Vibration of Circular Plates at Large Amplitudes

The vibration of circular plates when the amplitude is large is governed by nonlinear partial differential equations. An approximate formulation of these equations for the static case has previously been proposed by H. M. Berger. These equations are here extended to the dynamic case. A simplification in the statement of the problem is introduced by requiring that the in-plane displacement at the boundary of the plate vanish. A modified Galerkin procedure is then used for solving the resulting equations. It is shown that for both simply supported and clamped circular plates the vibration can be expressed in terms of elliptic functions. Numerical results are given for the calculation of frequencies and stresses. A method is suggested for solving forced vibration problems.