Research Papers

Theoretical Analysis and Experimental Identification of a Vibration Isolator With Widely-Variable Stiffness

[+] Author and Article Information
Zhan Hu

School of Aerospace Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: huzhan1029@163.com

Xing Wang

Department of Mechanical Engineering,
University of Bristol,
Bristol BS8 1TR, UK;
School of Aerospace Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: wangxingbuaa@163.com

Hongxiang Yao

School of Aerospace Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: yaohongxiang543@sina.com

Guangyuan Wang

Beijing Institute of Spacecraft System
Beijing 100094, China
e-mail: zhuichilun@126.com

Gangtie Zheng

School of Aerospace Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: gtzheng@tsinghua.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 November 28, 2017; final manuscript received February 21, 2018; published online April 26, 2018. Assoc. Editor: Izhak Bucher.

J. Vib. Acoust 140(5), 051014 (Apr 26, 2018) (11 pages) Paper No: VIB-17-1514; doi: 10.1115/1.4039537 History: Received November 28, 2017; Revised February 21, 2018

This paper develops an adjustable high-static-low-dynamic (AHSLD) vibration isolator with a widely variable stiffness. By adjusting deformations of its horizontal springs, the natural frequency of the isolator can be substantially changed starting from a quasi-zero value. In this paper, the nonlinear static and dynamic analyses of the AHSLD isolator are presented. Effects of horizontal adjustments on the variation range of the stiffness and nonlinear dynamic characteristics are investigated. Good performance of the stiffness variation is validated by free-vibration tests. The wide-range variable stiffness from 0.33 N/mm to 23.2 N/mm is achieved in tests, which changes the natural frequency of the isolator from an ultra-low value of 0.72 Hz to 5.99 Hz. Besides, its nonlinear dynamic characteristics are also experimentally identified by applying the Hilbert transform. Both analytical and experimental results demonstrate the weakly hardening nonlinearity in the tested AHSLD isolator, which will not degrade its performance in practical applications.

