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Microvibration isolation in sensitive payloads: methodology and design

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Abstract

Microvibration is a severe issue that is present in many components on spacecraft, such as cryocoolers, thrusters, solar arrays, and momentum/reaction wheel assemblies (M/RWAs), which can severely downgrade the working accuracy of sensitive payloads. To address this dilemma, recently, the development of passive, active or hybrid active–passive and semi-active isolation techniques for microvibration has attracted considerable interest, especially because of the increasing demand in boosting isolation performance for ultraprecision instruments subjected to very small amplitudes. As a useful complement to several existing reviews in the recent literature on microvibration isolation technology, in this paper, several isolation methods considering passive, active, hybrid active–passive and semi-active systems are investigated, exploring both theoretical and experimental results of these techniques. In general, passive approaches are first employed in orbit spacecraft due to their high stability and lack of exogenous energy consumption. Active techniques, however, are usually developed to isolate low-frequency vibrations, which are common in ultraprecision equipment and spacecraft. Hybrid active–passive methods embrace the advantages of both passive and active systems and have also been successfully applied in aerospace engineering for many years. In semi-active techniques, the trade-off between isolation performance and external energy input can adapt well to variations in the spacecraft environment. Additionally, important outcomes of the published work are reviewed. Notably, this paper focuses on a review of state-of-the-art vibration isolation theory and/or techniques that have been developed, mainly over the last decade, and can specifically or potentially be used for microvibration isolation.

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References

  1. Agletti, G., Langley, R., Gabriel, S.: Model building and verification for active control of microvibrations with probabilistic assessment of the effects of uncertainties. Proc. Inst. Mech. Eng. Part C-J. Eng. Mech. Eng. Sci. 218(4), 389–399 (2004)

    Google Scholar 

  2. Stabile, A., Yotov, V., Aglietti, G., et al.: Effect of boundary conditions on a high-performance isolation hexapod platform. Mech. Mach. Theory 177, 105020 (2022)

    Google Scholar 

  3. Li, L., Zhou, M., Zhu, Y., et al.: Satellite microvibration measurement based on distributed compressed sensing. Measurement 203, 112031 (2022)

    Google Scholar 

  4. Liu, C., Jing, X., Daley, S., et al.: Recent advances in micro-vibration isolation. Mech. Syst. Sign. Proc. 56–57, 55–80 (2015)

    Google Scholar 

  5. Yi, S., Zhang, Q., Sun, X., et al.: Simultaneous micropositioning and microvibration control of a magnetostrictive Stewart platform with synthesized strategy. Mech. Syst. Signal Proc. 187, 109925 (2023)

    Google Scholar 

  6. Makihara, K., Onoda, J., Minesugi, K.: New approach to semi-active vibration isolation to improve the pointing performance of observation satellites. Smart Mater. Struct. 15(2), 342–350 (2006)

    Google Scholar 

  7. Sun, Y., Gong, D., Zhou, J., et al.: Low frequency vibration control of railway vehicles based on a high static low dynamic stiffness dynamic vibration absorber. Sci. China-Technol. Sci. 62(1), 60–69 (2019)

    Google Scholar 

  8. Wang, X., Guo, L., Li, Y., et al.: Noise-robust vibration phase compensation for satellite ISAL imaging by frequency descent minimum entropy optimization. IEEE Trans. Geosci. Rem. Sens. 60, 1–17 (2022)

    Google Scholar 

  9. Shih, Y., Wu, G.: Effect of vibration on fatigue crack growth of an edge crack for a rectangular plate. Int. J. Fatigue 24(5), 557–566 (2002)

    MATH  Google Scholar 

  10. Foster, C., Tinker, M., Nurre, G., et al.: Solar-array-induced disturbance of the hubble space telescope pointing system. J. Spacecr. Rockets 32(4), 634–644 (1995)

    Google Scholar 

  11. Bely, P., Lupie, O., Hershey, J.: Line-of-sight jitter of the hubble space telescope. In: Proceedings of SPIE 1945, Space Astronomical Telescopes and Instruments II, pp. 55–61, Orlando (1993)

  12. Tang, X., Xie, J., Zhu, H., et al.: Overview of earth observation satellite platform microvibration detection methods. Sensors 20(3), 736 (2020)

    Google Scholar 

  13. Laskin, R., Sirlin, S.: Future payload isolation and pointing system technology. J. Guid. Control. Dyn. 9(4), 136–146 (1986)

    Google Scholar 

  14. Ibrahim, R.: Recent advances in nonlinear passive vibration isolators. J. Sound Vibr. 314(3), 371–452 (2008)

    Google Scholar 

  15. Ledezma-Ramirez, D., Tapia-Gonzalez, P., Ferguson, N., et al.: Recent advances in shock vibration isolation: an overview and future possibilities. Appl. Mech. Rev. 71(6), 060802 (2019)

    Google Scholar 

  16. Balaji, P., Selvakumar, K.: Applications of nonlinearity in passive vibration control: a review. J. Vib. Eng. Technol. 9(2), 183–213 (2021)

    Google Scholar 

  17. Yan, G., Zou, H., Wang, S., et al.: Bio-inspired vibration isolation: methodology and design. Appl. Mech. Rev. 73(2), 020801 (2021)

    Google Scholar 

  18. Korkmaz, S.: A review of active structural control: challenges for engineering informatics. Comput. Struct. 89(23), 2113–2132 (2011)

    Google Scholar 

  19. Liu, Y., Matsuhisa, H., Utsuno, H.: Semi-active vibration isolation system with variable stiffness and damping control. J. Sound Vibr. 313(1–2), 16–28 (2008)

    Google Scholar 

  20. Kandasamy, R., Cui, F., Townsend, N., et al.: A review of vibration control methods for marine offshore structures. Ocean Eng. 127, 279–297 (2016)

    Google Scholar 

  21. Liu, S., Deng, C., Wang, C., et al.: Microvibration modes reconstruction based on micro-doppler coincidence imaging. IEEE Trans. Geosci. Rem. Sens. 60, 1–16 (2022)

    Google Scholar 

  22. Jiang, T., Wen, L., Zhan, H., et al.: Micro-vibration modeling and verification of shutter mechanism of survey space telescope. Res. Astron. Astrophys. 23(1), 015020 (2023)

    Google Scholar 

  23. Qian, Y., Xie, Y., Jia, J., et al.: Design of active vibration isolation controller with disturbance observer-based linear quadratic regulator for optical reference cavities. Sensors 23(1), 302 (2023)

    Google Scholar 

  24. Niu, J., Song, K., Lim, C.: On active vibration isolation of floating raft system. J. Sound Vibr. 285(1), 391–406 (2005)

    Google Scholar 

  25. Oh, H., Lee, K., Jo, M.: A passive launch and on-orbit vibration isolation system for the spaceborne cryocooler. Aerosp. Sci. Technol. 28(1), 324–331 (2013)

    Google Scholar 

  26. Zhou, J., Wang, X., Xu, D., et al.: Nonlinear dynamic characteristics of a quasi-zero stiffness vibration isolator with cam-roller-spring mechanisms. J. Sound Vibr. 346(1), 53–69 (2015)

    Google Scholar 

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

    Google Scholar 

  28. Xu, D., Yu, Q., Zhou, J., et al.: Theoretical and experimental analyses of a nonlinear magnetic vibration isolator with quasi-zero-stiffness characteristic. J. Sound Vibr. 332(14), 3377–3389 (2013)

    Google Scholar 

  29. Yan, B., Wang, Z., Ma, H., et al.: A novel lever-type vibration isolator with eddy current damping. J. Sound Vibr. 494, 115862 (2021)

    Google Scholar 

  30. Yan, B., Ma, H., Zhang, L., et al.: Electromagnetic shunt damping for shock isolation of nonlinear vibration isolators. J. Sound Vibr. 479, 115370 (2020)

    Google Scholar 

  31. Griffin, S., Gussy, J., Lane, S., et al.: Virtual skyhook vibration isolation system. J. Vib. Acoust.-Trans. ASME 124(1), 63–67 (2002)

    Google Scholar 

  32. He, K., Li, Q., Liu, L., et al.: Active vibration isolation of ultra-stable optical reference cavity of space optical clock. Aerosp. Sci. Technol. 112, 106633 (2021)

