Synthesis of n ‐port resistive networks containing 2n terminals

Journal of Sound and Vibration

Shu

et al. 2015

185

This paper is concerned with the problem of analysis and optimisation of the inerter-based isolators based on a "uni-axial" single-degree-of-freedom isolation system. In the first part, in order to gain an in-depth understanding of inerter from the prospective of vibration, the frequency responses of both parallel-connected and series-connected inerters are analysed. In the second part, three other inerter-based isolators are introduced and the tuning procedures in both the H ∞ optimisation and the H 2 optimisation are proposed in an analytical manner. The achieved H 2 and H ∞ performance of the inerter-based isolators is superior to that achieved by the traditional dynamic vibration absorber (DVA) when the same inertance-tomass (or mass) ratio is considered. Moreover, the inerter-based isolators have two unique properties, which are more attractive than the traditional DVA: first, the inertance-to-mass ratio of the inerter-based isolators can easily be larger than the mass ratio of the traditional DVA without increasing the physical mass of the whole system; second, there is no need to mount an additional mass on the object to be isolated.

Section: Introductionmentioning

confidence: 99%

Analysis and optimisation for inerter-based isolators via fixed-point theory and algebraic solution

Journal of Sound and Vibration

Shu

et al. 2015

185

“…Considering that would contradict the assumption that the condition of Theorem 2 does not hold, it follows that together with the condition of paramountcy. Since yields (16), it follows that . As a consequence, the values of elements as expressed in (11)-(15) must be positive and finite.…”

Section: Appendix a Proof Of Theoremmentioning

confidence: 95%

“…When , although the realizability of admittances as -port resistive networks containing terminals has been solved [2], [5], [6], [22], how to obtain a testable realizability condition for the realizability of general -port resistive networks is still an open problem (see [18]). Recently, Chen et al [16] obtained some new results on the realizability of -port resistive networks containing terminals. Moreover, unlike the synthesis of one-port networks, minimal realizations of -port resistive networks in terms of the total number of elements have seldom been discussed, which, however, has important practical implications.…”

Section: Introductionmentioning

confidence: 99%

Minimal Realizations of Three-Port Resistive Networks

Wang

IEEE Trans. Circuits Syst. I

2015

Self Cite

This paper is concerned with the minimal realization problem of a third-order real symmetric matrix as the admittance of three-port resistive networks. First, a necessary and sufficient condition is derived for a real symmetric matrix to be realizable as the admittance of three-port resistive networks with four terminals and at most elements, where . Since it is well-known that the matrix must be paramount, necessary and sufficient conditions are obtained for any paramount matrix to be realizable as the admittance of three-port resistive networks with at most elements, where . Moreover, a necessary and sufficient condition is derived for a paramount matrix that cannot be realized with less than five elements to be realizable as the admittance of three-port resistive networks with five elements. Finally, some numerical examples are presented to illustrate the results. The results of this paper can contribute to solving minimal realization problems of one-port and multi-port transformerless networks with more than one kind of elements.Index Terms-Paramountcy, passive network synthesis, threeport resistive networks.

“…Since the initial application in Formula One racing car suspension systems [2], inerters have been applied to various mechanical systems including vehicle suspensions [3][4][5][6][7][8][9], motorcycle steering systems [10], building vibration control [11] and train suspensions [12,13]. The interest in passive network synthesis has also been rekindled [14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis for isolation system with inerter

Proceedings of the 33rd Chinese Control Conference

Shu

et al. 2014

Self Cite

Fundamental analysis of vibration system with inerter is carried out in this paper based on a "uni-axial" singledegree-of-freedom isolation system. The condition that force and displacement transmissibilities are identical is derived for all passive isolators composed of springs, dampers and inerters. Specifically, the inerter in parallel connection and the one in series connection are analyzed in terms of the invariant points and isolating bandwidth of the considered transmissibilities. It is analytically demonstrated that both the parallel-connected and the series-connected inerters can effectively lower the invariant points and enlarge the isolating bandwidth. It is also shown that the series-connected inerter can depict some mixed-behaviours between the configuration with only a spring and the configuration with a parallel connection of a spring and an inerter, due to its inherent property of the physical structure. The weakness of isolation at high frequency caused by inerter is also analytically demonstrated.