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A novel quasi-zero-stiffness isolation platform via tunable positive and negative stiffness compensation mechanism

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Abstract

Various quasi-zero stiffness (QZS) systems with high-static and low-dynamic stiffness (HSLDS) have been applied extensively to attenuate low-frequency vibrations. However, in the majority of cases, the negative stiffness unit exhibits nonlinear stiffness behaviors, and the method of realizing QZS is limited to compensate the nonlinear negative stiffness through linear springs. Hence, a novel linkage anti-vibration structure (LAVS) via linear positive and negative stiffness compensation mechanism is proposed and studied for exploring its advantages in low-frequency vibration isolation. The LAVS is composed of a symmetric polygonal structure (SPS) and a vertical spring. The static stiffness behavior is first investigated, revealing the inherent positive and negative stiffness compensation mechanism of linear springs to the SPS. By tuning structural parameters, the linear spring can completely compensate the linear negative stiffness of the SPS to achieve enhanced QZS over a larger stroke. Numerical simulations are carried out to verify the theoretical result and demonstrate the effectiveness of the presented stiffness compensation mechanism. Based on the Lagrange principle, a dynamic equation is established and then solved via the multiple scales method to obtain the displacement transmissibility. The effects of key parameters such as the rod lengths, equilibrium points and damping factors on the amplitude–frequency characteristics and vibration transmissibility are analyzed. Compared with a SMD and a typical X-shaped QZS isolation systems, the presented LAVS exhibits an enhanced QZS zone with a larger load capacity and can realize superb vibration isolation performance with guaranteed stable equilibrium. The proposed linear positive and negative stiffness compensation mechanism presents new insights for passive vibration isolation design in many engineering applications.

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References

  1. Steier, F., Runte, T., Monsky, A., Klock, T., Laduree, G.: Managing the microvibration impact on satellite performances. Acta Astronaut. 162, 61–468 (2019)

    Google Scholar 

  2. Li, L., Tan, L., Kong, L., Wang, D., Yang, H.: The influence of flywheel micro vibration on space camera and vibration suppression. Mech. Syst. Signal Process. 100, 360–370 (2018)

    Google Scholar 

  3. Hao, R.B., Lu, Z.Q., Ding, H., Chen, L.Q.: Orthogonal six-DOFs vibration isolation with tunable high-static-low-dynamic stiffness: experiment and analysis. Int. J. Mech. Sci. 222, 107237 (2022)

    Google Scholar 

  4. Ostasevicius, V., Gaidys, R., Rimkeviciene, J., Dauksevicius, R.: An approach based on tool mode control for surface roughness reduction in high-frequency vibration cutting. J. Sound Vib. 329, 4866–4879 (2010)

    Google Scholar 

  5. Le, T.D., Ahn, K.K.: Experimental investigation of a vibration isolation system using negative stiffness structure. Int. J. Mech. Sci. 70, 99–112 (2013)

    Google Scholar 

  6. Chai, Y., Jing, X., Chao, X.: X-shaped mechanism based enhanced tunable QZS property for passive vibration isolation. Int. J. Mech. Sci. 218, 107077 (2022)

    Google Scholar 

  7. Jing, X., Zhang, L., Feng, X., Sun, B., Li, Q.: A novel bio-inspired anti-vibration structure for operating hand-held jackhammers. Mech. Syst. Signal Process. 118, 317–339 (2019)

    Google Scholar 

  8. Zhou, J., Wang, K., Xu, D., Ouyang, H., Fu, Y.: Vibration isolation in neonatal transport by using a quasi-zero-stiffness isolator. J. Vib. Control 24, 3278–3291 (2018)

    Google Scholar 

  9. Sun, X., Wang, F., Xu, J.: A novel dynamic stabilization and vibration isolation structure inspired by the role of avian neck. Int. J. Mech. Sci. 193, 106166 (2021)

    Google Scholar 

  10. Gatti, G.: Statics and dynamics of a nonlinear oscillator with quasi-zero stiffness behaviour for large deflections. Commun. Nonlinear Sci. Numer. Simul. 83, 105143 (2020)

    MathSciNet  Google Scholar 

  11. Zhang, Z., Zhang, Y.W., Ding, H.: Vibration control combining nonlinear isolation and nonlinear absorption. Nonlinear Dyn. 100, 2121–2139 (2020)