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Guan, X. , and Zheng, G. , 2012, “ Integrated Design of Space Telescope Vibration Isolation and Attitude Control,” 12th European Conference on Spacecraft Structures, Materials and Environmental Testing, Noordwijk, The Netherlands, Mar. 20–23, p. 22.
Wie, B. , and Byun, K. , 1989, “ New Generalized Structural Filtering Concept for Active Vibration Control Synthesis,” J. Guid., Control, Dyn., 12(2), pp. 147–154. [CrossRef]
Wie, B. , and Bernstein, D. S. , 1992, “ Benchmark Problems for Robust Control Design,” J. Guid., Control, Dyn., 15(5), pp. 1057–1059. [CrossRef]
Liu, C. , Jing, X. , Daley, S. , and Li, F. , 2015, “ Recent Advances in Micro-Vibration Isolation,” Mech. Syst. Signal Process., 56–57, pp. 55–80. [CrossRef]
Azadi, M. , Behzadipour, S. , and Faulkner, G. , 2009, “ Antagonistic Variable Stiffness Elements,” Mech. Mach. Theory, 44(9), pp. 1746–1758. [CrossRef]
Azadi, M. , Behzadipour, S. , and Faulkner, G. , 2011, “ Performance Analysis of a Semi-Active Mount Made by a New Variable Stiffness Spring,” J. Sound Vib., 330(12), pp. 2733–2746. [CrossRef]
Azadi, M. , Behzadipour, S. , and Faulkner, G. , 2013, “ Introducing a New Semi-Active Engine Mount Using Force Controlled Variable Stiffness,” Veh. Syst. Dyn., 51(5), pp. 721–736. [CrossRef]
Jeong, H.-K. , Lee, J. , Han, J.-H. , and Wereley, N. M. , 2016, “ Design of Frequency-Tunable Mesh Washer Isolators Using Shape Memory Alloy Actuators,” J. Intell. Mater. Syst. Struct., 27(9), pp. 1265–1280. [CrossRef]
Zhou, N. , and Liu, K. , 2010, “ A Tunable High-Static–Low-Dynamic Stiffness Vibration Isolator,” J. Sound Vib., 329(9), pp. 1254–1273. [CrossRef]
Wu, T.-H. , and Lan, C.-C. , 2016, “ A Wide-Range Variable Stiffness Mechanism for Semi-Active Vibration Systems,” J. Sound Vib., 363, pp. 18–32. [CrossRef]
Carrella, A. , Brennan, M. , and Waters, T. , 2007, “ Static Analysis of a Passive Vibration Isolator With Quasi-Zero-Stiffness Characteristic,” J. Sound Vib., 301(3–5), pp. 678–689. [CrossRef]
Carrella, A. , Brennan, M. , Waters, T. , and Lopes, V. , 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]
Abolfathi, A. , Brennan, M. J. , Waters, T. , and Tang, B. , 2015, “ On the Effects of Mistuning a Force-Excited System Containing a Quasi-Zero-Stiffness Vibration Isolator,” ASME J. Vib. Acoust., 137(4), p. 044502. [CrossRef]
Xu, D. , Zhang, Y. , Zhou, J. , and Lou, J. , 2014, “ On the Analytical and Experimental Assessment of the Performance of a Quasi-Zero-Stiffness Isolator,” J. Vib. Control, 20(15), pp. 2314–2325. [CrossRef]
Lan, C.-C. , Yang, S.-A. , and Wu, Y.-S. , 2014, “ Design and Experiment of a Compact Quasi-Zero-Stiffness Isolator Capable of a Wide Range of Loads,” J. Sound Vib., 333(20), pp. 4843–4858. [CrossRef]
Le, T. D. , and Ahn, K. K. , 2011, “ A Vibration Isolation System in Low Frequency Excitation Region Using Negative Stiffness Structure for Vehicle Seat,” J. Sound Vib., 330(26), pp. 6311–6335. [CrossRef]
Le, T. D. , and Ahn, K. K. , 2013, “ Experimental Investigation of a Vibration Isolation System Using Negative Stiffness Structure,” Int. J. Mech. Sci., 70, pp. 99–112. [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]
Fulcher, B. A. , Shahan, D. W. , Haberman, M. R. , Seepersad, C. C. , and Wilson, P. S. , 2014, “ Analytical and Experimental Investigation of Buckled Beams as Negative Stiffness Elements for Passive Vibration and Shock Isolation Systems,” ASME J. Vib. Acoust., 136(3), p. 031009. [CrossRef]
Carrella, A. , and Friswell, M. , 2008, “ A Passive Vibration Isolator Incorporating a Composite Bistable Plate,” Sixth EUROMECH Nonlinear Dynamics Conference, Saint Petersburg, Russia, June 30–July 4.
Shaw, A. , Neild, S. , Wagg, D. , Weaver, P. , and Carrella, A. , 2013, “ A Nonlinear Spring Mechanism Incorporating a Bistable Composite Plate for Vibration Isolation,” J. Sound Vib., 332(24), pp. 6265–6275. [CrossRef]
Ishida, S. , Uchida, H. , Shimosaka, H. , and Hagiwara, I. , 2017, “ Design and Numerical Analysis of Vibration Isolators With Quasi-Zero-Stiffness Characteristics Using Bistable Foldable Structures,” ASME J. Vib. Acoust., 139(3), p. 031015. [CrossRef]
Ishida, S. , Suzuki, K. , and Shimosaka, H. , 2017, “ Design and Experimental Analysis of Origami-Inspired Vibration Isolator With Quasi-Zero-Stiffness Characteristic,” ASME J. Vib. Acoust., 139(5), p. 051004. [CrossRef]
Shan, Y. , Wu, W. , and Chen, X. , 2015, “ Design of a Miniaturized Pneumatic Vibration Isolator With High-Static-Low-Dynamic Stiffness,” ASME J. Vib. Acoust., 137(4), p. 045001. [CrossRef]
Wang, J. , and Gu, S. S. , 2005, Principles of Automatic Control, Metallurgical Industry Press, Beijing, China.
Worden, K. , and Tomlinson, G. R. , 2000, Nonlinearity in Structural Dynamics: Detection, Identification and Modelling, CRC Press, Boca Raton, FL. [CrossRef]
Hu, Z. , and Zheng, G. , 2016, “ A Combined Dynamic Analysis Method for Geometrically Nonlinear Vibration Isolators With Elastic Rings,” Mech. Syst. Signal Process., 76–77, pp. 634–648. [CrossRef]
Wang, X. , and Zheng, G. , 2016, “ Two-Step Transfer Function Calculation Method and Asymmetrical Piecewise-Linear Vibration Isolator Under Gravity,” J. Vib. Control, 22(13), pp. 2973–2991. [CrossRef]
Wang, X. , Guan, X. , and Zheng, G. , 2016, “ Inverse Solution Technique of Steady-State Responses for Local Nonlinear Structures,” Mech. Syst. Signal Process., 70–71, pp. 1085–1096. [CrossRef]
Capecchi, D. , and Vestroni, F. , 1990, “ Periodic Response of a Class of Hysteretic Oscillators,” Int. J. Nonlinear Mech., 25(2–3), pp. 309–317. [CrossRef]
Feldman, M. , 2011, “ Hilbert Transform in Vibration Analysis,” Mech. Syst. Signal Process., 25(3), pp. 735–802. [CrossRef]
Feldman, M. , 1997, “ Non-Linear Free Vibration Identification Via the Hilbert Transform,” J. Sound Vib, 208(3), pp. 475–489. [CrossRef]
Feldman, M. , 2006, “ Time-Varying Vibration Decomposition and Analysis Based on the Hilbert Transform,” J. Sound Vib., 295(3–5), pp. 518–530. [CrossRef]
Huang, N. E. , Shen, Z. , and Long, S. R. , 1999, “ A New View of Nonlinear Water Waves: The Hilbert Spectrum,” Annu. Rev. Fluid Mech., 31(1), pp. 417–457. [CrossRef]
Rato, R. , Ortigueira, M. D. , and Batista, A. , 2008, “ On the HHT, Its Problems, and Some Solutions,” Mech. Syst. Signal Process., 22(6), pp. 1374–1394. [CrossRef]
Hu, Z. , Wang, X. , and Zheng, G. , 2017, “ Free Vibration Identification of the Geometrically Nonlinear Isolator With Elastic Rings by Using Hilbert Transform,” Nonlinear Dynamics, Vol. 1, Springer, Cham, Switzerland, p. 69. [CrossRef] [PubMed] [PubMed]


