Free vibration analysis of orthotropic rectangular plates with variable thickness and general boundary conditions

A discrete method is developed for analyzing the free vibration problem of orthotropic rectangular plates with variable thickness. The Green function, which is obtained by transforming the differential equations into integral equations and using numerical integration, is used to establish the characteristic equation of the free vibration. The effects of the aspect ratios, boundary conditions, the variation of the thickness on the frequencies are considered. By comparing the numerical results obtained by the present method with the those previously published, the efficiency and accuracy of the present method are investigated. The frequency parameters are obtained for the orthotropic plates with general boundary conditions and variable thickness in one or two directions. The model shapes are given for some of the square plates with three kinds of thickness variations.