We developed an approximate method for treating the transverse vibration of an orthotropic circular plate subjected to an arbitrary edge constraint. First a proper form of the transverse deflection function was chosen based on three considerations: both the boundary conditions at the edge and the geometrical conditions at the center are satisfied, and it would produce the correct linear angular frequencies for special cases. This function turns out to be dependent on the material constants through its expansion coefficients. The compatibility equation was subsequently solved and the constants of integration were determined by boundary conditions. We then employed the Galerkin procedure to obtain the equation of motion for the time function which is a Duffing equation as expected. By solving this equation two important relations were obtained; one connects the ratio of nonlinear period to linear period and the amplitude for the case of free vibration, and the other is one between the ratio of applied frequency to linear frequency and the amplitude for the case of forced vibration under a sinusoidal applied force. Application was made to a very important case: the partially clamped and partially simply supported edge.
