| 任宝生,陈殿云,张以忠.计算圆板大振幅非线性振动频率的平均刚度法[J].计算力学学报,1995,12(2): |
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| 计算圆板大振幅非线性振动频率的平均刚度法 |
| The stiffness-averaging method for calculating the fundamentalfrequency of finite amplitude non-linear vibratlon of a circular plates |
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| DOI：10.7511/jslx19952025 |
| 中文关键词: 非线性振动 刚度 迭代／圆板 |
| 英文关键词:non-linear vibration,stiffness,iteration/circular plate, |
| 基金项目: |
| 任宝生 陈殿云 张以忠 |
| 西安交通大学，洛阳工学院，西安交通大学 |
| 摘要点击次数: 1560 |
| 全文下载次数: 1 |
| 中文摘要: |
| 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。 |
| 英文摘要: |
| 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. |
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