Frequency split and vibration localization in imperfect rings
Frequency split and vibration localization in imperfect rings
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DOI：
10.1016/j.jsv.2007.06.027
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发表时间：
2007-10-09
影响因子：
4.7
通讯作者：
Caruso, Giovanni
中科院分区：
文献类型：
--
作者：
Bisegna, Paolo;Caruso, Giovanni
本文研究了线弹性、有缺陷圆环在其平面内振动的动力学问题。缺陷被建模为扰动，均匀的线性质量密度和弯曲刚度的一个完美的环。采用摄动展开和谱表示，得到了振动问题的变分形式，并在变分形式中只保留首阶项，得到了线性理论.线性理论产生简单的，封闭形式的本征频率和模态振型的表达式，这是准确的，当缺陷是足够小。本文还推导了一种改进的非线性理论，该理论即使在环缺陷不小的情况下也是精确的：在这种情况下，本文提出了一种迭代求解方法。通过考虑一些案例研究问题，并以Ritz-Rayleigh解为基准，对所提出的理论进行了验证。最后，将线性理论应用于缺陷环的频率修整问题。一个简单的，封闭形式的表达的修剪群众，有效的修剪任何选定的本征模的数量。(c)2007爱思唯尔有限公司保留所有权利。
The dynamics of linearly elastic, imperfect rings vibrating in their own plane is considered in this paper. Imperfections are modeled as perturbations of, the uniform linear mass density and bending stiffness of a perfect ring. A perturbation expansion and a spectral representation are employed, and a variational formulation of the vibration problem is obtained.A linear theory is deduced by retaining only the leading-order terms in the variational formulation. The linear theory yields simple, closed-form expressions for the eigenfrequencies and the modal shapes, which are accurate when the imperfections are sufficiently small. An enhanced, nonlinear theory is also derived, which is accurate even when the ring imperfections are not small: in this case, an iterative solution procedure is developed.The proposed theories are validated by considering some case-study problems and using the Ritz-Rayleigh solution as a benchmark.Finally, the linear theory is applied to the frequency trimming problem of an imperfect ring. A simple, closed-form expression for the trimming masses is presented, valid for trimming any selected number of eigenmodes. (c) 2007 Elsevier Ltd. All rights reserved.