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Fig. 1

Schematic diagrams of the AHSLD model: (a) initial position; (b) static equilibrium analysis; and (c) horizontal position

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Fig. 2

Effect of horizontal adjustment on stiffness at the horizontal position

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Fig. 3

(a) The restoring force-to-displacement curves and (b) the stiffness-to-displacement curves

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Fig. 4

Schematic diagram of the AHSLD isolator: (a) without adjustments and (b) with adjustments

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Fig. 5

Comparisons between exact results (ER) and approximate results: (a) the relative restoring force and (b) the stiffness

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Fig. 7

Transmissibility amplitude of absolute displacement of the AHSLD isolator and the linear isolator under: (a) the small base excitation of P̂=0.01; and (b) the large base excitation of P̂=0.03 ((i) x̂h = 0.142; (ii) x̂h = 0.1; (iii) x̂h = −0.0452; and (iv) x̂h = −0.3)

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Fig. 6

Theoretical frequency responses (unstable), numerically integral frequency responses of the amplitude of the relative displacement and BC under: (a) the small base excitation of P̂=0.01; (b) the large base excitation of P̂=0.03 ((i) x̂h = 0.142; (ii) x̂h = 0.1; (iii) x̂h = −0.0452; (iv) x̂h= −0.3)

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Fig. 8

Computer-aided design prototype of the AHSLD isolator

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Fig. 9

Details of computer-aided design models: (a) inner components of the AHSLD isolator; (b) horizontal mechanism; (c) vertical mechanism; and (d) horizontal adjustment with the lead screw

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Fig. 11

Time-domain displacements and amplitudes with different horizontal adjustments: (a) xh = −0.60 mm; (b) xh = 2.00 mm; (c) xh = 3.60 mm; (d) xh = 5.60 mm; (e) xh = 6.80 mm; and (f) xh = 7.06 mm

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Fig. 12

Instantaneous natural frequency with different horizontal adjustments

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Fig. 13

Comparisons of the modal frequency between theoretical, experimental, and linear results

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Fig. 10

Adjustable HSLD isolator testing system: (a) diagrammatic sketch and (b) photograph

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Fig. 14

Comparisons of backbone curves between theoretical and experimental results (i) xh = 7.06 mm; (ii) xh = 6.80 mm; (iii) xh = 5.60 mm; (iv) xh = 3.60 mm; (v) xh = 2.00 mm; and (vi) xh = −0.60 mm)

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Fig. 15

Comparisons of the relative restoring force between TR and ER: (a) xh = 7.06 and 6.80 mm and (b) xh = 5.60, 3.60, 2.00, and −0.60 mm

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Fig. 16

Comparisons of the stiffness between TR and ER

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Fig. 17

ER and fitted results of damping ratios: (a) ξ and (b) ξ0

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Fig. 18

Comparisons of theoretical frequency responses between experimental frequency responses and experimental backbone curves (i) xh = 7.06 mm and P = 0.0807 mm; (ii) xh = 6.80 mm and P = 0.0625 mm; (iii) xh = 5.60 mm and P = 0.0189 mm; (iv) xh =3.60 mm and P = 0.00619 mm; (v) xh = 2.00 mm and P = 0.00539 mm; and (vi) xh = −0.60 mm and P = 0.00347 mm)



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