Hu, Y and Chen, MZQ and Smith, MC (2018) *Natural frequency assignment for mass-chain systems with inerters.* Mechanical Systems and Signal Processing, 108. pp. 126-139. ISSN 0888-3270

## Abstract

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.

Item Type: | Article |
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Subjects: | UNSPECIFIED |

Divisions: | Div F > Control |

Depositing User: | Cron Job |

Date Deposited: | 03 Feb 2018 20:11 |

Last Modified: | 09 Sep 2021 00:56 |

DOI: | 10.1016/j.ymssp.2018.01.038 |