0
Research Papers

Dynamics and Realization of a Feedback-Controlled Nonlinear Isolator With Variable Time Delay

[+] Author and Article Information
Xiuting Sun

School of Mechanical Engineering,
University of Shanghai for Science and
Technology,
516 JunGong Road,
Shanghai 200093, China
e-mail: sunxiuting@usst.edu.cn

Feng Wang

School of Aerospace Engineering and
Applied Mechanics,
Tongji University,
1239 Siping Road,
Shanghai 200092, China
e-mail: 15wangfeng@tongji.edu.cn

Jian Xu

School of Aerospace Engineering and
Applied Mechanics,
Tongji University,
1239 Siping Road,
Shanghai 200092, China
e-mail: xujian@tongji.edu.cn

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 19, 2018; final manuscript received August 28, 2018; published online October 23, 2018. Assoc. Editor: Stefano Lenci.

J. Vib. Acoust 141(2), 021005 (Oct 23, 2018) (13 pages) Paper No: VIB-18-1272; doi: 10.1115/1.4041369 History: Received June 19, 2018; Revised August 28, 2018

In this paper, time-delayed feedback (TD-FB) control is introduced for a nonlinear vibration isolator (NL-VI), and the isolation effectiveness features are investigated theoretically and experimentally. In the feedback control loop, compound control with constant and variable time delays is considered. First, a stability analysis is conducted to determine the range of control parameters for stable zero equilibrium without excitation. Next, the nonlinear resonance frequency and the nonlinear vibration attenuation are studied by the method of multiple scales (MMS) to demonstrate the mechanism of TD-FB control. The results of the nonlinear vibration performances show that large variable time delays can improve the vibration suppression. Additionally, the mechanism for the time delay is not only to tune the equivalent stiffness and damping but also to induce effective isolation bandgap at high frequency. Therefore, the variable time delay is assumed as the function of frequency to meet different requirements at different frequency bands. The relevant experiment verifies the improvement of designed variable time delay on isolation performances in different frequency bands. Due to the improvement of isolation performances by compound time delay feedback control on nonlinear systems, it can be applied in the fields of ships, flexible structure in aerospace and aviation.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Ibrahim, R. A. , 2008, “ Recent Advances in Nonlinear Passive Vibration Isolators,” J. Sound Vib., 314(3–5), pp. 371–452. [CrossRef]
Lee, C. M. , Goverdovskiy, V. N. , and Temnikov, A. I. , 2007, “ Design of Springs With Negative Stiffness to Improve Vehicle Driver Vibration Isolation,” J. Sound Vib., 302(4–5), pp. 865–874. [CrossRef]
Huang, X. , Liu, X. , Sun, J. , Zhang, Z. , and Hua, H. , 2014, “ Vibration Isolation Characteristics of a Nonlinear Isolator Using Euler Buckled Beam as Negative Stiffness Corrector: A Theoretical and Experimental Study,” J. Sound Vib., 333(4), pp. 1132–1148. [CrossRef]
Zheng, Y. , Zhang, X. , Luo, Y. , Yan, B. , and Ma, C. , 2016, “ Design and Experiment of a High-Static-Low-Dynamic Stiffness Isolator Using a Negative Stiffness Magnetic Spring,” J. Sound Vib., 360, pp. 31–52. [CrossRef]
Sun, X. T. , and Jing, X. J. , 2015, “ Multi-Direction Vibration Isolation With Quasi-Zero Stiffness by Employing Geometrical Nonlinearity,” Mech. Syst. Signal Process., 62–63, pp. 149–163. [CrossRef]
Zhou, J. X. , Wang, X. , Xu, D. L. , and Bishop, S. , 2015, “ Nonlinear Dynamic Characteristics of a Quasi-Zero Stiffness Vibration Isolator With Cam–Roller–Spring Mechanisms,” J. Sound Vib., 346(1), pp. 53–69. [CrossRef]
Carrella, A. , Brennan, M. J. , Waters, T. P. , and Lopes , V., Jr , 2012, “ Force and Displacement Transmissibility of a Nonlinear Isolator With High-Static-Low-Dynamic-Stiffness,” Int. J. Mech. Sci., 55(1), pp. 22–29. [CrossRef]
