A NEW ANALYTICAL SOLUTION TO FREE TRANSVERSE VIBRATIONOF CIRCULAR PLATES WITH CONCENTRIC ELASTIC RING SUPPORTS

This paper studies the problem of free transverse vibration of circular plates with an arbitrary number of the concentric elastic ring supports, a new analytical solution is presented. The analytical solution of dynamic response of the circular plate is obtained by regarding the reaction forces of the elastic ring supports as the unknown external forces acted on the plate. The integral constants of the solution are decided by the boundary conditions of the plate. The reaction forces of elastic ring supports are decided by the linear relationship of the reaction forces and the displacements at supports. The frequency equation is described by a determinant whose order is equal to the number of the elastic ring supports. The eigen-frequencies can be given by the searching root method of determinant. The mode shape functions are described by an analytical representation. Finally, an example is given and the numerical results are compareed with those obtained.