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The nonlinear dynamic analysis of optimum nonlinear inertial amplifier base isolators for vibration isolation

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Abstract

The nonlinear inertial amplifier base isolators (NIABI) for dynamic response mitigation of structures are introduced in this paper. The nonlinear inertial amplifiers are installed inside the core of the traditional base isolators (TBI) to upgrade their vibration reduction capacity. The equivalent linearization method applies to linearize each element from highly nonlinear equations of motion of nonlinear NIABI to derive the optimal closed-form solutions for nonlinear NIABI. Therefore, \(H_{2}\) and \(H_{\infty }\) optimization methods are applied to derive the exact closed-form expressions for optimal design parameters of NIABI, linearized NIABI, and TBI analytically. Initially, the dynamic responses of the structures isolated by the NIABI, linearized NIABI, and TBI are obtained through the transfer function formation. Thus, the dynamic response reduction capacities of \(H_2\) and \(H_\infty \) optimized NIABI are significantly \(38.55 \%\) and \(65.14 \%\) superior to the \(H_2\) and \(H_\infty \) optimized TBI. In addition, the nonlinear dynamic responses of the isolated structures are also derived analytically through the harmonic balancing method. Therefore, the dynamic response reduction capacities of \(H_{2}\) and \(H_\infty \) optimized nonlinear NIABI are significantly \(44.51 \%\), \(39.80 \%\), \(35.81 \%\) and \(90.10 \%\), \(77.49 \%\), \(67.66 \%\) superior to the \(H_{2}\) and \(H_\infty \) optimized TBI, inertial amplifier base isolator (IABI), linearized version of nonlinear inertial amplifier base isolator (linearized NIABI). The effectiveness of the optimum NIABI has been studied further by a numerical study using the Newmark-beta method with near-field earthquake base excitations (pulse records). Accordingly, the displacement and acceleration response reduction capacities of the optimum NIABI are \(14.47 \%\) and \(22.23 \%\) superior to the optimum TBI. The overall result shows that the nonlinearity of the inertial amplifiers increases the dynamic response reduction capacity of the traditional base isolators and inertial amplifier base isolators. All of the results are mathematically accurate and suitable for practical applications.

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Data availability statement

All data, models, and code generated or used during the study appear in the submitted article.

References

  1. Ebrahimi, B., Bolandhemmat, H., Khamesee, M.B., Golnaraghi, F.: A hybrid electromagnetic shock absorber for active vehicle suspension systems. Veh. Syst. Dyn. 49(1–2), 311–332 (2011)

    Google Scholar 

  2. 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 

  3. Aly, A.A., Salem, F.A.: Vehicle suspension systems control: a review. Int. J. Control Autom. Syst. 2(2), 46–54 (2013)

    Google Scholar 

  4. Esmailzadeh, E.: Optimization of pneumatic vibration isolation system for vehicle suspension (1978)

  5. Wei, X., Lui, H., Qin, Y.: Fault isolation of rail vehicle suspension systems by using similarity measure. In: Proceedings of 2011 IEEE International Conference on Service Operations, Logistics and Informatics, pp. 391–396. IEEE (2011)

  6. Tsai, H.-C.: The effect of tuned-mass dampers on the seismic response of base-isolated structures. Int. J. Solids Struct. 32(8–9), 1195–1210 (1995)

    MATH  Google Scholar 

  7. De Domenico, D., Ricciardi, G.: An enhanced base isolation system equipped with optimal tuned mass damper inerter (TMDI). Earthq. Eng. Struct. Dyn. 47(5), 1169–1192 (2018)

    Google Scholar 

  8. De Domenico, D., Impollonia, N., Ricciardi, G.: Soil-dependent optimum design of a new passive vibration control system combining seismic base isolation with tuned inerter damper. Soil Dyn. Earthq. Eng. 105, 37–53 (2018)

    Google Scholar 

  9. Touaillon, J.: Improvement in buildings, U.S. Patent No. 99,973 (1870)

  10. Han, H., Sorokin, V., Tang, L., Cao, D.: Lightweight origami isolators with deployable mechanism and quasi-zero-stiffness property. Aerosp. Sci. Technol. 121, 107319 (2022)

