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Natural frequency assignment for mass-chain systems with inerters

机译：具有惰性器的质量链系统的固有频率分配

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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 ofnmasses 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 ofninerters andnsprings. In particular, it is shown that an eigenvalue of multiplicitymmay occur only ifn⩾2m-1. However, it is proved thatn-1inerters andnsprings are necessary and sufficient to freely assign an arbitrary set ofdistinctpositive numbers as the natural frequencies of ann-degree-of-freedom mass-chain system.
机译：本文研究了具有惰性的质量链系统的固有频率分配问题。这是确定是否可以将任意一组正数分配为纳米矩阵链的固有频率的问题，在纳米矩阵链中，每个元素的质量均固定，并通过弹簧和惯性的平行组合与其相邻元素连接。事实证明，具有惰性的质量链系统可能具有多个固有频率，这与固有频率总是简单的常规质量链系统（无惰性）不同。结果表明，选择斜度和弹簧不可能随意分配包括多重性的固有频率。特别地，表明仅当n⩾2m-1时才出现多重性的特征值。然而，事实证明，n-1个惰性物和n个弹簧对于自由地分配任意一组离散的正数作为n自由度质量链系统的固有频率是必要和充分的。

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