    Google Scholar 

  33. Yan, B., Ma, H., Jian, B., et al.: Nonlinear dynamics analysis of a bi-state nonlinear vibration isolator with symmetric permanent magnets. Nonlinear Dyn. 97(4), 2499–2519 (2019)

    MATH  Google Scholar 

  34. Carrella, A., Brennan, M., Kovacic, I., et al.: On the force transmissibility of a vibration isolator with quasi-zero-stiffness. J. Sound Vibr. 322(4–5), 707–717 (2009)

    Google Scholar 

  35. Zhou, Z., Chen, X., Zhou, X.: Feedforward compensation in vibration isolation system subject to base disturbance. J. Vib. Control 21(6), 1201–1209 (2015)

    Google Scholar 

  36. Shen, Y., Xu, Y., Sheng, X., et al.: Microvibration transfer and suppression of satellite under multi-source coupling disturbances based on energy flow analysis. Adv. Space Res. 71(8), 3222–3233 (2023)

    Google Scholar 

  37. Li, Z., Li, X., Chen, X.: Generic vibration criteria–based dual-chamber pneumatic spring vibration isolation table design. Proc. Inst. Mech. Eng. Part B-J. Eng. Manuf. 228(12), 1621–1629 (2014)

    Google Scholar 

  38. Cobb, R., Sullivan, J., Das, A., et al.: Vibration isolation and suppression system for precision payloads in space. Smart Mater. Struct. 198(6), 798–812 (1999)

    Google Scholar 

  39. Sullivan, L., Fuentes, R., Babuska, V., et al.: On-orbit active vibration isolation: the satellite ultraquiet isolation technologies experiment (SUITE). In: AIAA Space 2003 Conference & Exposition, pp. 6358, Long Beach (2003)

  40. Lee, D., Park, G., Han, J.: Development of vibration isolation platform for low amplitude vibration. In: Proceedings of SPIE 9057, Active and Passive Smart Structures and Integrated Systems, pp. 905708, San Diego (2014)

  41. Voigtlander, B., Coenen, P., Cherepanov, V., et al.: Low vibration laboratory with a singlestage vibration isolation for microscopy applications. Rev. Sci. Instrum. 89(1), 023703 (2017)

    Google Scholar 

  42. Zhang, Q., Wang, G., Zheng, G.: Micro-vibration attenuation methods and key techniques for optical remote sensing satellite. J. Astronaut 36(2), 125–132 (2015)

    Google Scholar 

  43. Davis, P., Cunningham, D., Harrell, J.: Advanced 1.5 Hz passive viscous isolation system. In: 35th Structures, Structural Dynamics, and Materials Conference, pp. 2655–2665, South Carolina (1994)

  44. Stabile, A., Aglietti, G., Richardson, G., et al.: A 2-collinear-DoF strut with embedded negative-resistance electromagnetic shunt dampers for spacecraft micro-vibration. Smart Mater. Struct. 26(4), 045031 (2017)

    Google Scholar 

  45. Oh, H., Onoda, J., Minesugi, K.: Characteristics of a liquid-crystal type ER-fluid variable damper for semiactive vibration suppression. J. Vib. Acoust. 122(4), 412–419 (2000)

    Google Scholar 

  46. Wu, T., Lan, C.: A wide-range variable stiffness mechanism for semi-active vibration systems. J. Sound Vibr. 363, 18–32 (2016)

    Google Scholar 

  47. Davis, L., Carter, D., Hyde, T.: Second-generation hybrid D-strut. In: Proceedings of SPIE 2445, Smart Structures and Materials: Passive Damping, pp. 161–175, San Diego (1995)

  48. Davis, T., Davis, P., Sullivan, J., et al.: High performance passive viscous isolator element for active/passive (hybrid) isolation. In: Proceedings of of SPIE 2720, Smart Structures and Materials, pp. 281–292, San Diego (1996)

  49. Huang, X., Sun, J., Hua, H., et al.: Design scheme of a passive isotropic multi-strut vibration isolation platform constructed by three-parameter isolators based on the optimum damping frequency concept. J. Vib. Control 24(17), 3931–3943 (2018)

    MathSciNet  Google Scholar 

  50. Ruzicka, J., Derby, T.: Influence of Damping in Vibration Isolation. Shock and Vibration Information Center, Washington (1971)

    Google Scholar 

  51. Lin, Y., Cunningham, D.: Stiffness and stress of a fluid-filled circular diaphragm. In: 33rd Structures, Structural Dynamics and Materials Conference, pp. 2272, Dallas (1992)

  52. Wilson, G., Wolke, P.: Performance prediction of D-Strut isolation systems. In: Proceedings of SPIE 3045, Smart Structures and Materials: Passive Damping and Isolation, pp. 236–250, San Diego (1997)

  53. Kamesh, D., Pandiyan, P., Ghosal, A.: Passive vibration isolation of reaction wheel disturbances using a low frequency flexible space platform. J. Sound Vibr. 331(6), 1310–1330 (2012)

    Google Scholar 

  54. Brennan, M., CarRella, A., Waters, T., et al.: On the dynamic behaviour of a mass supported by a parallel combination of a spring and an elastically connected damper. J. Sound Vibr. 309(3), 83–837 (2008)

    Google Scholar 

  55. Rivin, E.: Passive Vibration Isolation. ASME Press (2003)

    Google Scholar 

  56. Zhou, W., Li, D.: Design and analysis of an intelligent vibration isolation platform for reaction/momentum wheel assemblies. J. Sound Vibr. 331(13), 2984–3005 (2012)

    MathSciNet  Google Scholar 

  57. Lu, Z.Q., Gu, D.H., Ding, H., et al.: Nonlinear vibration isolation via a circular ring. Mech. Syst. Signal Process. 136, 106490 (2020)

    Google Scholar 

  58. Carrella, A., Brennan, M., Waters, T.: Optimization of a quasi-zero-stiffness isolator. J. Mech. Sci. Technol. 21(6), 946–949 (2007)

    Google Scholar 

  59. Kovacic, I., Brennan, M., Waters, T.: A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic. J. Sound Vibr. 315(3), 700–711 (2008)

    Google Scholar 

  60. Liu, C., Yu, K.: A high-static–low-dynamic-stiffness vibration isolator with the auxiliary system. Nonlinear Dyn. 94(3), 1549–1567 (2018)

    MathSciNet  Google Scholar 

  61. Wang, K., Zhou, J., Chang, Y., et al.: A nonlinear ultra-low-frequency vibration isolator with dual quasi-zero-stiffness mechanism. Nonlinear Dyn. 101(2), 755–773 (2020)

    Google Scholar 

  62. Lu, Z.Q., Wu, D., Ding, H., et al.: Vibration isolation and energy harvesting integrated in a Stewart platform with high static and low dynamic stiffness. Appl. Math. Model. 89, 249–267 (2021)

    MathSciNet  MATH  Google Scholar 

  63. Lee, C., Goverdovskiy, V., Samoilenko, S.: Prediction of non-chaotic motion of the elastic system with small stiffness. J. Sound Vibr. 272(3), 643–655 (2004)

    Google Scholar 

  64. Carrella, A., Brennan, M., Waters, T.: Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. J. Sound Vibr. 301(3), 678–689 (2007)

    Google Scholar 

  65. Liu, C., Tang, J., Yu, K., et al.: On the characteristics of a quasi-zero-stiffness vibration isolator with viscoelastic damper. Appl. Math. Model. 88, 367–381 (2020)

    MathSciNet  MATH  Google Scholar 

  66. Liu, C., Yu, K.: Accurate modeling and analysis of a typical nonlinear vibration isolator with quasi-zero stiffness. Nonlinear Dyn. 100(3), 2141–2165 (2020)

    Google Scholar 

  67. Liu, C., Yu, K., Tang, J.: New insights into the damping characteristics of a typical quasi-zero-stiffness vibration isolator. Int. J. Mech. Sci. 124, 103511 (2020)

    Google Scholar 

  68. Le, T., Ahan, K.: A vibration isolation system in low frequency excitation region using negative stiffness structure for vehicle seat. J. Sound Vibr. 330(26), 6311–6335 (2011)

    Google Scholar 

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

    Google Scholar 

  70. Le, T., Ahan, K.: Active pneumatic vibration isolation system using negative stiffness structures for a vehicle seat. J. Sound Vibr. 333(5), 1245–1268 (2014)

