Vibrations of elastically restrained rectangular plates

摘要

In this study, an approximation method based on Fourier sine series were investigated for the vibration analysis of rectangular plates elastically restrained along all the edges. The transverse displacement of the elastic supported plate consisted of linear combination of Fourier sine series and an auxiliary polynomial function. In order to eliminate possible discontinuities; an auxiliary polynomial was used in Fourier solution function. For that, a displacement solution function that could be derived at least three times was adopted by letting series function to satisfy the governing differential equation for all the boundary conditions at every point. All the unknown Fourier expansion coefficients and natural frequencies of the plate were determined by employing the Galerkin discretization procedure. Unlike the existing techniques, the proposed method does not require a very tedious solution process, potential difficulties or non-linear hyperbolic functions. In the all performed calculations, the Kirchhoff plate theory, which is also called the classical plate theory, was employed. Several numerical examples were presented to demonstrate the accuracy and convergence of the current solutions.