Nonlinear Transient Dynamics of Skew Porous Graded Composite Plates supported on Multi-Parameter Elastic Foundations: Winkler–Pasternack/Kerr Models

This study investigates the nonlinear vibration characteristics of skew porous graded composite (SPGC) plates resting on elastic foundations, particularly emphasizing the comparative influence of Winkler–Pasternak (W–P) and Kerr foundation models. The displacement fields are derived using the first-order shear deformation theory (FSDT) in conjunction with von Kármán-type geometric nonlinearity and solved within the finite element framework. Effective material properties are evaluated through an improved power-law distribution, explicitly considering both even and centrally distributed porosity patterns. The principal equations are formulated based on the principle of virtual work. They are solved using a direct iterative scheme and Newmark’s time integration algorithm for the time-dependent nonlinear responses. The proposed formulation is verified and validated against the established benchmark results, ensuring the reliability of the nonlinear analysis of graded composite (GC) skew plates. The effect of geometrical parameters, such as porosity distribution patterns, skew angles, coefficient of porosity, side-to-thickness ratio, and foundation stiffness parameters, on the nonlinear frequency and dynamic responses for different foundation models is analyzed in detail. The investigation provides a comprehensive framework for analyzing coupled effects of porosity, skewness, and elastic foundations on the nonlinear dynamic and transient responses, providing a basis for designing advanced GC structural components subjected to elastic foundation support.