Vertical Vibration Control of Nonlinear Viscoelastic Isolation Systems With Time Delay Feedback

WANG Daohang; SUN Bo; LIU Chunxia; ZHOU Ziyi; LIU Yu

doi:10.21656/1000-0887.450037

Volume 46 Issue 2

Feb. 2025

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Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(2): 199-207

WANG Daohang, SUN Bo, LIU Chunxia, ZHOU Ziyi, LIU Yu. Vertical Vibration Control of Nonlinear Viscoelastic Isolation Systems With Time Delay Feedback[J]. Applied Mathematics and Mechanics, 2025, 46(2): 199-207. doi: 10.21656/1000-0887.450037

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Vertical Vibration Control of Nonlinear Viscoelastic Isolation Systems With Time Delay Feedback

doi: 10.21656/1000-0887.450037

WANG Daohang^1
,,
SUN Bo¹,
LIU Chunxia^{2
,
,},
ZHOU Ziyi¹,
LIU Yu¹

1.
Faculty of Public Security and Emergency Management, Kunming University of Science and Technology, Kunming 650000, P.R.China
2.
Department of Mathematics, School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650000, P.R.China

Received Date: 2024-02-22
Rev Recd Date: 2024-05-10
Publish Date: 2025-02-01

Abstract

Abstract

The vertical vibration control of nonlinear viscoelastic vibration isolation systems with time delay feedback was studied. Based on the viscoelastic nonlinear Zener model, a time delay controller was introduced to establish the mathematical model for time delay feedback viscoelastic vibration isolation system. The approximate analytical solution under the condition of primary resonance was obtained with the multiscale method. The stability conditions of the system were obtained based on the Routh-Hurwitz theory. Finally, the correlation between the time delay parameters and the vibration behavior of the viscoelastic vibration isolation system was analyzed. The results show that, the time delay controller can effectively control the unstable behaviors and vibration amplitudes of the viscoelastic vertical vibration system, and the time delay parameters can be used as independent variables to regulate the vibration characteristics of the system. The work provides a theoretical guidance for the application of time delay control to improve the vertical vibration stability of viscoelastic vibration isolation systems.
- viscoelastic isolator,
- nonlinear vibration,
- time delay feedback control,
- Zener model,
- multiscale method,
- stability

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致谢: 本文作者衷心感谢云南财经大学引进人才项目(2023D41)和昆明理工大学自然科学研究基金(人培项目)(241120230015)对本文的资助.

References(22)

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