Fu, J. , Li, P. , Liao, G. , Lai, J. , and Yu, M. , 2016, “ Development and Dynamic Characterization of a Mixed Mode Magnetorheological Elastomer Isolator,” IEEE Trans. Magn., 53(1), pp. 1–4. [CrossRef]
Hao, Z. F. , Cao, Q. J. , and Wiercigroch, M. , 2016, “ Two-Sided Damping Constraint Control Strategy for High-Performance Vibration Isolation and End-Stop Impact Protection,” Nonlinear Dyn., 86(4), pp. 1–16. [CrossRef]
Andreaus, U. , Baragatti, P. , Angelis, M. D. , and Perno, S. , 2017, “ Shaking Table Tests and Numerical Investigation of Two-Sided Damping Constraint for End-Stop Impact Protection,” Nonlinear Dyn., 90(4), pp. 1–35. [CrossRef]
Hao, Z. F. , Cao, Q. J. , and Wiercigroch, M. , 2017, “ Nonlinear Dynamics of the Quasi-Zero-Stiffness SD Oscillator Based Upon the Local and Global Bifurcation Analyses,” Nonlinear Dyn., 87(2), pp. 1–28. [CrossRef]
Han, N. , and Cao, Q. J. , 2017, “ A Parametrically Excited Pendulum With Irrational Nonlinearity,” Int. J. Nonlinear Mech., 88, pp. 122–134. [CrossRef]
Vyhlídal, T. , Anderle, M. , Bušek, J. , and Niculescu, S. I. , 2017, “ Time Delay Algorithms for Damping Oscillations of Suspended Payload by Adjusting the Cable Length,” IEEE/ASME Trans. Mechatronics, 22(5), pp. 2319–2328. [CrossRef]
Anubi, M. , and Crane, C. , 2014, “ A New Semiactive Variable Stiffness Suspension System Using Combined Skyhook and Nonlinear Energy Sink-Based Controllers,” IEEE Trans. Control Syst. Technol., 23(3), pp. 937–947. [CrossRef]
Chen, M. Z. Q. , Hu, Y. , Li, C. , and Chen, G. , 2014, “ Performance Benefits of Using Inerter in Semiactive Suspensions,” IEEE Trans. Control Syst. Technol., 23(4), pp. 1571–1577. [CrossRef]
Casciati, F. , Rodellar, J. , and Yildirim, U. , 2012, “ Active and Semi-Active Control of Structures-Theory and Applications: A Review of Recent Advances,” J. Intell. Mater. Syst. Struct., 23(11), pp. 1181–1195. [CrossRef]
Roy, S. , Kar, I. N. , and Lee, J. , 2017, “ Toward Position-Only Time-Delayed Control for Uncertain Euler–Lagrange Systems: Experiments on Wheeled Mobile Robots,” IEEE Rob. Autom. Lett., 2(4), pp. 1925–1932. [CrossRef]
Lee, J. , Chang, P. H. , and Jin, M. , 2017, “ Adaptive Integral Sliding Mode Control With Time-Delay Estimation for Robot Manipulators,” IEEE Trans. Ind. Electron., 64(8), pp. 6796–6804. [CrossRef]
Olgac, N. , and Jalili, N. , 1998, “ Modal Analysis of Flexible Beams With Delayed Resonator Vibration Absorber: Theory and Experiments,” J. Sound Vib., 218(2), pp. 307–331. [CrossRef]
Xu, J. , and Sun, Y. X. , 2015, “ Experimental Studies on Active Control of a Dynamic System Via a Time-Delayed Absorber,” Acta Mech. Sin., 31(2), pp. 229–247. [CrossRef]
Xu, Q. , Stepan, G. , and Wang, Z. H. , 2016, “ Delay-Dependent Stability Analysis by Using Delay-Independent Integral Evaluation,” Automatica, 70, pp. 153–157. [CrossRef]
Ramachandran, P. , and Ram, Y. M. , 2012, “ Stability Boundaries of Mechanical Controlled System With Time Delay,” Mech. Syst. Signal Process., 27(1), pp. 523–533. [CrossRef]
Zhang, X. X. , Xu, J. , and Ji, J. C. , 2018, “ Modelling and Tuning for a Time-Delayed Vibration Absorber With Friction,” J. Sound Vib., 424, pp. 137–157. [CrossRef]
Zhang, X. X. , and Xu, J. , 2015, “ Identification of Time Delay in Nonlinear Systems With Delayed Feedback Control,” J. Franklin Inst., 352(8), pp. 2987–2998. [CrossRef]
Sun, Y. X. , and Xu, J. , 2015, “ Experiments and Analysis for a Controlled Mechanical Absorber Considering Delay Effect,” J. Sound Vib., 339, pp. 25–37. [CrossRef]
Zhou, J. X. , Xu, D. L. , and Li, Y. L. , 2011, “ An Active-Passive Nonlinear Vibration Isolation Method Based on Optimal Time-Delay Feedback Control,” J. Vib. Eng., 24(9–10), pp. 639–645.
Sun, X. T. , Xu, J. , Jing, X. J. , and Cheng, L. , 2014, “ Beneficial Performance of a Quasi-Zero-Stiffness Vibration Isolator With Time-Delayed Active Control,” Int. J. Mech. Sci., 82(1), pp. 32–40. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