    Google Scholar 

  12. Pu, H., Yuan, S., Peng, Y., Meng, K., Zhao, J., Xie, R., Huang, Y., Sun, Y., Yang, Y., Xie, S., Luo, J., Chen, X.: Multi-layer electromagnetic spring with tunable negative stiffness for semi-active vibration isolation. Mech. Syst. Signal Process. 121, 942–960 (2019)

    Google Scholar 

  13. Wang, C., Chen, Y., Zhang, Z.: Simulation and experiment on the performance of a passive/active micro-vibration isolator. J. Vib. Control 24, 453–465 (2018)

    Google Scholar 

  14. Chai, Y., Gao, W., Ankay, B., Li, F., Zhang, C.: Aeroelastic analysis and flutter control of wings and panels: a review. Int. J. Mech. Syst. Dyn. 1, 5–34 (2021)

    Google Scholar 

  15. Chai, Y.Y., Song, Z.G., Li, F.M.: Active aerothermoelastic flutter suppression of composite laminated panels with time-dependent boundaries. Compos. Struct. 179, 61–76 (2017)

    Google Scholar 

  16. Chai, Y., Li, F., Song, Z., Zhang, C.: Aerothermoelastic flutter analysis and active vibration suppression of nonlinear composite laminated panels with time-dependent boundary conditions in supersonic airflow. J. Intel. Mat. Syst. Str. 29, 653–668 (2018)

    Google Scholar 

  17. Ma, H., Yan, B., Zhang, L., Zheng, W., Wang, P., Wu, C.: On the design of nonlinear damping with electromagnetic shunt damping. Int. J. Mech. Sci. 175, 105513 (2020)

    Google Scholar 

  18. Ibrahim, R.A.: Recent advances in nonlinear passive vibration isolators. J. Sound Vib. 314, 371–452 (2008)

    Google Scholar 

  19. Chai, Y., Li, F., Song, Z., Zhang, C.: Analysis and active control of nonlinear vibration of composite lattice sandwich plates. Nonlinear Dyn. 102, 2179–2203 (2020)

    Google Scholar 

  20. Bian, J., Jing, X.: Superior nonlinear passive damping characteristics of the bio-inspired limb-like or X-shaped structure. Mech. Syst. Signal Process. 125, 21–51 (2019)

    Google Scholar 

  21. Zhou, X.H., Tan, Y.C., Ke, K., Yam, M.C.H., Zhang, H.Y., Xu, J.Y.: An experimental and numerical study of brace-type long double C-section steel slit dampers. J. Build. Eng. 64, 105555 (2023)

    Google Scholar 

  22. Ke, K., Yam, M.C.H., Zhang, P., Shi, Y., Li, Y., Liu, S.: Self-centring damper with multi-energy-dissipation mechanisms: Insights and structural seismic demand perspective. J. Constr. Steel Res. 204, 107837 (2023)

    Google Scholar 

  23. Chai, Y., Jing, X.: Low-frequency multi-direction vibration isolation via a new arrangement of the X-shaped linkage mechanism. Nonlinear Dyn. 109, 2383–2421 (2022)

    Google Scholar 

  24. Ye, K., Ji, J.C., Brown, T.: Design of a quasi-zero stiffness isolation system for supporting different loads. J. Sound Vib. 471, 115198 (2020)

    Google Scholar 

  25. Bian, J., Jing, X.: Analysis and design of a novel and compact X-structured vibration isolation mount (X-Mount) with wider quasi-zero-stiffness range. Nonlinear Dyn. 101, 2195–2222 (2020)

    Google Scholar 

  26. Wang, Y., Li, S., Neild, S.A., Jiang, J.Z.: Comparison of the dynamic performance of nonlinear one and two degree-of-freedom vibration isolators with quasi-zero stiffness. Nonlinear Dyn. 88, 635–654 (2017)

    Google Scholar 

  27. Bian, J., Jing, X.: A nonlinear X-shaped structure based tuned mass damper with multi-variable optimization (X-absorber). Commun. Nonlinear Sci. 99, 105829 (2021)

    MathSciNet  Google Scholar 

  28. Su, N., Bian, J., Peng, S., Chen, Z., Xia, Y.: Balancing static and dynamic performances of TMD with negative stiffness. Int. J. Mech. Sci. 243, 108068 (2023)