    Google Scholar 

  11. Zhang, W., Zhao, J.: Analysis on nonlinear stiffness and vibration isolation performance of scissor-like structure with full types. Nonlinear Dyn. 86(1), 17–36 (2016)

    Google Scholar 

  12. Lindberg, E., Östberg, M., Hörlin, N.-E., Göransson, P.: A vibro-acoustic reduced order model using undeformed coupling interface substructuring-application to rubber bushing isolation in vehicle suspension systems. Appl. Acoust. 78, 43–50 (2014)

    Google Scholar 

  13. Bai, X.-X., Jiang, P., Qian, L.-J.: Integrated semi-active seat suspension for both longitudinal and vertical vibration isolation. J. Intell. Mater. Syst. Struct. 28(8), 1036–1049 (2017)

    Google Scholar 

  14. Cheng, X., Jing, W., Gong, L.: Simplified model and energy dissipation characteristics of a rectangular liquid-storage structure controlled with sliding base isolation and displacement-limiting devices. J. Perform. Constr. Facil. 31(5), 04017071 (2017)

    Google Scholar 

  15. Abalı, E., Uckan, E.: Parametric analysis of liquid storage tanks base isolated by curved surface sliding bearings. Soil Dyn. Earthq. Eng. 30(1–2), 21–31 (2010)

    Google Scholar 

  16. Sierra, I.E.M., Losanno, D., Strano, S., Marulanda, J., Thomson, P.: Development and experimental behavior of HDR seismic isolators for low-rise residential buildings. Eng. Struct. 183, 894–906 (2019)

    Google Scholar 

  17. Mazza, F.: Effects of the long-term behaviour of isolation devices on the seismic response of base-isolated buildings. Struct. Control. Health Monit. 26(4), e2331 (2019)

    Google Scholar 

  18. Furinghetti, M., Pavese, A., Quaglini, V., Dubini, P.: Experimental investigation of the cyclic response of double curved surface sliders subjected to radial and bidirectional sliding motions. Soil Dyn. Earthq. Eng. 117, 190–202 (2019)

    Google Scholar 

  19. Furinghetti, M., Lanese, I., Pavese, A.: Experimental assessment of the seismic response of a base-isolated building through a hybrid simulation. Recent Advances and Applications of Seismic Isolation and Energy Dissipation Devices (2020)

  20. Furinghetti, M., Yang, T., Calvi, P.M., Pavese, A.: Experimental evaluation of extra-stroke displacement capacity for curved surface slider devices. Soil Dyn. Earthq. Eng. 146, 106752 (2021)

    Google Scholar 

  21. Tubaldi, E., Mitoulis, S.A., Ahmadi, H.: Comparison of different models for high damping rubber bearings in seismically isolated bridges. Soil Dyn. Earthq. Eng. 104, 329–345 (2018)

    Google Scholar 

  22. Sheng, T., Liu, G.-B., Bian, X.-C., Shi, W.-X., Chen, Y.: Development of a three-directional vibration isolator for buildings subject to metro-and earthquake-induced vibrations. Eng. Struct. 252, 113576 (2022)

    Google Scholar 

  23. de Haro Moraes, F., Silveira, M., Gonçalves, P.J.P.: On the dynamics of a vibration isolator with geometrically nonlinear inerter. Nonlinear Dyn. 93(3), 1325–1340 (2018)

    Google Scholar 

  24. Han, C., Kang, B.-H., Choi, S.-B., Tak, J.M., Hwang, J.-H.: Control of landing efficiency of an aircraft landing gear system with magnetorheological dampers. J. Aircr. 56(5), 1980–1986 (2019)

    Google Scholar 

  25. Hwang, J., Chiou, J.: An equivalent linear model of lead-rubber seismic isolation bearings. Eng. Struct. 18(7), 528–536 (1996)