(a) The mechanical model of time-delayed NL-VI and (b) feedback control loop with inherent time delay τ1 and artificial variable time delay τ2

Grahic Jump Location
Fig. 2

The boundary for the stability of equilibrium on the parametrical plane (τk2, g2) of τk1=0.1 for (a) g1 = −0.2, (b) g1 = –0.1, (c) g1 = 0.0, (d) g1 = 0.1, and (e) g1 = 0.2; the boundary of g1 = 0.05 for (f) τk1 = 0.2, (g) τk1 = 0.4, (h) τk1 = 0.6, (i) τk1 = 0.8, and (j) τk1=1.0

Grahic Jump Location
Fig. 3

For increasing τk2, the maximum attenuation rate for (a) g1 = −0.05 and (b) g1 = 0.05; the values of all resonance frequencies for (c) g1 = −0.05 and (d) g1 = 0.05

Grahic Jump Location
Fig. 4

The two maximum values of ξn (first curve for the largest value and second for the second largest one) for different τk2 of (a) g2 = 0.05, (c) g2 = 0.15, and (e) g2 = 0.3; the designed function of adjustable time delay τk2 for different values of frequency Ω for (b) g2 = 0.05, (d) g2 = 0.15, and (f) g2 = 0.3

Grahic Jump Location
Fig. 5

The vibration attenuation coefficient ξn and the variation of the designed variable time delay τk2(Ω) for (a) g2 = 0.05, (b) g2 = 0.2, and (c) g2 = 0.4; comparison of the displacement transmissibility on the frequency bands between the designed time delay τk2(Ω) and a constant small-value time delayτk2 for (d) g2 = 0.05, (e) g2 = 0.2, and (f) g2 = 0.4

Grahic Jump Location
Fig. 6

The experimental prototype, elastic components, and control modules: (a) the experimental assembly; (b) the NL-VI system; (c) the construction of the NL-N stiffness component; and (d) the timed-delayed actuator

Grahic Jump Location
Fig. 7

(a) Structural diagram of the time-delayed control NL-VI; (b) deformation of the steel sheets; and (c) deformation of the right-side predeformed NL-N component

Grahic Jump Location
Fig. 8

(a) The displacement transmissibility at the resonance frequency band for identification of damping and the inherent time delay and (b) time-series signals measured

Grahic Jump Location
Fig. 9

(a) Displacement transmissibility of the frequency band for different control strengths; comparison of the time series of the responses between the platform and the base for (b) g2 = 0.1, (c) g2 = 0.2, and (d) g2 = 0.3

Grahic Jump Location
Fig. 10

The beginning frequency Ωe of the effective isolation for different values of the control strength g2 and the structural parameter γk

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In