| 应祖光,陈昭晖,倪一清,高赞明.多自由度参激系统稳定性的数值分析[J].计算力学学报,2007,24(5):678~682 |
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| 多自由度参激系统稳定性的数值分析 |
| Numerical analysis of the parametrically excited stability of multi-degree-of-freedom systems |
| 修订日期：2005-07-14 |
| DOI：10.7511/jslx20075133 |
| 中文关键词: 参激稳定性,多自由度系统,数值直接法,特征值 |
| 英文关键词:parametrically excited stability,multi-degree-of-freedom system,direct numerical method,eigenvalue |
| 基金项目:浙江省自然科学基金(101046)，香港RGC(PolyU5051/02E)资助项目 |
| 应祖光 陈昭晖 倪一清 高赞明 |
浙江大学力学系 浙江杭州310027(应祖光，陈昭晖)
，香港理工大学土木及结构工程系 香港九龙(倪一清，高赞明)
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| 摘要点击次数: 1417 |
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| 中文摘要: |
| 提出多自由度周期参激系统稳定性的数值直接法。通过将扰动方程表示成状态方程形式,再根据Flo-quet理论将扰动解表示成指数特征分量与周期分量之积,并将其周期分量与系统周期系数展成Fourier级数,导出一系列代数方程,建立矩阵特征值问题,从而由数值求解特征值可直接确定参激系统的稳定性。该方法可用于一般周期参激阻尼系统,特征值矩阵不含逆子阵。应用于斜拉索在支座周期运动激励下的参激振动不稳定性分析,数值结果表明该方法的有效性。 |
| 英文摘要: |
| A direct numerical method for the stability of multidegree-of-freedom systems with period parameters was proposed.The perturbation equation of a parametrically excited system is first rewritten in the form of state equation.The perturbation solution is expressed as the product of exponential characteristic component and periodic component according to the Floquet theory.The periodic component and periodic system parameters are further expanded into the Fourier series.Then a series of algebraic equations are derived and the matrix eigenvalue problem is established.The stability of the parametrically excited system can be determined directly by using the eigenvalues solved numerically.The proposed method is applicable to damped systems with general period-parameter excitation and the final eigenvalue matrix has not any inverse sub-matrix.Also it is applied to the parametrically excited instability analysis of an inclined stay cable under periodic support motion excitation.Numerical results illustrate the effectiveness of the proposed direct numerical method for parametrically excited stability. |
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