A Novel of Low-Frequency Vibration Isolation with High-Static Low-Dynamic Stiffness Characteristic

Abstract

The efficiency of quasi-zero stiffness vibration isolator will decrease when getting overloaded and underloaded. Given the variability of load in general engineering application, this paper aims at presenting a newly designed type of vibration isolation system with positive stiffness in parallel with elements of negative stiffness, which has variable carrying capacity. The vibration isolation performance of system requires overall analysis. Firstly, static analysis is applied to obtain the optimal vibration isolation parameters of the system at the equilibrium position and to verify the high-static low-dynamic stiffness characteristic of the system. Then, the nonlinear dynamic equation of the system is established. Meanwhile, the influence of excitation amplitude on the transmissibility of the system is analyzed under three different conditions by harmonic balance method. Finally, the response curves of the system to sinusoidal excitation and multi-frequency excitation are analyzed by numerical simulation. The result of numerical simulation shows that the vibration isolation system still has good low-frequency vibration isolation characteristics when dealing with different loads. The problem of poor vibration isolation performance of general quasi-zero stiffness isolators under load changes is well solved.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Abbreviations

\( A_{0} \) :

Constant term of the steady-state solution

\( A_{1} \) :

Amplitude of harmonic term of the steady-state solution

\( A_{0}^{f} \) :

Peak amplitude of \( A_{0} \) for the force excitation

\( A_{0}^{\text{z}} \) :

Peak amplitude of \( A_{0} \) for the displacement excitation

\( A_{1}^{\text{f}} \) :

Peak amplitude of \( A_{1} \) for the force excitation

\( A_{1}^{z} \) :

Peak amplitude of \( A_{1} \) for the displacement excitation

\( {\text{a}} \) :

The horizontal distance between the tilted spring end and the equilibrium point

\( {\text{a}}_{0} \) :

The original horizontal distance between the tilted spring end and the equilibrium point

c :

Damping coefficient

F :

The external load

F V :

The restoring force of vertical spring

F s :

The restoring force of inclined spring

F 1 :

The restoring force of the system under harmonic force excitation

F 2 :

The restoring force of the system under harmonic displacement excitation

\( {\text{f}}_{m} \) :

Dynamic force transmitted to the base

\( {\text{f}}_{{\text{md}}} \) :

Damping force

\( {\text{f}}_{{\text{me}}} \) :

Elastic force

\( F_{{\text{me}0}} \) :

Constant term of \( {\text{f}}_{{\text{me}}} \)

\( F_{{\text{me}1}} \) :

Amplitude of harmonic term of \( f_{{\text{me}}} \)

\( F_{{\text{md}}} \) :

Amplitude of harmonic term of \( f_{{\text{md}}} \)

\( {\text{h}}_{0} \) :

The distance between the initial position and the initial equilibrium point

K:

The system stiffness

\( k_{\text{s}} \) :

Stiffness of horizontal spring

\( k_{\text{v}} \) :

Stiffness of vertical spring

L :

The length of the inclined spring

\( L_{0} \) :

The original length of the inclined spring

m:

Mass

\( T_{\text{f}} \) :

The force transmissibility of ideal system

\( T_{z} \) :

The absolute displacement transmissibility of the system

\( T_{\text{l}} \) :

The force transmissibility of equivalent linear system

\( {\text{u}}_{0} \) :

The deviation from the desired position

\( v \) :

The displacement with the equilibrium position

x :

The displacement at the equilibrium point

y :

Relative displacement (y = u z)

z :

Absolute displacement response of base

Z :

Amplitude of base absolute displacement

\( \alpha \) :

Stiffness ratio

\( \beta \) :

The included angle between the guide track and the horizontal plane

\( \theta \) :

The included angle between the inclined spring and the horizontal plane

\( \xi \) :

Dimensionless viscous damping coefficient

\( \rho \) :

The amplitude of harmonic excitation

\( \omega \) :

