期刊
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
卷 108, 期 -, 页码 126-139出版社
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ymssp.2018.01.038
关键词
Natural frequency assignment; Inverse eigenvalue problem; Pole placement; Passive vibration control; Inerter
资金
- National Natural Science Foundation of China [61603122, 61374053]
- Natural Science Foundation of Jiangsu Province of China [BK20160873]
- Fundamental Research Funds for the Central Universities of China [2016B03814]
This paper studies the problem of natural frequency assignment for mass-chain systems with inerters. This is the problem to determine whether an arbitrary set of positive numbers may be assigned as the natural frequencies of a chain of n masses in which each element has fixed mass and is connected to its neighbour by a parallel combination of a spring and inerter. It is proved that mass-chain systems with inerters may have multiple natural frequencies, which is different from conventional mass-chain systems (without inerters) whose natural frequencies are always simple. It is shown that arbitrary assignment of natural frequencies including multiplicities is not possible with the choice of n inerters and n springs. In particular, it is shown that an eigenvalue of multiplicity m may occur only if n >= 2m - 1. However, it is proved that n - 1 inerters and n springs are necessary and sufficient to freely assign an arbitrary set of distinct positive numbers as the natural frequencies of an n-degree-of-freedom mass-chain system. (C) 2018 Published by Elsevier Ltd.
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