An improved Fourier series solution for free vibration analysis of the moderately thick laminated composite rectangular plate with non-uniform boundary conditions

Abstract

In this investigation, an improved Fourier series method is presented for the free vibration analysis of the moderately thick laminated composite rectangular plate with non-uniform boundary conditions, a class of problems which are rarely attempted in the literatures. Under the current framework, the displacement and rotation functions are generally sought, regardless of boundary conditions, in spectral form, as a double Fourier cosine series and three supplementary functions. These supplementary functions are introduced to remove the potential discontinuities associated with the original displacement functions along the edges when they are viewed as periodic functions defined within the entire coordinates of laminate plate. The boundary conditions can be readily realized by setting the stiffness of the five types restraining springs. All the series expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. Unlike most of the existing studies, the presented method can be readily and universally applied to a wide spectrum of plate vibration problems involving different boundary conditions, varying material, and geometric properties with no need of modifying the basic functions or adapting solution procedures. The excellent accuracy of the current result is validated by comparing the present results with those Finite Element Method (FEM) data. Numerous new results for free vibration of moderately thick rectangular plates with various multi-points supported and non-uniform partially supported boundary conditions are presented, which may serve as benchmark solution for future researches in the field.