    Google Scholar 

  26. Kazeminezhad, E., Kazemi, M.T., Mirhosseini, S.M.: Assessment of the vertical stiffness of elastomeric bearing due to displacement and rotation. Int. J. Non-Linear Mech. 119, 103306 (2020)

    Google Scholar 

  27. Kelly, J.M.: Base isolation: linear theory and design. Earthq. Spectra 6(2), 223–244 (1990)

    Google Scholar 

  28. Adhikari, S., Woodhouse, J.: Identification of damping: part 2, non-viscous damping. J. Sound Vib. 243(1), 63–88 (2001)

    Google Scholar 

  29. Adhikari, S.: Structural Dynamic Analysis with Generalized Damping Models: Analysis. Wiley (2013)

    MATH  Google Scholar 

  30. Nguyen, X.B., Komatsuzaki, T., Truong, H.T.: Adaptive parameter identification of Bouc-wen hysteresis model for a vibration system using magnetorheological elastomer. Int. J. Mech. Sci. 213, 106848 (2022)

    Google Scholar 

  31. Chowdhury, S., Banerjee, A., Adhikari, S.: The optimum inerter-based additional viscoelastic mass dampers for dynamic response mitigation of structures. Mech. Based Des. Struct. Mach. 1–24 (2023)

  32. Roberts, J.B., Spanos, P.D.: Random vibration and statistical linearization. Courier Corporation (2003)

  33. Buckle, I.G.: New Zealand seismic base isolation concepts and their application to nuclear engineering. Nucl. Eng. Des. 84(3), 313–326 (1985)

    Google Scholar 

  34. Robinson, W.H.: Lead-rubber hysteretic bearings suitable for protecting structures during earthquakes. Earthq. Eng. Struct. Dyn. 10(4), 593–604 (1982)

    MathSciNet  Google Scholar 

  35. Jangid, R.: Computational numerical models for seismic response of structures isolated by sliding systems. Struct. Control. Health Monit. 12(1), 117–137 (2005)

    Google Scholar 

  36. Chowdhury, S.: Nonlinear dynamic analysis of torsionally coupled isolated structures. Pract. Period. Struct. Des. Constr. 26(3), 04021023 (2021)

    Google Scholar 

  37. Jangid, R.: Optimum friction pendulum system for near-fault motions. Eng. Struct. 27(3), 349–359 (2005)

    Google Scholar 

  38. Shakib, H., Fuladgar, A.: Response of pure-friction sliding structures to three components of earthquake excitation. Comput. Struct. 81(4), 189–196 (2003)

    Google Scholar 

  39. Jangid, R., Londhe, Y.: Effectiveness of elliptical rolling rods for base isolation. J. Struct. Eng. 124(4), 469–472 (1998)

    Google Scholar 

  40. Jangid, R.: Stochastic seismic response of structures isolated by rolling rods. Eng. Struct. 22(8), 937–946 (2000)

    Google Scholar 

  41. Matsagar, V.A., Jangid, R.: Influence of isolator characteristics on the response of base-isolated structures. Eng. Struct. 26(12), 1735–1749 (2004)

    Google Scholar 

  42. Datta, T.K.: Seismic Analysis of Structures. Wiley (2010)

    Google Scholar 

  43. Sun, H., Zuo, L., Wang, X., Peng, J., Wang, W.: Exact h2 optimal solutions to inerter-based isolation systems for building structures. Struct. Control. Health Monit. 26(6), e2357 (2019)

    Google Scholar 

  44. Cheng, Z., Palermo, A., Shi, Z., Marzani, A.: Enhanced tuned mass damper using an inertial amplification mechanism. J. Sound Vib. 475, 115267 (2020)

    Google Scholar 

  45. Chen, M.Z., Hu, Y.: Analysis for inerter-based vibration system. In: Inerter and Its Application in Vibration Control Systems, pp. 19–39. Springer (2019)

  46. Asami, T., Nishihara, O., Baz, A.M.: Analytical solutions to \(h_{\infty }\) and \(h_2\) optimization of dynamic vibration absorbers attached to damped linear systems. J. Vib. Acoust. 124(2), 284–295 (2002)

