Effect of orthotropic Pasternak foundation on free vibration of porous orthotropic laminated plates

Abstract Porous orthotropic laminated plates are increasingly used in lightweight structural applications due to their high stiffness-to-weight ratio and tunable mechanical behavior. However, their vibrational performance is strongly affected by the distribution of porosity, the lamination scheme, and interaction with the underlying support medium, particularly when resting on elastic foundations. This study aims to analyze the fundamental natural frequencies of porous orthotropic laminated plates considering various porosity distribution patterns (PDP, UDP, NUDP1-3), lamination sequences, and two types of elastic foundation models: Winkler and orthotropic Pasternak foundations. The equations of motion are derived using Hamilton’s principle and higher-order shear deformation theory (HSDT) and solved analytically via Galerkin’s method. A comprehensive parametric study is conducted to assess the impact of foundation stiffness, shear layer stiffness ratio, porosity coefficient, orthotropy ratio, aspect ratio, side-to-thickness ratio, and fiber orientation angle on the dynamic response. The results reveal that increasing foundation stiffness significantly enhances natural frequencies and reduces the adverse effects of porosity on structural stiffness. Orthotropic shear interactions further amplify frequency gains, particularly in soft porosity distributions. Lamination sequences with higher in-plane stiffness and lower fiber angles exhibit better vibrational capacity. Additionally, geometric and material orthotropy parameters significantly impact the frequency trends, with elastic foundations enhancing configuration-specific behaviors.