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首页> 外文期刊>International Journal of Mechanical Engineering Education >Applying eigenvalue perturbation theory to solve problems in structural dynamics
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Applying eigenvalue perturbation theory to solve problems in structural dynamics

机译：应用特征值摄动理论解决结构动力学问题

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In this paper the eigenvalue perturbation theory is applied to solve various problems in structural dynamics. Detailed derivations are presented along with examples to demonstrate the utility of the approach and its accuracy. In undergraduate classes on mechanical vibration, the eigenvalue perturbation theory is rarely taught, but it can be extremely valuable. The approach can be used to analyze the effects of design changes on the modes of vibration of a dynamical system, to determine the approximate eigensolutions of a nearly uniform continuous system, and to obtain the approximate complex eigencharacteristics of a lightly damped system. This paper shows that the eigenvalue perturbation theory can be easily introduced at the undergraduate level, because to understand the derivations only a first course in linear algebra is required, well within the capability of an undergraduate engineering student.
机译：本文采用特征值摄动理论来解决结构动力学中的各种问题。给出了详细的推导以及示例，以证明该方法的实用性及其准确性。在机械振动的本科课程中，很少讲授特征值微扰理论，但它可能非常有价值。该方法可用于分析设计变更对动力系统振动模式的影响，确定近似均匀连续系统的近似本征解，并获得轻阻尼系统的近似复杂本征特征。本文表明，本征值摄动理论可以轻松地在本科层次上引入，因为要理解这些推导，只需要线性代数的第一门课程，这在工程学本科生的能力范围内。

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