Collapse of the Keldysh Chains and Stability of Continuous Nonconservative Systems
Collapse of the Keldysh Chains and Stability of Continuous Nonconservative Systems
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凯尔迪什链的崩溃和连续非保守系统的稳定性
DOI：
10.1137/s0036139902414720
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
Oleg N. Kirillov
中科院分区：
文献类型：
--
作者：
A. P. Seyranian;Oleg N. Kirillov
本文研究了光滑依赖于真实的参数向量的非自伴线性微分算子的特征值问题。研究了参数空间中特征值沿沿着光滑曲线的分叉问题。研究了任意长度Keldysh链的重特征值问题。利用伴随本征值问题的本征函数和伴随函数以及微分算子在参数空间初始点的导数，得到了描述本征值分支的显式表达式.这些结果对非保守系统的稳定性问题和灵敏度分析具有重要意义。作为一个力学应用，考虑并详细讨论了受部分切向随动力作用的弹性柱稳定性的扩展Beck问题。
In the present paper, eigenvalue problems for non-self-adjoint linear differential operators smoothly dependent on a vector of real parameters are considered. Bifurcation of eigenvalues along smooth curves in the parameter space is studied. The case of a multiple eigenvalue with the Keldysh chain of arbitrary length is investigated. Explicit expressions describing bifurcation of eigenvalues are found. The obtained formulas use eigenfunctions and associated functions of the adjoint eigenvalue problems as well as the derivatives of the differential operator taken at the initial point of the parameter space. These results are important for the stability problems and sensitivity analysis of nonconservative systems. As a mechanical application, the extended Beck problem of stability of an elastic column subjected to a partially tangential follower force is considered and discussed in detail.