    Google Scholar 

  47. Baduidana, M., Kenfack-Jiotsa, A.: Optimal design of inerter-based isolators minimizing the compliance and mobility transfer function versus harmonic and random ground acceleration excitation. J. Vib. Control 27(11–12), 1297–1310 (2021)

    MathSciNet  Google Scholar 

  48. Čakmak, D., Tomičević, Z., Wolf, H., Božić, Ž, Semenski, D.: Stability and performance of supercritical inerter-based active vibration isolation systems. J. Sound Vib. 518, 116234 (2021)

    Google Scholar 

  49. Hu, Y., Chen, M.Z.: Performance evaluation for inerter-based dynamic vibration absorbers. Int. J. Mech. Sci. 99, 297–307 (2015)

    Google Scholar 

  50. Palazzo, B., Petti, L.: Optimal structural control in the frequency domain: control in norm \(h_{\infty }\) and \(h_{2}\). J. Struct. Control. 6(2), 205–221 (1999)

    Google Scholar 

  51. Qian, F., Luo, Y., Sun, H., Tai, W.C., Zuo, L.: Optimal tuned inerter dampers for performance enhancement of vibration isolation. Eng. Struct. 198, 109464 (2019)

    Google Scholar 

  52. Crandall, S.H., Mark, W.D.: Random Vibration in Mechanical Systems. Academic Press (2014)

    Google Scholar 

  53. Chowdhury, S., Banerjee, A.: The exact closed-form expressions for optimal design parameters of resonating base isolators. Int. J. Mech. Sci. 224, 107284 (2022)

    Google Scholar 

  54. Patro, S.R., Banerjee, A., Adhikari, S., Ramana, G.: Kaimal spectrum based h2 optimization of tuned mass dampers for wind turbines. J. Vib. Control 10775463221092838 (2022)

  55. Chowdhury, S., Banerjee, A., Adhikari, S.: The optimum enhanced viscoelastic tuned mass dampers: exact closed-form expressions. J. Vib. Control 10775463231156240 (2023)

  56. Cheung, Y., Wong, W.O.: \(h_{\infty }\) optimization of a variant design of the dynamic vibration absorber-revisited and new results. J. Sound Vib. 330(16), 3901–3912 (2011)

    Google Scholar 

  57. Allen, J.C.: \(H_{\infty }\) Engineering and Amplifier Optimization. Springer (2012)

    Google Scholar 

  58. Chun, S., Lee, Y., Kim, T.-H.: \(h_{\infty }\) optimization of dynamic vibration absorber variant for vibration control of damped linear systems. J. Sound Vib. 335, 55–65 (2015)

    Google Scholar 

  59. Hua, Y., Wong, W., Cheng, L.: Optimal design of a beam-based dynamic vibration absorber using fixed-points theory. J. Sound Vib. 421, 111–131 (2018)

    Google Scholar 

  60. Chowdhury, S., Banerjee, A., Adhikari, S.: Optimal negative stiffness inertial-amplifier-base-isolators: exact closed-form expressions. Int. J. Mech. Sci. 218, 107044 (2022)

    Google Scholar 

  61. Den Hartog, J.P.: Mechanical vibrations, Courier Corporation (1985)

  62. Chowdhury, S., Banerjee, A., Adhikari, S.: The optimal configuration of negative stiffness inerter-based base isolators in multi-storey buildings. Structures 50, 1232–1251 (2023)

    Google Scholar 

  63. Smith, M.C.: The inerter: a retrospective. Ann. Rev. Control Robot. Auton. Syst. 3, 361–391 (2020)

    Google Scholar 

  64. Smith, M.C., Wang, F.-C.: Performance benefits in passive vehicle suspensions employing inerters. Veh. Syst. Dyn. 42(4), 235–257 (2004)

    Google Scholar 

  65. Wang, F.-C., Liao, M.-K., Liao, B.-H., Su, W.-J., Chan, H.-A.: The performance improvements of train suspension systems with mechanical networks employing inerters. Veh. Syst. Dyn. 47(7), 805–830 (2009)

