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力学与实践 ›› 2005, Vol. 27 ›› Issue (5): 0-0.doi: 10.6052/1000-0992-2004-473

• 应用研究 •    

挠性根部梁的动力学建模

肖世富 陈滨   

  1. 四川绵阳中国工程物理研究院结构力学研究所 北京大学力学与工程科学系,100871
  • 收稿日期:2004-12-13 修回日期:1900-01-01 出版日期:2005-10-10 发布日期:2005-10-10

DYNAMIC MODELING OF BEAMS WITH FLEXIBLE SUPPORT

  • Received:2004-12-13 Revised:1900-01-01 Online:2005-10-10 Published:2005-10-10

摘要: 挠性根部梁具有整体平动和转动自由度,其传统模型只适宜根部 挠性很小的梁. 采用柔性多体系统的建模方法建立了挠性根部Euler-Bernoulli梁的非 线性动力学模型及线性耦合模型,所建模型不受根部挠性大小的限制;既可描述挠性根部梁 的耦合振动,也可分别退化为固支梁或刚性梁的动力学模型;且线性耦合模型可线性变换为 挠性根部梁传统模型. 作为算例,采用假设模态法分析了两类线性模型的振动特性,表明线 性耦合模型优于挠性根部梁传统模型.

关键词: 柔性多体系统,挠性根部,Euler-Bernoulli, 梁,Hamilton变分原理,

Abstract: The beams with flexible support have translational and rotational degrees of freedom. The classical model of the beams with flexible support can be adopted only when the flexibility of the support is very small. In the present work, the nonlinear and linear coupling dynamic models of the Euler-Bernoulli's beam with flexible support are established by employing the modeling method of flexible multi-body systems. The models are applicable to the beams with any flexible support and can describe the coupling vibration of the bending of the beam and the overall motions due to the flexibility of the support. Furthermore, the models can be simplified as the dynamic models of the cantilever beam and the rigid beam, and the bending vibration equation of the linear coupling model can be linearly transformed as that of the classic linear model of the beams with flexible support. As an example, vibration frequencies of two linear models are calculated by employing Assumed Modes Method. The results indicate that the linear coupling model is better than the classical model for beams with flexible support.

Key words: flexible multi-body systems, flexible support,