Free vibration analysis of rectangular plates with variable thickness and point supports

A discrete method is developed for analyzing the free vibration problem of rectangular plates with point supports. The fundamental differential equations involving Dirac's delta function are established for the bending problem of the plate with point supports. By transforming these differential equations into integral equations and using numerical integration, the solution of these equations is obtained and used as Green function to obtain the characteristic equation of the free vibration. The effects of the point support, the boundary condition, the variable thickness and aspect ratio on the frequencies are considered. By comparing the numerical results obtained by the present method with those previously published, the efficiency and accuracy of the present method are investigated.