Abstract: Based on the nonlinear dynamic equilibrium equations for elastic plates, a coordinate transformation is carried out. The trapezoidal domain of plate is mapped onto a square domain. The governing equation and boundary conditions of the plate are transformed onto the square domain. An intermediate variable is introduced to reduce the order of governing equations, and some mathematical and physical relationships are employed to further simplify the boundary conditions. Applying Galerkin's procedure to the controlling equation of plate at the square domain results in a simple one-dimensional nonlinear dynamic equation in time domain. A parameter perturbation method is adopted for the study of geometrical nonlinear free vibration and dynamic response of trapezoidal plates.