ABSTRACT
Large amplitude vibrations of thin elastic plates of any shape under clamped edge boundary conditions is discussed, based on von Kármán governing equations. The conformal mapping is introduced to transform the domain into a unit circle. The deflection function is taken satisfying the prescribed boundary conditions. The stress function is solved taking only the first term of the mapping function. The Galerkin technique is used to solve the transformed differential equations for obtaining the second order nonlinear differential equation in terms of the unknown time function. This equation is then solved in terms of the Jacobian elliptic function. The nonlinear static case has been discussed in this connection for different plates. Frequency of nonlinear oscillations without loading term for plates of different shapes have been calculated both for immovable and movable edge conditions. From the comparative study of different results, it is observed that the first-term approximation of the mapping function yields fairly accurate results with less computational effort.
