计算圆板大振幅非线性振动频率的平均刚度法

本文用平均刚度法研究圆板大振幅非线性振动的频率问题，导出了相应的非线性广义特征值方程，构造了一种避免发散并能加速收敛的加权平均迭代法，计算结果与Ｋａｎｔｏｒｏｖｉｃｈ时间平均法的解十分吻合。

The stiffness-averaging method for calculating the fundamentalfrequency of finite amplitude non-linear vibratlon of a circular plates

It is of great value to study the frequencies of a circular plate for various boundary con-ditions.when the amplitude of vibration is of the same order of magnitude as the thicknessof the plate,the membrane effects of the middle plane must be considered and the motion e-quations of the plate are the dynamic von Karman equations,which are non-linear and cou-pled.At present,it's impossible to solve the equations with analytical methods,and the on-ly way is by the numerical approximate methods. Using three nodes element,this paper studles the finite amplitude non-linear vibrationof an isotropic circular plate with a concentric rigid mass. For the more,the stiffnessaver-aging method is presented to calculate the frequencies of the plate,the non-linear generalizedeigenproblem is obtained by means of the mathod and the fundamental freouencies of theplate are calcuiated.As some elements of the stiffness matrix have non-linear terms,whichdepend on the amplitude of the plate,iteration is necessary.And for avoiding divergence andaccelerating the convergence in iteration process,the weighted average iteration is given.The results obtained in this paper agree well with the solutions by using the Kantorovichtimeaveraging method.