    Google Scholar 

  71. Liu, X., Huang, X., Hua, X.: On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector. J. Sound Vibr. 332(14), 3359–3376 (2013)

    Google Scholar 

  72. Zhou, X., Zhao, D., Xiao, X., et al.: An asymmetric quasi-zero stiffness vibration isolator with long stroke and large bearing capacity. Nonlinear Dyn. 108(3), 1903–1930 (2022)

    Google Scholar 

  73. Chen, C., Li, S., Wang, Y., et al.: Force and displacement transmissibility of a quasi-zero stiffness vibration isolator with geometric nonlinear damping. Nonlinear Dyn. 87(4), 2267–2279 (2017)

    Google Scholar 

  74. Sun, X., Jing, X., Xu, J., et al.: Vibration isolation via a scissor-like structured platform. J. Sound Vibr. 333(9), 2404–2420 (2014)

    Google Scholar 

  75. Han, H., Sorokin, V., Tang, L., et al.: A nonlinear vibration isolator with quasi-zero-stiffness inspired by Miura-origami tube. Nonlinear Dyn. 105(2), 1313–1325 (2021)

    Google Scholar 

  76. Ye, K., Ji, J.: An origami inspired quasi-zero stiffness vibration isolator using a novel truss-spring based stack Miura-ori structure. Mech. Syst. Signal Proc. 165, 108383 (2022)

    Google Scholar 

  77. Ahn, H.: Performance limit of a passive vertical isolator using a negative stiffness mechanism. J. Mech. Sci. Technol. 22(6), 2357–2364 (2008)

    Google Scholar 

  78. Trung, P., Kim, K., Ahn, H.: A nonlinear control of an QZS isolator with flexures based on a lyapunov function. Int. J. Precis. Eng. Manuf. 14(6), 919–924 (2013)

    Google Scholar 

  79. Kim, K., You, Y., Ahn, H.: Optimal design of a QZS isolator using flexures for a wide range of payload. Int. J. Precis. Eng. Manuf. 14(6), 911–917 (2013)

    Google Scholar 

  80. Liu, Y., Xu, L., Song, C., et al.: Dynamic characteristics of a quasi-zero stiffness vibration isolator with nonlinear stiffness and damping. Arch. Appl. Mech. 89(9), 1743–1759 (2019)

    Google Scholar 

  81. Sun, M., Song, G., Li, Y., et al.: Effect of negative stiffness mechanism in a vibration isolator with asymmetric and high-static-low-dynamic stiffness. Mech. Syst. Signal Proc. 124, 388–407 (2019)

    Google Scholar 

  82. Zuo, S., Wang, D., Zhang, Y., et al.: Design and testing of a parabolic cam-roller quasi-zero-stiffness vibration isolator. Int. J. Mech. Sci. 220, 107146 (2020)

    Google Scholar 

  83. Li, M., Cheng, W., Xie, R.: A quasi-zero-stiffness vibration isolator using a cam mechanism with user-defined profile. Int. J. Mech. Sci. 189, 105938 (2021)

    Google Scholar 

  84. Ye, K., Ji, J., Brown, T.: A novel integrated quasi-zero stiffness vibration isolator for coupled translational and rotational vibrations. Mech. Syst. Signal Proc. 149, 10730 (2021)

    Google Scholar 

  85. Yan, G., Zou, H., Wang, S., et al.: Large stroke quasi-zero stiffness vibration isolator using three-link mechanism. J. Sound Vibr. 478, 115344 (2020)

    Google Scholar 

  86. Liu, J., Ju, L., Blair, D.: Vibration isolation performance of an ultra-low frequency folded pendulum resonator. Phys. Lett. A 228(4), 243–249 (1997)

    Google Scholar 

  87. Wang, Y., Li, H., Cheng, C., et al.: Dynamic performance analysis of a mixed-connected inerter-based quasi-zero stiffness vibration isolator. Struct. Control. Health Monit. 27(10), 1–19 (2020)

    Google Scholar 

  88. Sun, X., Jing, X.: A nonlinear vibration isolator achieving high-static-low-dynamic stiffness and tunable anti-resonance frequency band. Mech. Syst. Signal Proc. 80, 166–188 (2016)

    Google Scholar 

  89. Sun, X., Chen, L., Xu, J.: A 3-D quasi-zero-stiffness- based sensor system for absolute motion measurement and application in active vibration control. IEEE-ASME Trans. Mechatron. 20(1), 254–262 (2015)

    Google Scholar 

  90. Carrella, A., Brennan, M., Waters, T., et al.: Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness. Int. J. Mech. Sci. 55(1), 22–29 (2012)

    Google Scholar 

  91. Lu, Z., Brennan, M., Yang, T., et al.: An investigation of a two-stage nonlinear vibration isolation system. J. Sound Vibr. 332(6), 1456–1464 (2013)

    Google Scholar 

  92. Xu, J., Sun, X.: A multi-directional vibration isolator based on quasi-zero- stiffness structure and time-delayed active control. Int. J. Mech. Sci. 100(1), 126–135 (2015)

    Google Scholar 

  93. Wang, Y., Li, S., Neild, S., et al.: Comparison of the dynamic performance of nonlinear one and two degree-of-freedom vibration isolators with quasi-zero stiffness. Nonlinear Dyn. 88(1), 635–654 (2017)

    Google Scholar 

  94. Wang, X., Liu, H., Chen, Y., et al.: Beneficial stiffness design of a high-static-low-dynamic-stiffness vibration isolator based on static and dynamic analysis. Int. J. Mech. Sci. 142–143(1), 235–244 (2018)

    Google Scholar 

  95. Huang, X., Liu, X., Sun, J., et al.: Vibration isolation characteristics of a nonlinear isolator using Euler buckled beam as negative stiffness corrector: a theoretical and experimental study. J. Sound Vibr. 333, 1132–1148 (2014)

    Google Scholar 

  96. Shahraeeni, M., Sorokin, V., Mace, B., et al.: Effect of damping nonlinearity on the dynamics and performance of a quasi-zero-stiffness vibration isolator. J. Sound Vibr. 526, 116822 (2022)

    Google Scholar 

  97. Shekhar, N., Hatwal, H., Mallik, A.: Response of non-linear dissipative shock isolators. J. Sound Vibr. 214(4), 589–603 (1998)

    Google Scholar 

  98. Huang, X., Sun, J., Hua, H., et al.: The isolation performance of vibration systems with general velocity-displacement-dependent nonlinear damping under base excitation: numerical and experimental study. Nonlinear Dyn. 85(2), 777–796 (2016)

    MathSciNet  Google Scholar 

  99. Jing, X., Lang, Z., Billings, S., et al.: The parametric characteristic of frequency response functions for nonlinear systems. Int. J. Control. 79(12), 1552–1564 (2006)

    MathSciNet  MATH  Google Scholar 

  100. Lang, Z., Billings, S., Yue, R., et al.: Output frequency response function of nonlinear Volterra systems. Automatica 43(5), 805–816 (2007)

    MathSciNet  MATH  Google Scholar 

  101. Jing, X., Lang, Z., Billings, S., et al.: Frequency domain analysis for suppression of output vibration from periodic disturbance using nonlinearities. J. Sound Vibr. 314(3), 536–557 (2008)

    Google Scholar 

  102. Jing, X., Lang, Z., Billings, S.: Output frequency response function-based analysis for nonlinear Volterra systems. Mech. Syst. Signal Proc. 22(1), 102–120 (2008)

    Google Scholar 

  103. Guo, P., Lang, Z., Peng, Z.: Analysis and design of the force and displacement transmissibility of nonlinear viscous damper based vibration isolation systems. Nonlinear Dyn. 67(4), 2671–2687 (2012)

    MathSciNet  MATH  Google Scholar 

  104. Jing, X., Lang, Z.: Frequency domain analysis of a dimensionless cubic nonlinear damping system subject to harmonic input. Nonlinear Dyn. 58(3), 469–485 (2009)

    MathSciNet  MATH  Google Scholar 

  105. Lang, Z., Jing, X., Billings, S., et al.: Theoretical study of the effects of nonlinear viscous damping on vibration isolation of sdof systems. J. Sound Vibr. 323(1), 352–365 (2009)

    Google Scholar 

  106. Laalej, H., Lang, Z., Daley, S., et al.: Application of non-linear damping to vibration isolation: an experimental study. Nonlinear Dyn. 69(1–2), 409–421 (2012)

