Skip Navigation Links
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn


Mechanisms with Negative Stiffnesses for Simplified Designs of Broad Band Passive Vibration Isolation

Journal of Vibration Testing and System Dynamics 6(2) (2022) 207--214 | DOI:10.5890/JVTSD.2022.06.003

Z.C. Feng

Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA

Download Full Text PDF

 

Abstract

Structures with nonlinear stiffnesses have been proposed for passive vibration isolation to achieve high static stiffness and low dynamic stiffness. Unfortunately, the design of nonlinear structures is very cumbersome because of the nonlinear geometry. Mechanisms with negative stiffnesses have found successful applications in industry. These mechanisms could be included in mechanical vibration courses since the design requires only the linear analysis. However, the stiffnesses of these structures with a compressive load are not available in the literature. This paper provides derivation of the stiffnesses of beam mechanisms with compressive loads. The derivation is based on the solution of the ordinary differential equation in the buckling analysis of columns.

References

  1. [1]  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, 678--689.
  2. [2]  Ibrahim, R.A. (2008), Recent advances in nonlinear passive vibration isolators, J. Sound Vib., 314, 371-452.
  3. [3]  Virgin, L.N., Santillan, S.T., and Plaut, R.H. (2008), Vibration isolation using extreme geometric nonlinearity, J. Sound Vib., 315(3), 721--731.
  4. [4]  Hao, Z., Cao, Q.J., and Wiercigroch, M. (2006), Nonlinear dynamics of the quasi-zero-stiffness SD oscillator based upon the local and global bifurcation analyses, Nonlinear Dyn., 87(2), 987--1014.
  5. [5]  Zhu, Y.P. Lang, Z.Q. (2017), Design of nonlinear systems in the frequency domain: an output frequency response function-based approach, IEEE Trans. Control Syst. Technol., 26(4), 1358--1371.
  6. [6]  Chang, Y.P., Zhou, J.X., Wang, K., and Xu, D.L. (2021), A quasi-zero-stiffness dynamic vibration absorber, J. Sound Vib., 494, 115859.
  7. [7]  Qiu, Y., Zhu, Y., Luo, Z.~et al. (2021), The analysis and design of nonlinear vibration isolators under both displacement and force excitations, Arch Appl Mech., https://doi.org/10.1007/s00419-020-01875-0.
  8. [8]  Yan, B., Ma, H., Jian, B., Wang, K., and Wu, C. (2019), Nonlinear dynamics analysis of a bi-state nonlinear vibration isolator with symmetric permanent magnets, Nonlinear Dynamics, 97, 2499-2519.
  9. [9]  Sun, Y., Zhao J., Wang, M., Sun, Y., Pu, H., Luo, J., Peng, Y., Xie, S., and Yang, Y. (2020), High-Static-Low-Dynamic Stiffness Isolator With Tunable Electromagnetic Mechanism, IEEE/ASME Transactions on Mechatronics, 25, pp.~316-326.
  10. [10]  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), 700--711.
  11. [11]  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), 870--883.
  12. [12]  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), 707--717.
  13. [13]  Carrella, A., Brennan, M.J., Waters, T.P., and Lopes, V. (2012), Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness, Int. J. Mech. Sci., 55(1), 22--29.
  14. [14]  {https://www.minusk.com/}.
  15. [15]  Platus, D.L. (1991), Negative Stiffness Mechanism Vibration Isolation Systems, SPIE Vibration Control in Microelectronics, Optics, and Metrology, p44.
  16. [16]  Platus, D.L. (1993) Smoothing Out Bad Vibes, Machine Design, 26, p.123.
  17. [17]  Platus, D.L. (1999), Negative Stiffness Mechanism Vibration Isolation Systems, SPIE Optomechanical Engineering and Vibration Control, p98.
  18. [18]  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, J.~Vib. Acoust., 136, p.~031009.
  19. [19]  Chang, Y., Zhou, J., Wang, K., and Xu, D. (2021), A quasi-zero-stiffness dynamic vibration absorber, Journal of Sound and Vibration, 494, 115859.