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
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.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Fig. 10

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



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