Free vibration solutions of functionally graded plates with various boundary conditions using unified finite integral transform approach
Jinghui Zhang, Yu Du, Qingxin Zhao, Jiale Lu, Taufeeq Ur Rehman Abbasi, Salamat Ullah, Weiqiu Chen
Abstract
This study presents a novel analytical framework for investigating the free vibration behavior of functionally graded plates (FGPs) subjected to complex boundary conditions (BCs), including rotationally restrained and free edges. Unlike conventional semi-analytical methods, which are limited in addressing such types of BCs, the proposed approach leverages integral transform theory to develop a unified and efficient solution procedure. By selecting an appropriate integral kernel, the free vibration problem is transformed into an eigenvalue problem of a simple matrix, enabling direct analytical solutions without requiring predefined deflection functions. The main advantage of this method is its ability to precisely satisfy both the governing partial differential equations and the associated boundary conditions, enhancing solution accuracy and computational efficiency. Rigorous validation is performed through numerical comparisons with finite element results from ABAQUS and existing analytical solutions, demonstrating excellent agreement and confirming the method’s reliability. Parametric studies underscore the significant influence of boundary conditions, aspect ratios, volume fraction exponent, and rotational restraints on the vibrational characteristics of FGPs. The findings provide critical benchmarks for the free vibration analysis of FGPs with rotationally-restrained supports, offering a valuable reference for future research in the field of advanced structural dynamics.