A Finite Integral Transform-Based Generalized Eigenvalue Solution for Free Vibration of Anisotropic Rectangular Plates with Rotationally Restrained Edges

A generalized eigenvalue formulation is developed for the free vibration analysis of anisotropic rectangular plates with rotationally restrained edges using the finite integral transform method. For free vibration problems, casting the governing equations into a generalized eigenvalue problem is particularly advantageous because it enables the direct and systematic extraction of multiple natural frequencies and their associated mode shapes within a unified framework, while avoiding the need for assumed trial functions or solution searching near initial guesses. In the present study, a two-dimensional sine integral transform is introduced into the governing equation of anisotropic plates with bending-twisting coupling, and the mechanical description of rotationally restrained boundary conditions is incorporated simultaneously, thereby converting the original partial differential boundary value problem into a generalized eigenvalue problem. The corresponding analytical solution is then established through the finite integral transform framework. The accuracy and reliability of the proposed method are verified through comparisons with finite element results and published data. Based on the obtained analytical solution, the effects of boundary conditions, rotational stiffness coefficients, aspect ratio, and key stiffness components on the vibration characteristics of anisotropic rectangular plates are further examined. The present study provides an effective analytical framework for free vibration analysis of anisotropic plates with nonclassical rotational restraints and offers theoretical support for the dynamic design and optimization of advanced composite plate structures.