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

Turn off MathJax

Article Contents

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

Citation:

PDF( 4101 KB)

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

FullText(HTML)

References(22)

References

[1]	FAN R, MENG G, YANG J, et al. Experimental study of the effect of viscoelastic damping materials on noise and vibration reduction within railway vehicles[J]. Journal of Sound and Vibration, 2009, 319 (1/2): 58-76.
[2]	SOONG T T, DARGUSH G F. Passive Energy Dissipation Systems in Structural Engineering[M]. New Jersey: John Wiley and Ltd, 1997: 128-143.
[3]	FILHO F J, LUERSEN M A, BAVASTRI C A. Optimal design of viscoelastic vibration absorbers for rotating systems[J]. Journal of Vibration and Control, 2011, 17 (5): 699-710. doi: 10.1177/1077546310374335
[4]	周颖, 李锐, 吕西林. 粘弹性阻尼器性能试验研究及参数识别[J]. 结构工程师, 2013, 29 (1): 83-91. doi: 10.3969/j.issn.1005-0159.2013.01.013 ZHOU Ying, LI Rui, LV Xilin. Experimental study and parameter identification of viscoelastic dampers[J]. Structural Engineers, 2013, 29 (1): 83-91. (in Chinese) doi: 10.3969/j.issn.1005-0159.2013.01.013
[5]	MURESAN C I, DULF E H, PRODAN O. A fractional order controller for seismic mitigation of structures equipped with viscoelastic mass dampers[J]. Journal of Vibration and Control, 2016, 22 (8): 1980-1992. doi: 10.1177/1077546314557553
[6]	范舒铜, 申永军. 多尺度法的推广及在非线性黏弹性系统的应用[J]. 力学学报, 2022, 54 (2): 495-502. FAN Shutong, SHEN Yongjun. Extension of multi-scale method and its application to nonlinear viscoelastic system[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54 (2): 495-502. (in Chinese)
[7]	BRENNAN M J, CARRELLA A, WATERS T P, et al. On the dynamic behaviour of a mass supported by a parallel combination of a spring and an elastically connected damper[J]. Journal of Sound and Vibration, 2008, 309 (3/4/5): 823-837.
[8]	WANG X, YAO H X, ZHENG G T. Enhancing the isolation performance by a nonlinear secondary spring in the Zener model[J]. Nonlinear Dynamics, 2017, 87 (4): 2483-2495. doi: 10.1007/s11071-016-3205-3
[9]	SILVA L D H, GONALVES P J P, WAGG D. On the dynamic behavior of the Zener model with nonlinear stiffness for harmonic vibration isolation[J]. Mechanical Systems and Signal Processing, 2018, 112 : 343-358. doi: 10.1016/j.ymssp.2018.04.037
[10]	SHAHRAEENI M, SOROKIN V, MACE B, et al. Effect of damping nonlinearity on the dynamics and performance of a quasi-zero-stiffness vibration isolator[J]. Journal of Sound and Vibration, 2022, 526 : 116822. doi: 10.1016/j.jsv.2022.116822
[11]	LIU Y J, LEE S M. Synchronization criteria of chaotic Lur'e systems with delayed feedback PD control[J]. Neurocomputing, 2016, 189 : 66-71. doi: 10.1016/j.neucom.2015.12.058%yz%$10.3390/rs14194711
[12]	TSIOTRAS P. Further passivity results for the attitude control problem[J]. IEEE Transactions on Automatic Control, 1998, 43 (11): 1597-1600. doi: 10.1109/9.728877
[13]	LIU C X, YAN Y, WANG W Q, et al. Optimal time delayed control of the combination resonances of viscoelastic graphene sheets under dual-frequency excitation[J]. Chaos, Solitons & Fractals, 2022, 165 : 112856.
[14]	孙秀婷, 钱佳伟, 齐志凤, 等. 非线性隔振及时滞消振方法研究进展[J]. 力学进展, 2023, 53 (2): 308-356. SUN Xiuting, QIAN Jiawei, QI Zhifeng, et al. Review on research progress of nonlinear vibration isolation and time-delayed suppression method[J]. Advances in Mechanics, 2023, 53 (2): 308-356. (in Chinese)
[15]	赵艳影, 徐鉴. 时滞非线性动力吸振器的减振机理[J]. 力学学报, 2008, 40 (1): 98-106. doi: 10.3321/j.issn:0459-1879.2008.01.012 ZHAO Yanying, XU Jian. Mechanism analysis of delayed nonlinear vibration absorber[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40 (1): 98-106. (in Chinese) doi: 10.3321/j.issn:0459-1879.2008.01.012
[16]	SUN X T, WANG F, XU J. Dynamics and realization of a feedback-controlled nonlinear isolator with variable time delay[J]. Journal of Vibration and Acoustics, 2019, 141 (2): 021005. doi: 10.1115/1.4041369
[17]	胡宇达, 刘超. 线载和弹性支承作用面内运动薄板磁固耦合双重共振[J]. 应用数学和力学, 2021, 42 (7): 713-722. HU Yuda, LIU Chao. Double resonance of magnetism-solid coupling of in-plane moving thin plates with linear loads and elastic supports[J]. Applied Mathematics and Mechanics, 2021, 42 (7): 713-722. (in Chinese)
[18]	尚慧琳, 张涛, 永蓬. 参数激励驱动微陀螺系统的非线性振动特性研究[J]. 振动与冲击, 2017, 36 (1): 102-107. SHANG Huilin, ZHANG Tao, YONG Peng. Nonlinear vibration behaviors of a micro-gyroscope system actuated by a parametric excitation[J]. Journal of Vibration and Shock, 2017, 36 (1): 102-107. (in Chinese)
[19]	LIU C X, YAN Y, WANG W Q. Primary resonance analysis of a nano beam with axial load by nonlocal continuum theory under time delay control[J]. Applied Mathematical Modelling, 2020, 85 (2): 124-140.
[20]	JI J C, ZHANG N. Suppression of the primary resonance vibrations of a forced nonlinear system using a dynamic vibration absorber[J]. Journal of Sound and Vibration, 2010, 329 (11): 2044-2056. doi: 10.1016/j.jsv.2009.12.020
[21]	JI J C, LEUNG A Y T. Resonances of a non-linear s. d. o. f. system with two time-delays in linear feedback control[J]. Journal of Sound and Vibration, 2002, 253 (5): 985-1000. doi: 10.1006/jsvi.2001.3974
[22]	LI X Y, JI J C, HANSEN C H, et al. The response of a Duffing-Van der Pol oscillator under delayed feedback control[J]. Journal of Sound and Vibration, 2006, 291 (3/4/5): 644-655.