    Google Scholar 

  66. Wang, F.-C., Yu, C.-H., Chang, M.-L., Hsu, M.: The performance improvements of train suspension systems with inerters. In: Proceedings of the 45th IEEE Conference on Decision and Control, pp. 1472–1477. IEEE (2006)

  67. Wang, F.-C., Hsieh, M.-R., Chen, H.-J.: Stability and performance analysis of a full-train system with inerters. Veh. Syst. Dyn. 50(4), 545–571 (2012)

    Google Scholar 

  68. Hu, Y., Chen, M.Z., Sun, Y.: Comfort-oriented vehicle suspension design with skyhook inerter configuration. J. Sound Vib. 405, 34–47 (2017)

    Google Scholar 

  69. Chen, M.Z., Hu, Y.: Inerter and Its Application in Vibration Control Systems, Springer (2019)

  70. Zhao, Z., Chen, Q., Zhang, R., Pan, C., Jiang, Y.: Energy dissipation mechanism of inerter systems. Int. J. Mech. Sci. 184, 105845 (2020)

    Google Scholar 

  71. Moghimi, G., Makris, N.: Seismic response of yielding structures equipped with inerters. Soil Dyn. Earthq. Eng. 141, 106474 (2020)

    Google Scholar 

  72. Zhao, Z., Chen, Q., Zhang, R., Pan, C., Jiang, Y.: Optimal design of an inerter isolation system considering the soil condition. Eng. Struct. 196, 109324 (2019)

    Google Scholar 

  73. Jiang, Y., Zhao, Z., Zhang, R., De Domenico, D., Pan, C.: Optimal design based on analytical solution for storage tank with inerter isolation system. Soil Dyn. Earthq. Eng. 129, 105924 (2020)

    Google Scholar 

  74. Zhao, Z., Zhang, R., Wierschem, N.E., Jiang, Y., Pan, C.: Displacement mitigation–oriented design and mechanism for inerter-based isolation system. J. Vib. Control 1077546320951662 (2020)

  75. Ayad, M., Karathanasopoulos, N., Ganghoffer, J.-F., Lakiss, H.: Higher-gradient and micro-inertia contributions on the mechanical response of composite beam structures. Int. J. Eng. Sci. 154, 103318 (2020)

    MathSciNet  MATH  Google Scholar 

  76. Ayad, M., Karathanasopoulos, N., Reda, H., Ganghoffer, J.-F., Lakiss, H.: Dispersion characteristics of periodic structural systems using higher order beam element dynamics. Math. Mech. Solids 25(2), 457–474 (2020)

    MathSciNet  MATH  Google Scholar 

  77. De Domenico, D., Deastra, P., Ricciardi, G., Sims, N.D., Wagg, D.J.: Novel fluid inerter based tuned mass dampers for optimised structural control of base-isolated buildings. J. Frankl. Inst. 356(14), 7626–7649 (2019)

    MATH  Google Scholar 

  78. Zhang, R., Zhao, Z., Pan, C.: Influence of mechanical layout of inerter systems on seismic mitigation of storage tanks. Soil Dyn. Earthq. Eng. 114, 639–649 (2018)

    Google Scholar 

  79. Zhang, R., Zhao, Z., Dai, K.: Seismic response mitigation of a wind turbine tower using a tuned parallel inerter mass system. Eng. Struct. 180, 29–39 (2019)

    Google Scholar 

  80. Qian, F., Luo Sr, Y., Sun, H., Tai, W.C., Zuo, L.: Performance enhancement of a base-isolation structure using optimal tuned inerter dampers. In: Active and Passive Smart Structures and Integrated Systems XIII, Vol. 10967, International Society for Optics and Photonics, 1096715 (2019)

  81. Kuhnert, W.M., Gonçalves, P.J.P., Ledezma-Ramirez, D.F., Brennan, M.J.: Inerter-like devices used for vibration isolation: a historical perspective. J. Frankl. Inst. (2020)

