0
Technical Brief

On the Effects of Mistuning a Force-Excited System Containing a Quasi-Zero-Stiffness Vibration Isolator

[+] Author and Article Information
Ali Abolfathi

Aeronautical and Automotive Engineering,
Stewart Miller Building,
Loughborough University,
Leicestershire LE11 3TU, UK
e-mail: ali.abolfathi2@gmail.com

M. J. Brennan

Professor
Department of Mechanical Engineering,
UNESP, Ilha Solteira,
Sao Paulo 15385-000, Brazil
e-mail: mjbrennan0@btinternet.com

T. P. Waters

Associate Professor
Institute of Sound and Vibration Research,
University of Southampton,
Southampton SO17 1BJ, UK
e-mail: tpw@isvr.soton.ac.uk

B. Tang

Associate Professor
Institute of Internal Combustion Engine,
Dalian University of Technology,
Dalian 116023, China
e-mail: btang@dlut.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 July 23, 2014; final manuscript received January 25, 2015; published online March 23, 2015. Assoc. Editor: Mohammed Daqaq.

J. Vib. Acoust 137(4), 044502 (Aug 01, 2015) (6 pages) Paper No: VIB-14-1264; doi: 10.1115/1.4029689 History: Received July 23, 2014; Revised January 25, 2015; Online March 23, 2015

Nonlinear isolators with high-static-low-dynamic-stiffness have received considerable attention in the recent literature due to their performance benefits compared to linear vibration isolators. A quasi-zero-stiffness (QZS) isolator is a particular case of this type of isolator, which has a zero dynamic stiffness at the static equilibrium position. These types of isolators can be used to achieve very low frequency vibration isolation, but a drawback is that they have purely hardening stiffness behavior. If something occurs to destroy the symmetry of the system, for example, by an additional static load being applied to the isolator during operation, or by the incorrect mass being suspended on the isolator, then the isolator behavior will change dramatically. The question is whether this will be detrimental to the performance of the isolator and this is addressed in this paper. The analysis in this paper shows that although the asymmetry will degrade the performance of the isolator compared to the perfectly tuned case, it will still perform better than the corresponding linear isolator provided that the amplitude of excitation is not too large.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Ungar, E. E., and Zapfe, J. A., 2006, “Vibration Isolation,” Noise and Vibration Control Engineering, 2nd ed., I. L.Ver and L. L.Beranek, eds., Wiley, Hoboken, NJ, Chap. 13.
Ibrahim, R. A., 2008, “Recent Advances in Nonlinear Passive Vibration Isolators,” J. Sound Vib., 314(3–5), pp. 371–452. [CrossRef]
Rivin, E. I., 2001, Passive Vibration Isolation, ASME Press, New York.
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]
Alabuzhev, P., Gritchin, A., Kim, L., Migirenko, G., Chon, V., and Stepanov, P., 1989, Vibration Protecting and Measuring Systems With Quasi-Zero Stiffness, Hemisphere Publishing Company, New York.
Carrella, A., Brennan, M. J., and Waters, T. P., 2007, “Static Analysis of a Passive Vibration Isolator With Quasi-Zero-Stiffness Characteristic,” J. Sound Vib., 301(3–5), pp. 678–689. [CrossRef]
Kovacic, I., Brennan, M. J., and Waters, T. P., 2008, “A Study of a Nonlinear Vibration Isolator With a Quasi-Zero Stiffness Characteristic,” J. Sound Vib., 315(3), pp. 700–711. [CrossRef]
Carrella, A., Brennan, M. J., Kovacic, I., and Waters, T. P., 2009, “On the Force Transmissibility of a Vibration Isolator With Quasi-Zero-Stiffness,” J. Sound Vib., 322(4–5), pp. 707–717. [CrossRef]
Le, T. D., and Ahn, K. K., 2011, “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., 2014, “Active Pneumatic Vibration Isolation System Using Negative Stiffness Structures for a Vehicle Seat,” J. Sound Vib., 333(5), pp. 1245–1268. [CrossRef]
Zhou, N., and Liu, K., 2010, “A Tunable High-Static-Low-Dynamic-Stiffness Isolator,” J. Sound Vib., 329(9), pp. 1254–1273. [CrossRef]
Shaw, A. D., Neild, S. A., and Wagg, D. J., 2013, “Dynamic Analysis of High Static Low Dynamic Stiffness Vibration Isolation Mounts,” J. Sound Vib., 332(6), pp. 1437–1455. [CrossRef]
Xu, D. L., Yu, Q. P., Zhou, J. X., and Bishop, S. R., 2013, “Theoretical and Experimental Analyses of a Nonlinear Magnetic Vibration Isolator With Quasi-Zero-Stiffness Characteristic,” J. Sound Vib., 332(14), pp. 3377–3389. [CrossRef]
Tech Products, 2015, “Bubble Mounts,” Tech Products Corp., Miamisburg, OH, accessed Feb. 3, 2015, http://www.novibes.com/Products#/filters=/detail=Bubble_Mounts
Abolfathi, A., 2012, “Nonlinear Vibration Isolators With Asymmetric Stiffness,” Ph.D. thesis, University of Southampton, Southampton, UK.
Kovacic, I., Brennan, M. J., and Lineton, B., 2008, “On the Resonance Response of an Asymmetric Duffing Oscillator,” Int. J. Non-Linear Mech., 43(9), pp. 858–867. [CrossRef]
Huang, X., Liu, X., Sun, J., Zhang, Z., and Hua, H., 2014, “Effect of the System Imperfections on the Dynamic Response of a High-Static-Low-Dynamic Stiffness Vibration Isolator,” Nonlinear Dyn., 76(2), pp. 1157–1167. [CrossRef]
Huang, X., Liu, X., and Hua, H., 2014, “Effects of Stiffness and Load Imperfection on the Isolation Performance of a High-Static-Low-Dynamic Stiffness Nonlinear Isolator Under Base Displacement Excitation,” Int. J. Non-Linear Mech., 65, pp. 32–43. [CrossRef]
Kovacic, I., Brennan, M. J., and Lineton, B., 2009, “Effect of a Static Force on the Dynamic Behaviour of a Harmonically Excited Quasi-Zero Stiffness System,” J. Sound Vib., 325(4–5), pp. 870–883. [CrossRef]
Kovacic, I., and Brennan, M. J., 2011, The Duffing Equation: Nonlinear Oscillators and Their Behaviour, Wiley, Chichester, UK.

