Analysis of free vibration characteristics of porous FGM skew plate using meshfree approach

Abstract

The present work attempts to study the free vibration of simply supported porous functionally graded material (PFGM) skew plate using five variable Higher-order shear deformation theory (HSDT). The material properties of the PFGM skew plate follow a power-law distribution and vary with thickness direction. The governing differential equations (GDEs) of motion for the FGM skew plate are developed using Hamilton's principle, and the GDEs are discretized using Wendland’s C2 function (WC2RBF). The corresponding natural frequencies and mode shapes are found using a meshfree technique. To verify their correctness and efficacy, the current results are cross-checked against published literature that is currently available. The study looks into how the natural frequency of PFGM plates is affected by grading index, porosity distribution, porosity index, span-to-thickness ratio, and skewness. The findings can be applied to designing and optimizing PFGM structures, where precise natural frequency and mode shape are crucial for ensuring their reliable and efficient performance. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.