonlinearity to capture coupled effects of porosity, lamination, and anisotropic foundation support. The governing nonlinear equations are reduced via Galerkin’s method to obtain explicit frequency–amplitude relations and are validated against analytical benchmarks and finite element results. The results show that both Winkler and orthotropic Pasternak foundations increase nonlinear frequencies, with the Pasternak shear layer providing a stronger stiffening effect. Increasing vibration amplitude induces a hardening-type response in all configurations, and higher in-plane orthotropy ratios (Eort) further amplify nonlinear frequencies, particularly with foundation support. Increasing porosity decreases frequencies due to stiffness loss; however, the PDP pattern consistently yields the highest frequencies, and foundation support mitigates porosity-induced reductions. Increasing fiber orientation (β) and foundation orthotropy angle (α) generally reduces frequencies, especially at low amplitudes and in foundation-free cases. Larger slenderness ratios (L/h) increase frequencies and diminish the sensitivity to lamination sequence, while the 0° layup remains stiffer than the 0°/90°/0° configuration. These findings provide practical guidance for vibration-sensitive lightweight structures supported by anisotropic media.