    Google Scholar 

  107. Xiao, Z., Jing, X., Cheng, L.: The transmissibility of vibration isolators with cubic nonlinear damping under both force and base excitations. J. Sound Vibr. 332(5), 1335–1354 (2013)

    Google Scholar 

  108. Peng, Z., Lang, Z., Zhao, L., et al.: The force transmissibility of MDOF structures with a non-linear viscous damping device. Int. J. Mech. Sci. 46(10), 1305–1314 (2011)

    Google Scholar 

  109. Lang, Z., Guo, P., Takewaki, I.: Output frequency response function based design of additional nonlinear viscous dampers for vibration control of multi-degree-of-freedom systems. J. Sound Vibr. 332(19), 4461–4481 (2013)

    Google Scholar 

  110. Tang, B., Brennan, M.: A Comparison of the effects of nonlinear damping on the free vibration of a single-degree-of-freedom system. J. Vib. Acoust.-Trans. ASME 34(2), 024501 (2012)

    Google Scholar 

  111. Tang, B., Brennan, M.: A comparison of two nonlinear damping mechanisms in a vibration isolator. J. Sound Vibr. 332(3), 510–520 (2013)

    Google Scholar 

  112. Sun, X., Huang, X., Liu, X., et al.: Study on the force transmissibility of vibration isolators with geometric nonlinear damping. Nonlinear Dyn. 74(4), 1103–1112 (2013)

    Google Scholar 

  113. Dong, G., Zhang, Y., Luo, Y., et al.: Enhanced isolation performance of a high-static- low-dynamic stiffness isolator with geometric nonlinear damping. Nonlinear Dyn. 93(4), 2339–2356 (2018)

    Google Scholar 

  114. Fratzl, P., Barth, F.: Biomaterial systems for mechanosensing and actuation. Nature 462(7272), 442–448 (2009)

    Google Scholar 

  115. Stroble, J., Stone, R., Watkins, S.: An overview of biomimetic sensor technology. Sens. Rev. 29(2), 112–119 (2009)

    Google Scholar 

  116. Chen, X., Yang, H., Shan, J., et al.: Bio-inspired passive optimized base-isolation system for seismic mitigation of building structures. J. Eng. Mech. 142(1), 04015061 (2016)

    Google Scholar 

  117. Sielmann, H.: My Year with the Woodpeckers. Barrie & Rockliff, London (1959)

    Google Scholar 

  118. Dai, H., Jing, X., Wang, Y., et al.: Post-capture vibration suppression of spacecraft via a bio-inspired isolation system. Mech. Syst. Signal Proc. 105, 214–240 (2018)

    Google Scholar 

  119. Wang, X., Yue, X., Dai, H., et al.: Vibration suppression for post-capture spacecraft via a novel bio-inspired Stewart isolation system. Acta Astronaut. 168, 1–22 (2020)

    Google Scholar 

  120. Yan, G., Wang, S., Zou, H., et al.: Bio-inspired polygonal skeleton structure for vibration isolation: Design, modelling, and experiment. Sci. China-Technol. Sci. 63(12), 1–14 (2020)

    Google Scholar 

  121. Deng, T., Wen, G., Ding, H., et al.: A bio-inspired isolator based on characteristics of quasi-zero stiffness and bird multi-layer neck. Mech. Syst. Signal Proc. 145, 106967 (2020)

    Google Scholar 

  122. Pan, H., Jing, X., Sun, W., et al.: A bioinspired dynamics-based adaptive tracking control for nonlinear suspension systems. IEEE Trans. Control Syst. Technol. 26(3), 903–914 (2018)

    Google Scholar 

  123. Wu, Z., Jing, X., Bian, J., et al.: Vibration isolation by exploring bio-inspired structural nonlinearity. Bioinspir. Biomim. 10(5), 056015 (2015)

    Google Scholar 

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

    Google Scholar 

  125. Feng, X., Jing, X.: Human body inspired vibration isolation: Beneficial nonlinear stiffness, nonlinear damping & nonlinear inertia. Mech. Syst. Signal Proc. 117, 786–812 (2019)

    Google Scholar 

  126. Feng, X., Jing, X., Xu, Z., et al.: Bio-inspired anti-vibration with nonlinear inertia coupling. Mech. Syst. Signal Proc. 124, 562–595 (2019)

    Google Scholar 

  127. Kim, G., Kang, J.: The V-shaped band-stop vibration isolator inspired by middle ear. Appl. Acoust. 150, 162–168 (2019)

    Google Scholar 

  128. Yoo, S., Roh, J., Kim, K.: Woodpecker-inspired shock isolation by microgranular bed. J. Phys. D-Appl. Phys. 42, 035501 (2009)

    Google Scholar 

  129. Bian, J., Jing, X.: Biomimetic design of woodpecker for shock and vibration protection. In: Proceedings of 2014 IEEE International Conference on Robotics and Biomimetics (ROBIO 2014), pp. 2238–2243, Bali (2014)

  130. Sabah, S., Kueh, A., Fasih, M.: Comparative low-velocity impact behavior of bio-inspired and conventional sandwich composite beams. Compos. Sci. Technol. 149, 64–74 (2017)

    Google Scholar 

  131. Dai, H., Jing, X., Sun, C., et al.: Accurate modeling and analysis of a bio-inspired isolation system: with application to on-orbit capture. Mech. Syst. Signal Proc. 109, 111–133 (2018)

    Google Scholar 

  132. Dai, H., Cao, X., Jing, X., et al.: Bio-inspired anti-impact manipulator for capturing non-cooperative spacecraft: theory and experiment. Mech. Syst. Signal Proc. 142, 106785 (2020)

    Google Scholar 

  133. Hu, F., Jing, X.: A 6-DOF passive vibration isolator based on Stewart structure with X-shaped legs. Nonlinear Dyn. 91(1), 157–185 (2018)

    Google Scholar 

  134. Pan, H., Jing, X., Sun, W., et al.: Analysis and design of a bioinspired vibration sensor system in noisy environment. IEEE-ASME Trans. Mechatron. 23(2), 845–855 (2018)

    Google Scholar 

  135. 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 

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

    Google Scholar 

  137. Zeng, R., Wen, G., Zhou, J., et al.: Limb-inspired bionic quasi-zero stiffness vibration isolator. Acta Mech. Sin. 37(7), 1–16 (2021)

    MathSciNet  Google Scholar 

  138. Cai, C., Zhou, J., Wu, L., et al.: Design and numerical validation of quasi-zero-stiffness metamaterials for very low-frequency band gaps. Compos. Struct. 236, 111862 (2020)

    Google Scholar 

  139. Lu, Z.Q., Zhao, L., Ding, H., et al.: A dual-functional metamaterial for integrated vibration isolation and energy harvesting. J. Sound Vib. 509, 116251 (2021)

    Google Scholar 

  140. Sun, H., Du, X., Pai, P.: Theory of metamaterial beams for broadband vibration absorption. J. Intell. Mater. Syst. Struct. 21, 1085–1101 (2010)

    Google Scholar 

  141. Liu, Z., Zhang, X., Mao, Y., et al.: Locally resonant sonic materials. Science 289(5485), 1734–1736 (2000)

    Google Scholar 

  142. Smith, D., Pendry, J., et al.: Metamaterials and negative refractive index. Science 305(5685), 788–792 (2004)

    Google Scholar 

  143. Zhu, R., Liu, X., Hu, G., et al.: A chiral elastic metamaterial beam for broadband vibration suppression. J. Sound Vibr. 333(10), 2759–2773 (2014)

    Google Scholar 

  144. Correa, D., Klatt, T., Cortes, S., et al.: Negative stiffness honeycombs for recoverable shock isolation. Rapid Prototyp. J. 21(2), 193–200 (2015)

    Google Scholar 

  145. Li, Y., Baker, E., Reissman, T., et al.: Design of mechanical metamaterials for simultaneous vibration isolation and energy harvesting. Appl. Phys. Lett. 111(25), 251903 (2017)

    Google Scholar 

  146. Jiang, H., Zhang, M., Liu, Y., et al.: Band gaps and vibration isolation of a three-dimensional metamaterial with a star structure. Materials 13(17), 3812 (2020)

