Free vibration analysis of the moderately thick laminated composite rectangular plate with multi-points supported boundary conditions

摘要

In this investigation, an improved Fourier series method is presented for the free vibration analysis of the moderately thick laminated composite rectangular plate with multi-points supported boundary conditions. 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. 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 applied to a wide spectrum of plate vibration problems with no need of modifying the basic functions or adapting solution procedures, such as different boundary conditions, varying material, and geometric properties. The excellent accuracy of the current result is validated by comparing the present results with those Finite Element Method (FEM) data. Numerous new results are also presented for free vibration of moderately thick rectangular plates with various multi-points supported boundary conditions.