Excitation frequency

\( \omega_{\text{n}} \) :

Natural frequency of the system

\( \varphi \) :

Phase difference

\( \varOmega \) :

Frequency ratio \( \omega / \omega_{\text{n}} \)

\( \varOmega^{\text{f}} \) :

Frequency corresponding to the peak response for force excitation

\( \varOmega^{\text{z}} \) :

Frequency corresponding to the peak response for displacement excitation

References

  1. Abbasi A, Khadem SE, Bab S (2018) Vibration control of a continuous rotating shaft employing high-static low-dynamic stiffness isolators. J VIib Control 24:760–783

    MathSciNet  Article  Google Scholar 

  2. Abolfathi A, Brennan MJ, Waters TP, Tang B (2015) On the effects of mistuning a force-excited system containing a quasi-zero-stiffness vibration isolator. J Vib Acoust 137:044502

    Article  Google Scholar 

  3. Asai T, Araki Y, Kimura K, Masui T (2017) Adjustable vertical vibration isolator with a variable ellipse curve mechanism. Earthq Eng Struct D 46:1345–1366

    Article  Google Scholar 

  4. Cai CQ, Zhou JX, Wu LC, Wang K, Xu DL, Ouyang HJ (2020) Design and numerical validation of quasi-zero-stiffness metamaterials for very low-frequency band gaps. Compos Struct 236:111862

    Article  Google Scholar 

  5. Cheng C, Li SM, Wang Y, Jiang XX (2017) Force and displacement transmissibility of a quasi-zero stiffness vibration isolator with geometric nonlinear damping. Nonlinear Dyn 87:2267–2279

    Article  Google Scholar 

  6. Davis RB, McDowell MD (2017) Combined Euler column vibration isolation and energy harvesting. Smart Mater Struct 26:055001

    Article  Google Scholar 

  7. Ding H, Chen LQ (2019) Nonlinear vibration of a slightly curved beam with quasi-zero-stiffness isolators. Nonlinear Dyn 95:2367–2382

    Article  Google Scholar 

  8. Dong GX, Zhang XN, Xie SL, Yan B, Luo YJ (2017) Simulated and experimental studies on a high-static-low-dynamic stiffness isolator using magnetic negative stiffness spring. Mech Syst Signal Process 86:188–203

    Article  Google Scholar 

  9. Dong GX, Zhang XN, Luo YJ, Zhang YH, Xie SL (2018a) Analytical study of the low frequency multi-direction isolator with high-static-low-dynamic stiffness struts and spatial pendulum. Mech Syst Signal Process 110:521–539

    Article  Google Scholar 

  10. Dong GX, Zhang YH, Luo YJ, Xie SL, Zhang XN (2018b) Enhanced isolation performance of a high-static–low-dynamic stiffness isolator with geometric nonlinear damping. Nonlinear Dyn 93:2339–2356

    Article  Google Scholar 

  11. Jurevicius M, Vekteris V, Turla V, Kilikevicius A, Viselga G (2019) Investigation of the dynamic efficiency of complex passive low-frequency vibration isolation systems. J Low Freq Noise V A 38:608–614

    Article  Google Scholar 

  12. Le TD, Nguyen VAD (2017) Low frequency vibration isolator with adjustable configurative parameter. Int J Mech Sci 134:224–233

    Article  Google Scholar 

  13. Ledezma-Ramirez DF, Ferguson NS, Brennan MJ, Tang B (2015) An experimental nonlinear low dynamic stiffness device for shock isolation. J Sound Vib 347:1–13

    Article  Google Scholar 

  14. Li YL, Xu DL (2016) Chaotification of quasi-zero-stiffness system with time delay control. Nonlinear Dyn 86:353–368

    MathSciNet  Article  Google Scholar 

  15. Li YL, Xu DL (2018) Force transmissibility of floating raft systems with quasi-zero-stiffness isolators. J VIib Control 24:3608–3616