  82. Čakmak, D., Tomičević, Z., Wolf, H., Božić, Ž, Semenski, D.: Stability and performance of supercritical inerter-based active vibration isolation systems. J. Sound Vib. 518, 116234 (2022)

    Google Scholar 

  83. Chowdhury, S., Banerjee, A.: The non-dimensional response spectra of impact oscillators subjected to pulse-type base excitation. Int. J. Dyn. Control 1–22 (2023)

  84. Yilmaz, C., Hulbert, G.M., Kikuchi, N.: Phononic band gaps induced by inertial amplification in periodic media. Phys. Rev. B 76(5), 054309 (2007)

    Google Scholar 

  85. Taniker, S., Yilmaz, C.: Design, analysis and experimental investigation of three-dimensional structures with inertial amplification induced vibration stop bands. Int. J. Solids Struct. 72, 88–97 (2015)

    Google Scholar 

  86. Yilmaz, C., Hulbert, G.: Theory of phononic gaps induced by inertial amplification in finite structures. Phys. Lett. A 374(34), 3576–3584 (2010)

    Google Scholar 

  87. Taniker, S., Yilmaz, C.: Phononic gaps induced by inertial amplification in BCC and FCC lattices. Phys. Lett. A 377(31–33), 1930–1936 (2013)

    Google Scholar 

  88. Frandsen, N.M., Bilal, O.R., Jensen, J.S., Hussein, M.I.: Inertial amplification of continuous structures: large band gaps from small masses. J. Appl. Phys. 119(12), 124902 (2016)

    Google Scholar 

  89. Hou, M., Wu, J.H., Cao, S., Guan, D., Zhu, Y.: Extremely low frequency band gaps of beam-like inertial amplification metamaterials. Mod. Phys. Lett. B 31(27), 1750251 (2017)

    Google Scholar 

  90. Yilmaz, G., Hulbert, G.M., Kikuchi, N.: Phononic band gaps induced by inertial amplification in periodic media. Phys. Rev. B 76, 054309 (2007)

    Google Scholar 

  91. Miniaci, M., Mazzotti, M., Amendola, A., Fraternali, F.: Inducing dispersion curves with negative group velocity in inertially amplified phononic crystals through the application of an external state of prestress. In: XI International Conference on Structural Dynamic, EURODYN 2020, pp. 612–620 (2020)

  92. Sun, F., Dai, X., Liu, Y., Xiao, L.: Seismic mitigation performance of periodic foundations with inertial amplification mechanism considering superstructure-foundation interaction. Smart Mater. Struct. 30(2), 025018 (2021)

    Google Scholar 

  93. Yuksel, O., Yilmaz, C.: Shape optimization of phononic band gap structures incorporating inertial amplification mechanisms. J. Sound Vib. 355, 232–245 (2015)

    Google Scholar 

  94. Taniker, S., Yilmaz, C.: Generating ultra wide vibration stop bands by a novel inertial amplification mechanism topology with flexure hinges. Int. J. Solids Struct. 106, 129–138 (2017)

    Google Scholar 

  95. Barys, M., Zalewski, R.: Analysis of inertial amplification mechanism with smart spring-damper for attenuation of beam vibrations. In: MATEC Web of Conferences, Vol. 157, EDP Sciences, p. 03002 (2018)

  96. Yilmaz, C., Hulbert, G.M.: Dynamics of locally resonant and inertially amplified lattice materials, Dynamics of Lattice Materials. In: Phani, A.S., Hussein, M.I. (eds.) p. 233 (2017)

  97. Zhou, J., Dou, L., Wang, K., Xu, D., Ouyang, H.: A nonlinear resonator with inertial amplification for very low-frequency flexural wave attenuations in beams. Nonlinear Dyn. 96(1), 647–665 (2019)

    MATH  Google Scholar 

  98. Barys, M., Jensen, J.S., Frandsen, N.M.: Efficient attenuation of beam vibrations by inertial amplification. Eur. J. Mech. A/Solids 71, 245–257 (2018)

