Ｏｎ Ｆｒｅｅ ｖｉｂｒａｔｉｏｎ ｏｆ ａ Ｒｅｃｔａｎｇｕｌａｒ Ｐｌａｔｅ ｂｙ Ｔｈｒｅｅ,Ｓｔｒｅｓｓ Ｅｑｕａｔｉｏｎ

摘要

The free vibration of a rectangular plate， especially with all edges free or clamped，has already been studied，because this is a very interesting characteristic value problem in the theory of elastity. A quite different method from previous studies is described in this paper. A plate is imagined to be divided into some numbers of strips (Finite Strip Method)，and the deflection w_r and M_r＝一Nd^2w/dy^2)_r on the nodal line r are regarded as unknown values.　Then the equilibrium equation of the shearing force and the continuity equation of the slope (three-stress equation)on r are corresponding to w_r，M_r，and the frequency equation can be obtained assuming that the inertia force acts on every node as a line load.　The number of strips n and terms m which comes from Finite Fourier Transforms have influence on the accuracy of the quantity of natural frequency. Numerical results are as follows ； we sdould take ，n≧4 in case of all edges simply supported rectangular plate in order to decrease error in less than 5％，n≧5 in case of the plate with two opposite edges simply supported and the other two clamped。n≧4 and ，m≧6 in sase of all edges clamped square plate.　The rectangular plate with stepwise varying thickness　in one　direction and equithickness in another direction will also be treated by the same method for any boundary conditions.