Free and forced vibration of functionally graded porous sandwich plates reinforced by arbitrarily oblique stiffeners

In this paper, the free vibration and dynamic response of functionally graded sandwich plates reinforced with arbitrarily oblique stiffeners and featuring a metal foam core (FGP-RAS) are investigated for the first time. The investigated sandwich plate comprises three layers, two face sheets characterized as functionally graded materials and the core layer composed of metal foam. Additionally, arbitrarily oblique functionally graded material stiffeners are reinforced to enhance structural integrity. The mathematical model is developed using Reddy's third-order plate theory, Lekhnitskii's smeared stiffeners technique, and the pb2-Ritz method. This formulation enables the analysis of plates under various boundary conditions. The free vibration characteristics of the plate are determined through the solution of an eigenvalue problem while the dynamic response is computed using the Newmark algorithm. The accuracy and convergence of the proposed model are validated through comparison examples. Furthermore, the influences of key parameters such as the volume fraction index, porosity coefficient, porosity distribution, core layer-to-face sheet thickness ratio, stiffener's dimensions, and stiffener's orientation on the vibration frequency and displacement response of the FGP-RAS plates are also investigated and highlighted.