Three-dimensional free vibration analysis of thick multi-directional functionally graded porous skew plates on Winkler–Pasternak foundation

Abstract

Skew plates have wide applications across various industries. Consequently, their mechanical behavior has attracted considerable attention from researchers. However, most prior studies on the vibration characteristics of these plates have predominantly focused on thin plates with gradual material property variations along the thickness direction, while the investigation of thick skew plates and the effects of porosity remain limited. This study examines the free vibration response of thick functionally graded porous skew plates resting on an elastic foundation. The governing equations of motion are initially formulated within the framework of three-dimensional elasticity theory using Cartesian coordinates and subsequently transformed into oblique coordinates via an appropriate coordinate transformation. The differential quadrature method is employed to discretize the resulting equations and assemble the necessary matrices. Modal analysis is conducted to extract the natural frequencies, which are validated against existing cases reported in the literature. The influence of gradual material property gradients along the three spatial directions, elastic foundation stiffness, plate thickness, porosity parameters, skew angle, and boundary conditions on the natural frequencies is investigated. The results provide valuable insights for optimizing the design of such plates to achieve desired natural frequency characteristics under operational conditions.