    Google Scholar 

  29. Su, N., Xia, Y., Peng, S.: Filter-based inerter location dependence analysis approach of tuned mass damper inerter (TMDI) and optimal design. Eng. Struct. 250, 113459 (2022)

    Google Scholar 

  30. Bian, J., Zhou, X., Ke, K., Yam, M.C.H., Wang, Y.: Seismic resilient steel substation with BI-TMDI: a theoretical model for optimal design. J. Constr. Steel Res. 192, 107233 (2022)

    Google Scholar 

  31. Su, N., Bian, J., Peng, S., Xia, Y.: Generic optimal design approach for inerter-based tuned mass systems. Int. J. Mech. Sci. 233, 107654 (2022)

    Google Scholar 

  32. Carrella, A., Brennan, M.J., Kovacic, I., Waters, T.P.: On the force transmissibility of a vibration isolator with quasi-zero-stiffness. J. Sound Vib. 322, 707–717 (2009)

    Google Scholar 

  33. Zhao, F., Ji, J., Ye, K., Luo, Q.: An innovative quasi-zero stiffness isolator with three pairs of oblique springs. Int. J. Mech. Sci. 192, 106093 (2020)

    Google Scholar 

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

    Google Scholar 

  35. Jing, X., Chai, Y., Chao, X., Bian, J.: In-situ adjustable nonlinear passive stiffness using X-shaped mechanisms. Mech. Syst. Signal Process. 170, 108267 (2021)

    Google Scholar 

  36. Zhou, J., Wang, X., Xu, D., Bishop, S.: Nonlinear dynamic characteristics of a quasi-zero stiffness vibration isolator with cam–roller–spring mechanisms. J. Sound Vib. 346, 53–69 (2015)

    Google Scholar 

  37. Fulcher, B.A., Shahan, D.W., Haberman, M.R., Seepersad, C.C., Wilson, P.S.: Analytical and experimental investigation of buckled beams as negative stiffness elements for passive vibration and shock isolation systems. J. Vib. Acoust. 136, 031009 (2014)

    Google Scholar 

  38. Huang, X., Liu, X., Sun, J., Zhang, Z., Hua, H.: Vibration isolation characteristics of a nonlinear isolator using Euler buckled beam as negative stiffness corrector: a theoretical and experimental study. J. Sound Vib. 333, 1132–1148 (2014)

    Google Scholar 

  39. Ma, H., Yan, B.: Nonlinear damping and mass effects of electromagnetic shunt damping for enhanced nonlinear vibration isolation. Mech. Syst. Signal Process. 146, 107010 (2021)

    Google Scholar 

  40. Yan, G., Wu, Z.Y., Wei, X.S., Wang, S., Zou, H.X., Zhao, L.C., Qi, W.H., Zhang, W.M.: Nonlinear compensation method for quasi-zero stiffness vibration isolation. J. Sound Vib. 523, 116743 (2022)

    Google Scholar 

  41. Yan, G., Qi, W.H., Shi, J.W., Yan, H., Zou, H.X., Zhao, L.C., Wu, Z.Y., Fang, X.Y., Li, X.Y., Zhang, W.M.: Bionic paw-inspired structure for vibration isolation with novel nonlinear compensation mechanism. J. Sound Vib. 525, 116799 (2022)

    Google Scholar 

  42. Sadeghi, S., Li, S.: Fluidic origami cellular structure with asymmetric quasi-zero stiffness for low-frequency vibration isolation. Smart Mater. Struct. 28, 065006 (2019)

    Google Scholar 

  43. Carrella, A., Brennan, M.J., Waters, T.P.: Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. J. Sound Vib. 301, 678–689 (2007)

    Google Scholar 

  44. Zhang, Y., Wei, G., Wen, H., Jin, D., Hu, H.: Design and analysis of a vibration isolation system with cam–roller–spring–rod mechanism. J. Vib. Control 28, 1781–1791 (2022)

    MathSciNet  Google Scholar 

  45. Liu, X., Huang, X., Hua, H.: On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector. J. Sound Vib. 332, 3359–3376 (2013)

    Google Scholar 

  46. Yan, B., Ma, H., Yu, N., Zhang, L., Wu, C.: Theoretical modeling and experimental analysis of nonlinear electromagnetic shunt damping. J. Sound Vib. 471, 115184 (2020)

