The Bending,Vibration And Buckling Of Rectangular Orthotropic Thin Plates

In this paper, using double Fourier Series, the bending ,vibration and buckling of rectangular orthotropic thin plates with different boundary conditions are analyzed.In order to solve this problem, Sine Series of a quarter of a cycle is used to reduce the governing differential equations to a series of algebraic equations. In the process, the symmetry principle and the superposition theory are used, and the method of double Fourier Series is generalized to deal with problems concerning free edges, therefore it becomes possible to use double Fourier Series to solve the problems of bending, buckling and free vibration of rectangular plates with different boundary conditions. Finally, the operation of equations is completed by computer, and the exact solutions are gained.Because of using double Fourier Series, the development of equations is very simple, the results have the advantages of uniform mathematic expression and it is easy to calculate using computer. According to the formulas and the superposition theory, author compiles programs using MATLAB. It greatly improves efficiency and precision of operation, makes up the disadvantage of slower astringency of double Fourier Series and makes double Fourier Series achieve sufficient precision. The examples in this paper are worked out by using MATLAB, and some distortion figures in different conditions are given. It is easy to contrast and check.The theories and the results in this paper enrich the flat plate theory. Also it is helpful and practical for the design and construction of all sort of rectangular orthotropic thin plates.