    Google Scholar 

  147. Chen, D., Zi, H., Li, Y., et al.: Low frequency ship vibration isolation using the band gap concept of sandwich plate-type elastic metastructures. Ocean Eng. 235, 109460 (2021)

    Google Scholar 

  148. Ji, J., Luo, Q., Ye, K., et al.: Vibration control based metamaterials and origami structures: a state-of-the-art review. Mech. Syst. Signal Proc. 161, 107945 (2021)

    Google Scholar 

  149. Rifaie, M., Abdulhadi, H., Mian, A.: Advances in mechanical metamaterials for vibration isolation: a review. Adv. Mech. Eng. 14(3), 1–20 (2022)

    Google Scholar 

  150. Fan, L., He, Y., Chen, X., et al.: Elastic metamaterial shaft with a stacklike resonator for low-frequency vibration isolation. J. Phys. D-Appl. Phys. 53(10), 105101 (2020)

    Google Scholar 

  151. Jin, Y., Zeng, S., Wen, Z., et al.: Deep-subwavelength lightweight metastructures for low-frequency vibration isolation. Mater. Des. 215, 110499 (2022)

    Google Scholar 

  152. Fan, H., Yang, L., Tian, Y., et al.: Design of metastructures with quasi-zero dynamic stiffness for vibration isolation. Compos. Struct. 243, 112244 (2020)

    Google Scholar 

  153. Wang, Z., Zhang, Q., Zhang, K., et al.: Tunable digital metamaterial for broadband vibration isolation at low frequency. Adv. Mater. 28(44), 9857–9861 (2016)

    Google Scholar 

  154. Anvar, V.: Numerical and experimental analysis of metamaterials with quasi-zero effect for vibration isolation. AIP Conf. Proc. 1, 020061 (1859)

    Google Scholar 

  155. Jiang, T., He, Q.: Dual-directionally tunable metamaterial for low-frequency vibration isolation. Appl. Phys. Lett. 110(2), 021907 (2017)

    Google Scholar 

  156. Li, Y., Zi, H., Wu, X., et al.: Flexural wave propagation and vibration isolation characteristics of sandwich plate-type elastic metamaterials. J. Vib. Control 27(13–14), 1443–1452 (2021)

    MathSciNet  Google Scholar 

  157. Dalela, S., Balaji, P., Jena, D.: Design of a metastructure for vibration isolation with quasizero-stiffness characteristics using bistable curved beam. Nonlinear Dyn. 108, 1931–1971 (2022)

    Google Scholar 

  158. Xu, X., Barnhart, M., Li, X., et al.: Tailoring vibration suppression bands with hierarchical metamaterials containing local resonators. J. Sound Vibr. 442, 237–248 (2019)

    Google Scholar 

  159. Zhang, Q., Guo, D., Hu, G.: Tailored mechanical metamaterials with programmable quasi-zero-stiffness features for full-band vibration isolation. Adv. Funct. Mater. 31(33), 2101428 (2021)

    Google Scholar 

  160. Li, C., Jiang, T., He, Q., et al.: Stiffness-mass-coding metamaterial with broadband tunability for low-frequency vibration isolation. J. Sound Vibr. 489, 115685 (2020)

    Google Scholar 

  161. Tany, A., Meurersy, T., Veresy, S., et al.: Robust control of microvibrations with experimental verification. Proc. Inst. Mech. Eng. Part C-J. Eng. Mech. Eng. Sci. 219(5), 435–460 (2005)

    Google Scholar 

  162. Grodsinsky, C., Whorton, M.: Survey of active vibration isolation systems for microgravity applications. J. Spacecr. Rockets 37(5), 586–596 (2000)

    Google Scholar 

  163. Labib, M., Piontek, D., Valsecchi, N., et al.: The Fluid Science Laboratory’s Microgravity Vibration Isolation Subsystem Overview and Commissioning Update. SpaceOps Conference, Huntsville (2007)

    Google Scholar 

  164. Liu, W., Zhang, Y., Li, Z., et al.: Control performance simulation and tests for microgravity active vibration isolation system onboard the tianzhou-1 cargo spacecraft. Astrodynamics 2(4), 339–360 (2018)

    Google Scholar 

  165. Jackson, M., Kim, Y., Whorton, M.: Design and analysis of the g-limit baseline vibration isolation control system. In: Proceedings of AIAA Guidance, Navigation, and Control Conference, pp. 1–7, Monterey (2002)

  166. Gong, Z., Ding, L., Yue, H., et al.: System integration and control design of a maglev platform for space vibration isolation. J. Vib. Control 0(0), 1–17 (2019)

    MathSciNet  Google Scholar 

  167. Edberg, D., Boucher, R., Schenck, D., et al.: Results of the stable microgravity vibration isolation flight experiment. In: 19th American Astronautical Society Guidance and Control Conference, pp. 567–581, San Diego (1996)

  168. DeLombard, R., Bushnell, G., Edberg, D., et al.: Microgravity environment countermeasures -panel discussion. In: The 35th Aerospace Sciences Meeting & Exhibit, Reno, pp. 1–7 (1997)

  169. Edberg, D., Boucher, R., Nurre, G., et al.: Performance assessment of the STABLE microgravity vibration isolation flight demonstration. In: Proceedings of 38th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA, pp. 1478–1485, Reston

  170. Nurre, G., Whorton, M., Kim, Y.: A treetops simulation of the stable microgravity vibration isolation system. In: NASA Technical Memorandum, pp. 209009 (1999)

  171. Whorton, M.: Survey of Microgravity Vibration Isolation Systems, Microgravity Environment Interpretation Tutorial (MEIT); Glenn Research Center, Cleveland (2004)

    Google Scholar 

  172. Whorton, M.: Microgravity Vibration Isolation for the International Space Station, pp. 605–610. American Institute of Physics, USA (2000)

    Google Scholar 

  173. Whorton, M.: g-LIMIT: a microgravity vibration isolation system for the international space station. In: Conference and Exhibit on International Space Station Utilization, Cape Canaveral, pp. 5090 (2001)

  174. Whorton, M.: Robust control for microgravity vibration isolation. J. Spacecr. Rockets 42(1), 12–160 (2005)

    Google Scholar 

  175. Tryggvason, B., Stewart, W., De. C., et al.: Acceleration levels and operation of the microgravity vibration isolation mount (MIM) on the shuttle and the MIR space station. In: 37th Aerospace Sciences Meeting and Exhibit, pp. 578, Reno (1999)

  176. Tryggvason, B.: The microgravity vibration isolation mount (MIM) development and flight test results. In: 48th International Astronautical Congress, Turin (1997)

  177. Duval, W., Tryggvason, B.: Effects of G-jitter on interfacial dynamics of two miscible liquids: application of MIM. In: NASA Center for Aerospace Information, NASA/TM2000-209789 (2000)

  178. Casgrain, C., Dejmek, M., Ruel, S., et al.: The Canadian space agency microgravity sciences program overview. In: Proceedings of 42nd AIAA Aerospace Sciences Meeting and Exhibit (2004)

  179. Zhang, Y., Dong, W., Liu, W., et al.: Verification of the microgravity active vibration isolation system based on air floating platform and parabolic flight. In: AIAA SPACE, pp. 5297, Long Beach (2016)

  180. Zhang, Y., Dong, W., Liu, W., et al.: Verification of the microgravity active vibration isolation system based on parabolic flight. Microgravity Sci. Technol. 29(6), 415–426 (2017)

    Google Scholar 

  181. Liu, W., Gao, Y., Dong, W., et al.: Flight test results of the microgravity active vibration isolation system in china’s tianzhou-1 mission. Microgravity Sci. Technol. 30(6), 995–1009 (2018)

    Google Scholar 

  182. Dong, W., Duan, W., Liu, W., et al.: Microgravity disturbance analysis on Chinese space laboratory. NPJ Microgravity 5(1), 1–6 (2019)

    Google Scholar 

  183. Gong, Z., Ding, L., Li, S., et al.: Payload-agnostic decoupling and hybrid vibration isolation control for a maglev platform with redundant actuation. Mech. Syst. Signal Proc. 146, 106985 (2021)

    Google Scholar 

  184. Gong, Z., Ding, L., Xing, H., et al.: Suppression in any configuration: a versatile coupling improved multi-objective manipulation framework for modular active vibration isolation system. Mech. Syst. Signal Proc. 166, 108478 (2022)