    MathSciNet  MATH  Google Scholar 

  99. Muhammad, S., Wang, S., Li, F., Zhang, C.: Bandgap enhancement of periodic nonuniform metamaterial beams with inertial amplification mechanisms. J. Vib. Control 1077546319895630 (2020)

  100. Karathanasopoulos, N., Dos Reis, F., Diamantopoulou, M., Ganghoffer, J.-F.: Mechanics of beams made from chiral metamaterials: tuning deflections through normal-shear strain couplings. Mater. Des. 189, 108520 (2020)

    Google Scholar 

  101. Ayad, M., Karathanasopoulos, N., Reda, H., Ganghoffer, J.-F., Lakiss, H.: On the role of second gradient constitutive parameters in the static and dynamic analysis of heterogeneous media with micro-inertia effects. Int. J. Solids Struct. 190, 58–75 (2020)

    Google Scholar 

  102. Banerjee, A., Das, R., Calius, E.P.: Waves in structured mediums or metamaterials: a review. Arch. Comput. Methods Eng. 26(4), 1029–1058 (2019)

    MathSciNet  Google Scholar 

  103. Huang, H., Sun, C.: Theoretical investigation of the behavior of an acoustic metamaterial with extreme young’s modulus. J. Mech. Phys. Solids 59(10), 2070–2081 (2011)

    MATH  Google Scholar 

  104. Cimellaro, G.P., Domaneschi, M., Warn, G.: Three-dimensional base isolation using vertical negative stiffness devices. J. Earthq. Eng. 24(12), 2004–2032 (2020)

    Google Scholar 

  105. Li, H., Li, Y., Li, J.: Negative stiffness devices for vibration isolation applications: a review. Adv. Struct. Eng. 23(8), 1739–1755 (2020)

    Google Scholar 

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

    Google Scholar 

  107. Xiang, S., Songye, Z.: A comparative study of vibration isolation performance using negative stiffness and inerter dampers. J. Frankl. Inst. 356(14), 7922–7946 (2019)

    MATH  Google Scholar 

  108. Dwivedi, A., Banerjee, A., Bhattacharya, B.: Simultaneous energy harvesting and vibration attenuation in piezo-embedded negative stiffness metamaterial. J. Intell. Mater. Syst. Struct. 31(8), 1076–1090 (2020)

    Google Scholar 

  109. Banerjee, A., Adhikari, S., Hussein, M.I.: Inertial amplification band-gap generation by coupling a levered mass with a locally resonant mass. Int. J. Mech. Sci. 207, 106630 (2021)

    Google Scholar 

  110. Yuksel, O., Yilmaz, C.: Realization of an ultrawide stop band in a 2-d elastic metamaterial with topologically optimized inertial amplification mechanisms. Int. J. Solids Struct. 203, 138–150 (2020)

    Google Scholar 

  111. Mi, Y., Yu, X.: Sound transmission of acoustic metamaterial beams with periodic inertial amplification mechanisms. J. Sound Vib. 499, 116009 (2021)

    Google Scholar 

  112. Adhikari, S., Banerjee, A.: Enhanced low-frequency vibration energy harvesting with inertial amplifiers. J. Intell. Mater. Syst. Struct. 1045389X211032281 (2021)

  113. Chowdhury, S., Banerjee, A., Adhikari, S.: Enhanced seismic base isolation using inertial amplifiers. Structures 33, 1340–1353 (2021). https://doi.org/10.1016/j.istruc.2021.04.089

    Article  Google Scholar 

  114. Zhou, S., Jean-Mistral, C., Chesne, S.: Optimal design of an inerter-based dynamic vibration absorber connected to ground. J. Vib. Acoust 141(5) (2019)

  115. Shen, Y., Peng, H., Li, X., Yang, S.: Analytically optimal parameters of dynamic vibration absorber with negative stiffness. Mech. Syst. Signal Process. 85, 193–203 (2017)

    Google Scholar 

  116. Carrella, A., Brennan, M., Waters, T.: Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. J. Sound Vib. 301(3–5), 678–689 (2007)