Figures

Grahic Jump Location
Fig. 1

Nonlinear isolation system: (a) baseline case with the isolator in its original configuration, (b) isolation system with an additional static load, and (c) isolation system with an additional mass attached

Grahic Jump Location
Fig. 2

Characteristics of the isolator: (a) nondimensional force–deflection characteristic, (b) nondimensional stiffness characteristic as a function of nondimensional displacement. Dotted line l∧ = 0.75; dashed line l∧ = 0.70; and solid line l∧ = 0.667 (QZS system). Also shown is the static displacement x∧s and stiffness k¯s for the QZS system with a static load of f∧s.

Grahic Jump Location
Fig. 3

Frequency response curves for the isolators in Fig. 1. (a.i) and (a.ii) The amplitudes of A0 and A1, respectively, for the system in Fig. 1(b), and (b.i) and (b.ii) are the amplitudes of A0 and A1, respectively, for the system in Fig. 1(c). The baseline case is shown as a black solid line; the dashed line is for either (a) f∧s = 0.2 or (b) μ = 0.2; and the thin line is for either (a) f∧s = 0.6 or (b) μ = 0.6. The thin dashed–dotted lines are the loci of the peaks. The dotted lines denote unstable solutions, and the markers are the solutions from numerical integration.

Grahic Jump Location
Fig. 4

Force transmissibility for the isolators in Fig. 1. (a) System in Fig. 1(b) and (b) system in Fig. 1(c). The baseline case is shown as a black solid line; the dashed line is for either (a) f∧s = 0.2 or (b) μ = 0.2; the thin line is for either (a) f∧s = 0.6 or (b) μ = 0.6; the dotted lines denote unstable solutions, and the markers are the solutions from numerical integration.

Grahic Jump Location
Fig. 5

Isolation frequency as a function of the asymmetry of the system for a nondimensional nonlinear stiffness of γ = 0.0783 and damping ratio of ζ = 0.025 for different dynamic loads. (a) Static preload f∧s and (b) mass ratio μ. The black solid line represents the isolation frequency of a linear isolator with a stiffness equal to the dynamic stiffness of the mistuned isolator (linear isolator 2). The dotted line is the isolation frequency of an isolator with no horizontal springs (linear isolator 1). The circles and the squares denote the isolation frequency for F∧e = 0.05 and F∧e = 0.1, respectively.

Tables

Errata

Discussions

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