    Google Scholar 

  185. Stewart, D.: A platform with six degrees of freedom. Proc. Inst. Mech. Eng. 180(1), 371–386 (1965)

    Google Scholar 

  186. Spanos, J., Rahman, Z., Blackwood, G.: A soft 6-axis active vibration isolator. In: Proceedings of American Control Conference, pp. 412–416, Seattle (1995)

  187. Hanieh, A.: Active isolation and damping of vibrations via Stewart platform, Ph.D. thesis (2003)

  188. Wang, X., Xie, X., Chen, Y., et al.: Investigation on active vibration isolation of a Stewart platform with piezoelectric actuators. J. Sound Vibr. 383, 1–19 (2016)

    Google Scholar 

  189. Hanieh, A., Preumont, A., Loix, N.: Piezoelectric Stewart platform for general purpose active damping interface and precision control. In: Proceedings of European Space Mechanisms & Tribology Symposium, pp. 331–334 (2001)

  190. Preumont, P., Horodinca, M., Romanescu, I.: A six-axis single-stage active vibration isolator based on Stewart platform. J. Sound Vibr. 300, 644–661 (2007)

    Google Scholar 

  191. Defendini, A., Vaillon, L., Trouve, F., et al.: Technology predevelopment for active control of vibration and very high accuracy pointing systems. In: Proceedings of 4th ESA International Conference of Spacecraft Guidance, Navigation and Control Systems, pp. 385–391, Noordwijk (2000)

  192. Fan, S., Cao, L.: The development of micro-vibration for satellite. In: 8th International Symposium on Precision Engineering Measurement and Instrumentation, pp. 87590–87597, Chengdu (2013)

  193. Vaillon, L., Sanctorum, B., Sperandei, J., et al.: Flight prototyping of active control of vibration & very high accuracy pointing systems. In: Proceedings of 5th ESA International Conference on Spacecraft Guidance, Frascati (2002)

  194. Anderson, E., Cash, M., Janzen, P., et al.: Precision, range, bandwidth, and other tradeoffs in hexapods with application to large ground-based telescopes. In: Proceedings of SPIE, the International Society for Optical Engineering, pp. 62731F–62731F-17 (2006)

  195. Hall, J., Pettit, G., Lindler, J., et al.: Compact lightweight six-axis point-and-hold positioning system. In: Smart Structures and Materials 2003: Industrial and Commercial Applications of Smart Structures Technologies, SPIE, 5054, pp. 287–300 (2003)

  196. Anderson, E., Fumo, J., Erwin, R.: Satellite ultraquiet isolation technology experiment (SUITE). 2000 IEEE aerospace conference. Proceedings (Cat. No. 00TH8484). IEEE 4, 299–313 (2000)

    Google Scholar 

  197. Anderson, E., Cash, M., Hall, J., et al.: Hexapods for precision motion and vibration control. In: American Society for Precision Engineering, Control of Precision Systems, pp. 1–5 (2004)

  198. Babuska, V., Erwin, R., Sullivan, L.: System identification of the suite isolation platform: comparison of ground and flight experiments. In: 44th AIAA Structures, Structural Dynamics, and Materials Conference, pp. 2185–2195, Reston (2003)

  199. Bushnell, G., Becraft, M.: Flight test of an international space station active rack isolation prototype system. Smart Mater. Struct. 8(6), 791–797 (1999)

    Google Scholar 

  200. Liu, J., Li, Y., Zhang, Y., et al.: Dynamics and control of a parallel mechanism for active vibration isolation in space station. Nonlinear Dyn. 76(3), 1737–1751 (2014)

    MathSciNet  Google Scholar 

  201. Bushnell, G., Becraft, M.: Microgravity performance flight characterization of an international space station active rack isolation prototype system. In: Proceedings of 16th IEEE Instrumentation and Measurement Technology Conference, Inst. of Electrical and Electronics Engineers, Piscataway (1999)

  202. Thayer, D., Campbell, M., Vagners, J., et al.: Six-axis vibration isolation system using soft actuators and multiple sensors. J. Spacecr. Rockets 39(2), 206–212 (2002)

    Google Scholar 

  203. Hauge, G., Campbell, M.: Sensors and control of a space-based six-axis vibration isolation system. J. Sound Vibr. 269(3), 913–931 (2004)

    Google Scholar 

  204. Neat, G., Melody, J., Lurie, B.: Vibration attenuation approach for spaceborne optical interferometers. IEEE Trans. Control Syst. Technol. 6(6), 689–700 (1998)

    Google Scholar 

  205. Lee, D., Park, G., Han, J.: Hybrid isolation of micro vibrations induced by reaction wheels. J. Sound Vibr. 363, 1–17 (2016)

    Google Scholar 

  206. Wang, X., Wu, H., Yang, B.: Micro-vibration suppressing using electromagnetic absorber and magnetostrictive isolator combined platform. Mech. Syst. Signal Proc. 139, 106606 (2020)

    Google Scholar 

  207. Kim, M., Kim, H., Gweon, D.: Design and optimization of voice coil actuator for six degree of freedom active vibration isolation system using Halbach magnet array. Rev. Sci. Instrum. 83(10), 105117 (2012)

    Google Scholar 

  208. Kim, Y., Kim, S., Park, P.: Magnetic force driven six degree-of-freedom active vibration isolation system using a phase compensated velocity sensor. Rev. Sci. Instrum. 80(4), 045108 (2009)

    Google Scholar 

  209. Li, W., Huang, H., Zhou, X., et al.: Design and experiments of an active isolator for satellite micro-vibration. Chin. J. Aeronaut. 27(6), 1461–1468 (2014)

    Google Scholar 

  210. Kim, M., Kim, H., Kim, H., et al.: Design and control of a 6-DOF active vibration isolation system using a halbach magnet array. IEEE-ASME Trans. Mechatron. 21(4), 2185–2196 (2016)

    MathSciNet  Google Scholar 

  211. Hong, J., Park, K.: Design and control of six degree-of-freedom active vibration isolation table. Rev. Sci. Instrum. 81(3), 035106 (2010)

    Google Scholar 

  212. Brien, J., Neat, G.: Micro-precision interferometer: pointing control system. In: Proceedings of 4th IEEE Conference on Control Applications, Albany, pp. 464–469, New York (1995)

  213. Nakamura, Y., Nakayama, M., Yasuda, M., et al.: Development of active six-degrees-of-freedom micro-vibration control system using hybrid actuators comprising air actuators and giant magnetostrictive actuators. Smart Mater. Struct. 15(4), 1133–1142 (2006)

    Google Scholar 

  214. Kamesh, D., Pandiyan, R., Ghosal, A.: Modeling, design and analysis of low frequency platform for attenuating micro-vibration in spacecraft. J. Sound Vibr. 329(17), 3431–3450 (2010)

    Google Scholar 

  215. Wang, C., Chen, Y., Zhang, Z.: Simulation and experiment on the performance of a passive/active micro-vibration isolator. J. Vib. Control 24(3), 453–465 (2018)

    Google Scholar 

  216. Lesieutre, G.: Vibration damping and control using shunted piezoelectric materials. Shock Vib. Digest 30(3), 187–195 (1998)

    Google Scholar 

  217. Halbach, K.: Design of permanent multipole magnets with oriented rare earth cobalt material. Nucl. Instrum. Methods 169(3), 1–10 (1980)

    Google Scholar 

  218. Oh, H., Onoda, J.: An experimental study of a semiactive magneto-rheological fluid variable damper for vibration suppression of truss structures. Smart Mater. Struct. 11(1), 156–162 (2002)

    Google Scholar 

  219. Oh, H.: Experimental demonstration of an improved magneto-rheological fluid damper for suppression of vibration of a space flexible structure. Smart Mater. Struct. 13(5), 1238–1244 (2004)

    Google Scholar 

  220. Gavin, H., Alhan, C.: Guidelines for low-transmissibility semi-active vibration isolation. Smart Mater. Struct. 14(2), 297–306 (2005)

    Google Scholar 

  221. Oh, H., Onoda, J., Minesugi, K.: Semiactive isolator with liquid-crystal type ER fluid for momentum-wheel vibration isolation. J. Vib. Acoust. 126(2), 272–277 (2004)

