Flexural Vibration of Free Square Plate Based on Method of Superposition and Comparison with Experimental Whole-Field Interferometry Vibration

The method of superposition is employed to analyze the symmetric and anti-symmetric free vibration modes of a square plate. It is shown that this method provides a simple, straightforward and highly accurate means of solution for this family of problems. Convergence to exact values is shown to be remarkably rapid. The symmetric and anti-symmetric model shapes for a square plate are accurately described by means of contour line drawings. The numerous advantages of this method over previously used methods are discussed. The most theorical solution to free vibration analysis of the completely free square plate is considered to be at best approximate in nature. This is because of the difficulties which have been encountered in trying to obtain solutions which satisfy the free edge conditions as well as the governing differential equation. In a new approach to this problem, by using the method of superposition, it is shown that solutions which satisfy identically the differential equation and which satisfy identically the differential equation and which satisfy the boundary conditions with any desired degree of accuracy are obtained. Also this paper presents a comparison between Taiwanian experimental results and theorical study of flexural symmetric and anti-symmetric vibration modes of a linear elastic plate based on superposition method. Our numerical experiments are compared with taiwanian experimental results and more modes are observed. Finally, it is resulted to more accurate realization and more mode frequency.