Hybrid method for vibration analysis of rectangular plates

This paper presents a semi-analytical approach for the dynamic analysis of rectangular plates. The mathematical model is developed using a hybrid combination of the finite element method and Sanders’ shell theory. The in-plane, membrane displacement components are modelled by bilinear polynomials and the out-of-plane, normal to mid-surface displacement component is modelled by an exponential function that represents a general form of the exact solution of the equations of motion. The displacement functions are obtained by exact solution of the equilibrium equations of the rectangular plates. The mass and stiffness matrices are then determined by exact analytical integration to establish the plate's dynamic equations. The effect of various geometrical parameters and boundary conditions on the dynamic responses of the rectangular plates has been explored in this work. The results are in satisfactory agreement with those of experiments and other theories.