    Google Scholar 

  222. Klass, D., Martinek, T.: Electroviscous fluids I. Rheological properties. J. Appl. Phys. 38(1), 67–74 (1967)

    Google Scholar 

  223. Gavin, H., Hanson, R., Filisko, F.: Electrorheological dampers: part II: testing and modeling. J. Appl. Mech. 63, 676–682 (1996)

    Google Scholar 

  224. Onoda, J., Oh, H., Minesugi, K.: Semiactive vibration suppression with electrorheological-fluid dampers. AIAA J. 35(12), 1844–1852 (1997)

    Google Scholar 

  225. Huang, Y., Sun, Y., Ding, J., et al.: Design and analysis of a stiffness and damping regulator based on giant electrorheological fluid under multilayered squeeze mode. J. Sound Vibr. 527, 116864 (2022)

    Google Scholar 

  226. Sun, Y., Huang, Y., Wang, M., et al.: Design, testing and modelling of a tuneable GER fluid damper under shear mode. Smart Mater. Struct. 29(8), 085011 (2020)

    Google Scholar 

  227. Choi, Y., Wereley, N., Jeon, Y.: Semi-active vibration isolation using magnetorheological isolators. J. Aircr. 42(5), 1244–1251 (2005)

    Google Scholar 

  228. Bai, X., Wereley, N., Hu, W.: Maximizing semi-active vibration isolation utilizing a magnetorheological damper with an inner bypass configuration. J. Appl. Phys. 117(17), 17C711 (2015)

    Google Scholar 

  229. Zhu, X., Jing, X., Cheng, L.: Magnetorheological fluid dampers: a review on structure design and analysis. J. Intell. Mater. Syst. Struct. 23(8), 839–873 (2012)

    Google Scholar 

  230. Goldasz, J., Alexandridis, A.: Medium-and high-frequency analysis of magnetorheological fluid dampers. J. Vib. Control 18(14), 2140–2148 (2011)

    Google Scholar 

  231. Oh, H.: Characteristics of a magneto-rheological fluid isolator obtained by permanent magnet arrangements. Smart Mater. Struct. 13(3), N29–N35 (2004)

    Google Scholar 

  232. Zhu, X., Jing, X., Cheng, L.: A magnetorheological fluid embedded pneumatic vibration isolator allowing independently adjustable stiffness and damping. Smart Mater. Struct. 20(8), 085025 (2011)

    Google Scholar 

  233. Zhu, X., Jing, X., Cheng, L.: Systematic design of a magnetorheological fluid embedded pneumatic vibration isolator subject to practical constraints. Smart Mater. Struct. 21(3), 035006 (2012)

    Google Scholar 

  234. Zhu, X., Jing, X., Cheng, X.: Optimal design of control valves in magneto-rheological fluid dampers using a non-dimensional analytical method. J. Intell. Mater. Syst. Struct. 24(1), 108–129 (2013)

    Google Scholar 

  235. Zapateiro, M., Pozo, F., Karimi, H., et al.: Semiactive control methodologies for suspension control with magnetorheological dampers. IEEE-ASME Trans. Mechatron. 17(2), 370–380 (2012)

    Google Scholar 

  236. Fallah, M., Bhat, R., Xie, W.: Optimized control of semiactive suspension systems using H ∞ robust control theory and current signal estimation. IEEE-ASME Trans. Mechatron. 17(4), 767–778 (2012)

    Google Scholar 

  237. Yang, J., Ning, D., Sun, S., et al.: A semi-active suspension using a magnetorheological damper with nonlinear negative-stiffness component. Mech. Syst. Signal Proc. 147, 107071 (2021)

    Google Scholar 

  238. Choi, S., Hong, S., Sung, K., et al.: Optimal control of structural vibrations using a mixed-mode magnetorheological fluid mount. Int. J. Mech. Sci. 50(3), 559–568 (2008)

    Google Scholar 

  239. Uchino, K., Sugiura, T.: Experimental study on oscillation amplitude reduction of a superconducting levitation system by an electromagnetic shunt damper. IEEE Trans. Appl. Supercond. 29(5), 3602704 (2019)

    Google Scholar 

  240. Behrens, S., Fleming, A., Moheimani, S.: Passive vibration control via electromagnetic shunt damping. IEEE-ASME Trans. Mechatron. 10(1), 118–122 (2005)

    Google Scholar 

  241. Niederberger, D., Behrens, S., Fleming, A., et al.: Adaptive electromagnetic shunt damping. IEEE-ASME Trans. Mechatron. 11(1), 13–108 (2006)

    Google Scholar 

  242. Efren, D., Rizzo, R., Jesus, G., et al.: Review of passive electromagnetic devices for vibration damping and isolation. Shock. Vib. (2019). https://doi.org/10.1155/2019/9139067

    Article  Google Scholar 

  243. Stabile, A., Aglietti, G., Richardson, G., et al.: Design and verification of a negative resistance electromagnetic shunt damper for spacecraft micro-vibration. J. Sound Vibr. 386, 38–49 (2017)

    Google Scholar 

  244. Sasaki, M., Sugiura, T.: Vibration reduction of rotor supported by superconducting magnetic bearing utilizing electromagnetic shunt damper. IEEE Trans. Appl. Supercond. 26(3), 8801204 (2016)

    Google Scholar 

  245. Sasaki, M., Kimura, J., Sugiura, T.: Vibration suppression in high-tc superconducting levitation system utilizing nonlinearly coupled electromagnetic shunt damper. IEEE Trans. Appl. Supercond. 25(3), 3700605 (2015)

    Google Scholar 

  246. Zhang, P., Deng, Z., Liang, L., et al.: Vibration Suppression of HTS maglev system based on negative resistance electromagnetic shunt damper. IEEE Trans. Appl. Supercond. 32(6), 3601005 (2022)

    Google Scholar 

  247. Ao, W., Reynolds, P.: Evaluation of optimal analysis, design, and testing of electromagnetic shunt damper for vibration control of a civil structure. Struct. Control. Health Monit. 27(3), 1–27 (2020)

    Google Scholar 

  248. Ma, H., Yan, B., Zhang, L., et al.: On the design of nonlinear damping with electromagnetic shunt damping. Int. J. Mech. Sci. 175, 105513 (2020)

    Google Scholar 

  249. Yan, B., Ma, H., Zheng, W., et al.: Nonlinear electromagnetic shunt damping for nonlinear vibration isolators. IEEE-ASME Trans. Mechatron. 24(4), 1851–1860 (2019)

    Google Scholar 

  250. Yan, B., Ma, H., Zhang, L., et al.: A bistable vibration isolator with nonlinear electromagnetic shunt damping. J. Sound Vibr. 136, 106504 (2020)

    Google Scholar 

  251. Cheng, T., Oh, I.: Vibration suppression of flexible beam using electromagnetic shunt damper. IEEE Trans. Magn. 45(6), 2758–2761 (2009)

    Google Scholar 

  252. Cheng, T., Oh, I.: A current-flowing electromagnetic shunt damper for multi-mode vibration control of cantilever beams. Smart Mater. Struct. 18, 095036 (2009)

    Google Scholar 

  253. Cheng, T., Oh, I.: Coil-based electromagnetic damper and actuator for vibration suppression of cantilever beams. J. Intell. Mater. Syst. Struct. 20, 2237–2247 (2009)

    Google Scholar 

  254. Jung, J., Cheng, T., Oh, I.: Electromagnetic synchronized switch damping for vibration control of flexible beams. IEEE-ASME Trans. Mechatron. 17(6), 1031–1038 (2012)

    Google Scholar 

  255. Bronowicki, A., Abhyankar, N., Griffin, S.: Active vibration control of large optical space structures. Smart Mater. Struct. 8(6), 740–752 (1999)

    Google Scholar 

  256. Clark, W.: Vibration control with state-switched piezoelectric materials. J. Intell. Mater. Syst. Struct. 11(4), 263–271 (2000)

    Google Scholar 

  257. Ji, H., Qiu, J., Badel, A., et al.: Semi-active vibration control of a composite beam by adaptive synchronized switching on voltage sources based on LMS algorithm. J. Intell. Mater. Syst. Struct. 20(8), 939–947 (2009)

    Google Scholar 

  258. Ji, H., Qiu, J., Badel, A., et al.: Semi-active vibration control of a composite beam using an adaptive SSDV approach. J. Intell. Mater. Syst. Struct. 20(4), 401–412 (2009)