    Google Scholar 

  47. Zhai, Z., Wang, Y., Lin, K., Wu, L., Jiang, H.: In situ stiffness manipulation using elegant curved origami. Sci. Adv. 6, eabe2000 (2020)

    Google Scholar 

  48. Chong, X., Wu, Z., Li, F.: Vibration isolation properties of the nonlinear X-combined structure with a high-static and low-dynamic stiffness: theory and experiment. Mech. Syst. Signal Process. 179, 109352 (2022)

    Google Scholar 

  49. Gatti, G., Ledezma-Ramirez, D.F., Brennan, M.J.: Performance of a shock isolator inspired by skeletal muscles. Int. J. Mech. Sci. 244, 108066 (2023)

    Google Scholar 

  50. Wang, Y., Jing, X., Dai, H., Li, F.M.: Subharmonics and ultra-subharmonics of a bio-inspired nonlinear isolation system. Int. J. Mech. Sci. 152, 167–184 (2019)

    Google Scholar 

  51. Chai, Y., Jing, X., Guo, Y.: A compact X-shaped mechanism based 3-DOF anti-vibration unit with enhanced tunable QZS property. Mech. Syst. Signal Process. 168, 108651 (2022)

    Google Scholar 

  52. Wang, Y., Jing, X., Guo, Y.: Nonlinear analysis of a bio-inspired vertically asymmetric isolation system under different structural constraints. Nonlinear Dyn. 95, 445–464 (2019)

    Google Scholar 

  53. Jiang, G., Jing, X., Guo, Y.: A novel bio-inspired multi-joint anti-vibration structure and its nonlinear HSLDS properties. Mech. Syst. Signal Process. 138, 106552 (2020)

    Google Scholar 

  54. Deng, T., Wen, G., Ding, H., Lu, Z.Q., Chen, L.Q.: A bio-inspired isolator based on characteristics of quasi-zero stiffness and bird multi-layer neck. Mech. Syst. Signal Process. 145, 106967 (2020)

    Google Scholar 

  55. Yan, G., Wang, S., Zou, H., Zhao, L., Gao, Q., Zhang, W.: Bio-inspired polygonal skeleton structure for vibration isolation: design, modelling and experiment. Sci. China Technol. Sci. 63, 2617–2630 (2020)

    Google Scholar 

  56. Yan, G., Zou, H.X., Wang, S., Zhao, L.C., Wu, Z.Y., Zhang, W.M.: Bio-inspired toe-like structure for low-frequency vibration isolation. Mech. Syst. Signal Process. 162, 108010 (2022)

    Google Scholar 

  57. Niu, M.Q., Chen, L.Q.: Analysis of a bio-inspired vibration isolator with a compliant limb-like structure. Mech. Syst. Signal Process. 179, 109348 (2022)

    Google Scholar 

  58. Sun, X., Qi, Z., Xu, J.: Vibration properties of a knee bio-inspired nonlinear isolation structure. Int. J. Nonlin. Mech. 147, 104245 (2022)

    Google Scholar 

  59. Chai, Y.Y., Li, F.M., Song, Z.G.: Nonlinear vibration behaviors of composite laminated plates with time-dependent base excitation and boundary conditions. Int. J. Nonlinear Sci. Numer. Simul. 18, 145–161 (2017)

    MathSciNet  Google Scholar 

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Acknowledgements

This research was supported by the China Postdoctoral Science Foundation (Grant No. 2022M720576), National Natural Science Foundation of China (Grant No. 52308144), Natural Science Foundation of Sichuan Province of China (No. 2023NSFSC1294) and the Fundamental Research Funds for the Central Universities (No. 2682023CX054).

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Authors and Affiliations

  1. Department of Civil Engineering, University of Siegen, 57068, Siegen, Germany

    Yuyang Chai

  2. School of Civil Engineering, Chongqing University, Chongqing, 400045, People’s Republic of China

    Jing Bian

  3. School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu, 610031, People’s Republic of China

    Meng Li

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  1. Yuyang Chai
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  2. Jing Bian
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Correspondence to Jing Bian.

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Chai, Y., Bian, J. & Li, M. A novel quasi-zero-stiffness isolation platform via tunable positive and negative stiffness compensation mechanism. Nonlinear Dyn 112, 101–123 (2024). https://doi.org/10.1007/s11071-023-09018-0

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