    MathSciNet  Article  Google Scholar 

  16. Li FS, Chen Q, Zhou JH (2018) Dynamic properties of a novel vibration isolator with negative stiffness. J Vib Eng Technol 6:239–247

    Article  Google Scholar 

  17. Liu CR, Yu KP (2018) A high-static–low-dynamic-stiffness vibration isolator with the auxiliary system. Nonlinear Dyn 94:1549–1567

    Article  Google Scholar 

  18. Sun XT, Xu J, Wang F, Zhang S (2018) A novel isolation structure with flexible joints for impact and ultralow-frequency excitations. Int J Mech Sci 146:366–376

    Article  Google Scholar 

  19. Sun MN, Song GQ, Li YM, Huang ZL (2019a) Effect of negative stiffness mechanism in a vibration isolator with asymmetric and high-static-low-dynamic stiffness. Mech Syst Signal Process 124:388–407

    Article  Google Scholar 

  20. Sun Y, Gong D, Zhou JS (2019b) Low frequency vibration control of railway vehicles based on a high static low dynamic stiffness dynamic vibration absorber. Sci China Technol Sci 62:60–69

    Article  Google Scholar 

  21. Tang B, Brennan MJ (2014) On the shock performance of a nonlinear vibration isolator with high-static-low-dynamic-stiffness. Int J Mech Sci 81:207–214

    Article  Google Scholar 

  22. Valeev A (2018) Dynamics of a group of quasi-zero stiffness vibration isolators with slightly different parameters. J Low Freq Noise V A 37:640–653

    Article  Google Scholar 

  23. Wang XL, Zhou JX, Xu DL, Ouyang HJ, Duan Y (2017) Force transmissibility of a two-stage vibration isolation system with quasi-zero stiffness. Nonlinear Dyn 87:633–646

    Article  Google Scholar 

  24. Wang Y, Li SM, Cheng C, Su Y (2018) Adaptive control of a vehicle-seat-human coupled model using quasi-zero-stiffness vibration isolator as seat suspension. J Mech Sci Technol 32:2973–2985

    Article  Google Scholar 

  25. Wang K, Zhou JX, Xu DL, Ouyang HJ (2019a) Lower band gaps of longitudinal wave in a one-dimensional periodic rod by exploiting geometrical nonlinearity. Mech Syst Signal Process 124:664–678

    Article  Google Scholar 

  26. Wang K, Zhou JX, Wang Q, Ouyang HJ, Xu DL (2019b) Low-frequency band gaps in a metamaterial rod by negative-stiffness mechanisms: design and experimental validation. Appl Phys Lett 114:251902

    Article  Google Scholar 

  27. Wu K, Li G, Hu H, Wang LJ (2017) Active low-frequency vertical vibration isolation system for precision measurements. Chin J Mech Eng 30:164–169

    Article  Google Scholar 

  28. Zhou J, Xu D, Bishop S (2015) A torsion quasi-zero stiffness vibration isolator. J Sound Vib 338:121–133

    Article  Google Scholar 

  29. Zhou JX, Wang K, Xu DL, Ouyang HJ, Fu YM (2018) Vibration isolation in neonatal transport by using a quasi-zero-stiffness isolator. J VIib Control 24:3278–3291

    Article  Google Scholar 

Download references

Funding

This work is supported by the National Natural Science Foundation of China (Project No. 51305444) and the Project Funded by Design of Robot Variable Stiffness Joint based on Electromagnetic Control.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Jiayu Zheng.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zheng, J., Yang, X., Xu, J. et al. A Novel of Low-Frequency Vibration Isolation with High-Static Low-Dynamic Stiffness Characteristic. Iran J Sci Technol Trans Mech Eng (2020). https://doi.org/10.1007/s40997-020-00370-9

Download citation

Keywords

  • Low-frequency vibration isolation
  • High-static low-dynamic
  • Variable load
  • Harmonic balance method