    Google Scholar 

  259. Onoda, J., Makihara, K., Minesugi, K.: Energy-recycling semi-active method for vibration suppression with piezoelectric transducers. AIAA J. 41(4), 711–719 (2003)

    Google Scholar 

  260. Makihara, K., Onoda, J., Minesugi, K.: Novel approach to self-sensing actuation for semi-active vibration suppression. AIAA J. 44(7), 1445–1453 (2006)

    Google Scholar 

  261. Onoda, J., Shimose, S., Minesugi, K.: Optimal configuration and combination of piezoelectric transducer and inductor for synchronized-switch-damping-on-an-inductor technique. J. Intell. Mater. Syst. Struct. 28(7), 888–906 (2017)

    Google Scholar 

  262. Oh, H., Izawa, K., Taniwaki, S.: Development of variable-damping isolator using bio-metal fiber for reaction wheel vibration isolation. Smart Mater. Struct. 14(5), 928–933 (2005)

    Google Scholar 

  263. Oh, H., Taniwaki, S., Kinjyo, N., et al.: Flywheel vibration isolation test using a variable-damping isolator. Smart Mater. Struct. 15(2), 365–370 (2006)

    Google Scholar 

  264. Oh, H., Choi, Y.: Enhancement of pointing performance by semi-active variable damping isolator with strategies for attenuating chattering effects. Sens. Actuator A-Phys. 165(2), 385–391 (2011)

    Google Scholar 

  265. Onoda, J., Sano, T., Kamiyama, K.: Active, passive, and semiactive vibration suppression by stiffness variation. AIAA J. 30(12), 2922–2929 (1992)

    Google Scholar 

  266. Corr, L., Clark, W.: Energy dissipation analysis of piezoceramic semi-active vibration control. J. Intell. Mater. Syst. Struct. 12(11), 729–736 (2001)

    Google Scholar 

  267. Jalili, N.: A comparative study and analysis of semi-active vibration-control systems. J. Vib. Acoust.-Trans. ASME 124(4), 593–605 (2002)

    MathSciNet  Google Scholar 

  268. Pu, H., Luo, X., Chen, X.: Modeling and analysis of dual-chamber pneumatic spring with adjustable damping for precision vibration isolation. J. Sound Vibr. 330(15), 3578–3590 (2011)

    Google Scholar 

  269. Liu, S., Feng, L., Zhao, D., et al.: A real-time controllable electromagnetic vibration isolator based on magnetorheological elastomer with quasi-zero stiffness characteristic. Smart Mater. Struct. 28(8), 085037 (2019)

    Google Scholar 

  270. Chen, Z., Sun, S., Deng, L., et al.: Investigation of a new metamaterial magnetorheological elastomer isolator with tunable vibration bandgaps. Mech. Syst. Signal Proc. 170, 108806 (2022)

    Google Scholar 

  271. Zhao, Y., Meng, G.: A bio-inspired semi-active vibration isolator with variable-stiffness dielectric elastomer: design and modeling. J. Sound Vibr. 485, 115592 (2020)

    Google Scholar 

  272. Shan, Y., Wu, W., Chen, X.: Design of a miniaturized pneumatic vibration isolator with high-static-low-dynamic stiffness. J. Vib. Acoust.-Trans. ASME 137(4), 045001 (2015)

    Google Scholar 

  273. Lee, J., Kim, K.: Modeling of nonlinear complex stiffness of dual-chamber pneumatic spring for precision vibration isolations. J. Sound Vibr. 301(3), 909–926 (2007)

    Google Scholar 

  274. Mikulowski, G.: Vibration isolation concept by switchable stiffness on a semi-active pneumatic actuator. Smart Mater. Struct. 30(7), 075019 (2021)

    Google Scholar 

  275. Lee, J., Kim, K.: A method of transmissibility design for dual-chamber pneumatic vibration isolator. J. Sound Vibr. 323(1), 67–92 (2009)

    Google Scholar 

  276. Zhou, N., Liu, K.: A tunable high-static-low-dynamic stiffness vibration isolator. J. Sound Vibr. 329(9), 1254–1273 (2010)

    Google Scholar 

  277. Pu, H., Yuan, S., Peng, Y., et al.: Multi-layer electromagnetic spring with tunable negative stiffness for semi-active vibration isolation. Mech. Syst. Signal Proc. 121, 942–960 (2019)

    Google Scholar 

  278. Hoque, M., Mizuno, T., Ishino, Y., et al.: A three-axis vibration isolation system using modified zero-power controller with parallel mechanism technique. Mechatronics 21, 1055–1062 (2011)

    Google Scholar 

  279. Zhang, F., Shao, S., Tian, Z., et al.: Active-passive hybrid vibration isolation with magnetic negative stiffness isolator based on Maxwell normal stress. Mech. Syst. Signal Proc. 123, 244–263 (2019)

    Google Scholar 

  280. Opie, S., Yim, S.: Design and control of a real-time variable stiffness vibration isolator. In: IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Singapore, pp.380–385 (2009)

  281. Du, H., Li, W., Zhang, N.: Semi-active variable stiffness vibration control of vehicle seat suspension using an MR elastomer isolator. Smart Mater. Struct. 20(10), 105003 (2011)

    Google Scholar 

  282. Rigbi, Z., Jilken, L.: The response of an elastomer filled with soft ferrite to mechanical and magnetic influences. J. Magn. Magn. Mater. 37(3), 267–276 (1983)

    Google Scholar 

  283. Fu, J., Li, P., Wang, Y., et al.: Model-free fuzzy control of a magnetorheological elastomer vibration isolation system: analysis and experimental evaluation. Smart Mater. Struct. 25(3), 035030 (2016)

    Google Scholar 

  284. Leng, D., Sun, S., Xu, K., et al.: A physical model of magnetorheological elastomer isolator and its dynamic analysis. J. Intell. Mater. Syst. Struct. 31(9), 1141–1156 (2020)

    Google Scholar 

  285. Fu, J., Lai, J., Liao, G., et al.: Genetic algorithm based nonlinear self-tuning fuzzy control for time-varying sinusoidal vibration of a magnetorheological elastomer vibration isolation system. Smart Mater. Struct. 27, 085010 (2018)

    Google Scholar 

  286. Xing, Z., Yu, M., Sun, S., et al.: A hybrid magnetorheological elastomer-fluid (MRE-F) isolation mount: development and experimental validation. Smart Mater. Struct. 25(1), 015026 (2016)

    Google Scholar 

  287. Yu, J., Dong, X., Qi, S., et al.: Development of a magnetorheological isolator with variable damping and variable stiffness for broadband vibration suppression. Smart Mater. Struct. 30(2), 025023 (2021)

    Google Scholar 

  288. Xu, Z., Suo, S., Lu, Y.: Vibration control of platform structures with magnetorheological elastomer isolators based on an improved SAVS law. Smart Mater. Struct. 25, 065002 (2016)

    Google Scholar 

  289. Fu, F., Li, P., Liao, G., et al.: Development and dynamic characterization of a mixed mode magnetorheological elastomer isolator. IEEE Trans. Magn. 53(1), 2800104 (2017)

    Google Scholar 

  290. Behrooz, M., Wang, X., Gordaninejad, F.: Performance of a new magnetorheological elastomer isolation system. Smart Mater. Struct. 23(4), 045014 (2014)

    Google Scholar 

  291. Yang, J., Sun, S., Tian, T., et al.: Development of a novel multi-layer MRE isolator for suppression of building vibrations under seismic events. Mech. Syst. Signal Proc. 70–71, 811–820 (2016)

    Google Scholar 

  292. Fu, J., Bai, J., Lai, J., et al.: Adaptive fuzzy control of a magnetorheological elastomer vibration isolation system with time-varying sinusoidal excitations. J. Sound Vibr. 456, 386–406 (2019)

    Google Scholar 

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Acknowledgements

The study was supported by the National Key R&D Program of China (Grant No. 2022YFC2204203, Grant No. 2020YFB2007302), the National Natural Science Foundation of China (Grant No.52075193). Simultaneously, the authors also thank the handling editors and anonymous reviewers for your time and effort in reviewing this paper.

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Yuan, Z., Zhang, Z., Zeng, L. et al. Microvibration isolation in sensitive payloads: methodology and design. Nonlinear Dyn 111, 19563–19611 (2023). https://doi.org/10.1007/s11071-023-08943-4

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