On the analysis of the tristable vibration isolation system with delayed feedback control under parametric excitation
On the analysis of the tristable vibration isolation system with delayed feedback control under parametric excitation
In this paper, the delayed feedback control of a tristable vibration isolation system (TVIS) under the stochastic parametric excitation is investigated. Firstly, theoretical solutions of the frequency response equation that governs the dynamical performance of the TVIS are derived. Meanwhile, the stability conditions are obtained. The controlled performance and response properties induced by the time delay, the feedback gains and the excitation amplitude are discussed. The existence of the time delay can considerably suppress the vibration amplitude. Particular phenomena induced by the time delay are observed. In addition, the first-order and second-order steady-state moments of the TVIS are obtained based on the Itô stochastic differential equations under the stochastic parametric excitation. The phenomenon of the time delay island about steady-state moments is found. The stationary probability density is discussed for the parametric resonance by means of the finite difference method. The variation of the noise bandwidth and the time delay can induce the transition of the stationary probability density between trivial solutions and non-trivial solutions. Overall, the response mechanism of the TVIS under the stochastic parametric excitation is revealed.
Nonlinearity, Physical mechanism, Theoretical solutions, Tristable
Huang, Dongmei
5ef3dac1-0e88-4700-9564-597a1b018afe
Zhou, Shengxi
c9ad9a91-4e40-47bb-909c-dcc41dfa4d20
Li, Ruihong
07d660ce-55ad-42a6-bf8a-98ed9e4588d0
Yurchenko, Daniil
51a2896b-281e-4977-bb72-5f96e891fbf8
16 July 2021
Huang, Dongmei
5ef3dac1-0e88-4700-9564-597a1b018afe
Zhou, Shengxi
c9ad9a91-4e40-47bb-909c-dcc41dfa4d20
Li, Ruihong
07d660ce-55ad-42a6-bf8a-98ed9e4588d0
Yurchenko, Daniil
51a2896b-281e-4977-bb72-5f96e891fbf8
Huang, Dongmei, Zhou, Shengxi, Li, Ruihong and Yurchenko, Daniil
(2021)
On the analysis of the tristable vibration isolation system with delayed feedback control under parametric excitation.
Mechanical Systems and Signal Processing, 164, [108207].
(doi:10.1016/j.ymssp.2021.108207).
Abstract
In this paper, the delayed feedback control of a tristable vibration isolation system (TVIS) under the stochastic parametric excitation is investigated. Firstly, theoretical solutions of the frequency response equation that governs the dynamical performance of the TVIS are derived. Meanwhile, the stability conditions are obtained. The controlled performance and response properties induced by the time delay, the feedback gains and the excitation amplitude are discussed. The existence of the time delay can considerably suppress the vibration amplitude. Particular phenomena induced by the time delay are observed. In addition, the first-order and second-order steady-state moments of the TVIS are obtained based on the Itô stochastic differential equations under the stochastic parametric excitation. The phenomenon of the time delay island about steady-state moments is found. The stationary probability density is discussed for the parametric resonance by means of the finite difference method. The variation of the noise bandwidth and the time delay can induce the transition of the stationary probability density between trivial solutions and non-trivial solutions. Overall, the response mechanism of the TVIS under the stochastic parametric excitation is revealed.
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Accepted/In Press date: 3 July 2021
e-pub ahead of print date: 16 July 2021
Published date: 16 July 2021
Additional Information:
Funding Information:
This work was supported by the National Natural Science Foundation of China (Grant nos. 11802237, 12072267, 12111530105), the Fundamental Research Funds for the Central Universities (No. JB210703), Young Talent Fund of University Association for Science and Technology in Shaanxi, China (No. 20200503), Bilateral governmental personnel exchange project between China and Slovenia for the years 2021-2023 (No. 12), the National Natural Science Foundation of Shaanxi Province (No. 2018JQ1055).
Publisher Copyright:
© 2021 Elsevier Ltd
Keywords:
Nonlinearity, Physical mechanism, Theoretical solutions, Tristable
Identifiers
Local EPrints ID: 468187
URI: http://eprints.soton.ac.uk/id/eprint/468187
ISSN: 0888-3270
PURE UUID: 21852a2e-64dd-4829-b557-54687f4a5cbc
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Date deposited: 04 Aug 2022 16:51
Last modified: 17 Mar 2024 04:11
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Contributors
Author:
Dongmei Huang
Author:
Shengxi Zhou
Author:
Ruihong Li
Author:
Daniil Yurchenko
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