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Assignment of natural frequencies by an added mass and one or more springs

机译：通过增加质量和一个或多个弹簧来分配固有频率

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摘要

The problem of assigning natural frequencies to a multi-degree-of-freedom undamped system by an added mass connected by one or more springs is addressed. The added mass and stiffnesses are determined using receptances from the original system. The modifications required to assign a single natural frequency may be obtained by the non-unique solution of a polynomial equation. If more than one frequency is to be assigned, then a system of non-linear multivariate polynomial equations must be solved. Such a modification involves not only an added mass and one or more stiffness terms, but also an added coordinate. The paper presents a methodology, using Groebner bases for the solution of the multivariate polynomials, together with examples of natural frequency assignment. Realistic modifications are found to be bounded within certain frequency ranges. The effect of the modification on the natural frequencies not assigned and the antiresonances is explained.
机译：解决了通过由一个或多个弹簧连接的附加质量将自然频率分配给多自由度无阻尼系统的问题。使用原始系统的接受度确定增加的质量和刚度。可以通过多项式方程的非唯一解来获得分配单个固有频率所需的修改。如果要分配一个以上的频率，则必须求解非线性多元多项式方程组。这种修改不仅涉及增加的质量和一个或多个刚度项，还涉及增加的坐标。本文介绍了一种使用Groebner基求解多元多项式的方法，并给出了自然频率分配的示例。发现现实的修改被限制在某些频率范围内。解释了修改对未分配的固有频率和反谐振的影响。

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