    Google Scholar 

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

    Google Scholar 

  118. Hao, Z., Cao, Q.: The isolation characteristics of an archetypal dynamical model with stable-quasi-zero-stiffness. J. Sound Vib. 340, 61–79 (2015)

    Google Scholar 

  119. Robertson, W.S., Kidner, M., Cazzolato, B.S., Zander, A.C.: Theoretical design parameters for a quasi-zero stiffness magnetic spring for vibration isolation. J. Sound Vib. 326(1–2), 88–103 (2009)

    Google Scholar 

  120. 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 (2021)

    Google Scholar 

  121. 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 

  122. Wu, Z., Jing, X., Sun, B., Li, F.: A 6dof passive vibration isolator using x-shape supporting structures. J. Sound Vib. 380, 90–111 (2016)

    Google Scholar 

  123. Cheng, C., Li, S., Wang, Y., Jiang, X.: On the analysis of a high-static-low-dynamic stiffness vibration isolator with time-delayed cubic displacement feedback. J. Sound Vib. 378, 76–91 (2016)

    Google Scholar 

  124. Zheng, Y., Zhang, X., Luo, Y., Yan, B., Ma, C.: Design and experiment of a high-static-low-dynamic stiffness isolator using a negative stiffness magnetic spring. J. Sound Vib. 360, 31–52 (2016)

    Google Scholar 

  125. Wu, J., Zeng, L., Han, B., Zhou, Y., Luo, X., Li, X., Chen, X., Jiang, W.: Analysis and design of a novel arrayed magnetic spring with high negative stiffness for low-frequency vibration isolation. Int. J. Mech. Sci. 216, 106980 (2022)

    Google Scholar 

  126. 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(4), 1132–1148 (2014)

    Google Scholar 

  127. Fulcher, B.A., Shahan, D.W., Haberman, M.R., Conner Seepersad, 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(3) (2014)

  128. 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(14), 3359–3376 (2013)

    Google Scholar 

  129. Winterflood, J., Blair, D.G., Slagmolen, B.: High performance vibration isolation using springs in Euler column buckling mode. Phys. Lett. A 300(2–3), 122–130 (2002)

    Google Scholar 

  130. Yuan, S., Sun, Y., Wang, M., Ding, J., Zhao, J., Huang, Y., Peng, Y., Xie, S., Luo, J., Pu, H., et al.: Tunable negative stiffness spring using Maxwell normal stress. Int. J. Mech. Sci. 193, 106127 (2021)

    Google Scholar 

  131. Iemura, H., Pradono, M.H.: Advances in the development of pseudo-negative-stiffness dampers for seismic response control. Struct. Control Health Monit. 16(7–8), 784–799 (2009)

    Google Scholar 

  132. Iemura, H., Igarashi, A., Pradono, M.H., Kalantari, A.: Negative stiffness friction damping for seismically isolated structures. Struct. Control Health Monit. 13(2–3), 775–791 (2006)

    Google Scholar 

  133. Wang, M., Sun, F.-F., Jin, H.-J.: Performance evaluation of existing isolated buildings with supplemental passive pseudo-negative stiffness devices. Eng. Struct. 177, 30–46 (2018)

    Google Scholar 

  134. Kapasakalis, K.A., Antoniadis, I.A., Sapountzakis, E.J.: Performance assessment of the KDamper as a seismic absorption base. Struct. Control. Health Monit. 27(4), e2482 (2020)

    Google Scholar 

  135. Kapasakalis, K.A., Antoniadis, I.A., Sapountzakis, E.J.: Constrained optimal design of seismic base absorbers based on an extended KDamper concept. Eng. Struct. 226, 111312 (2021)

    Google Scholar 

  136. Lakes, R.S., Lee, T., Bersie, A., Wang, Y.-C.: Extreme damping in composite materials with negative-stiffness inclusions. Nature 410(6828), 565–567 (2001)

    Google Scholar 

  137. Shi, X., Zhu, S.: Simulation and optimization of magnetic negative stiffness dampers. Sens. Actuators A 259, 14–33 (2017)

    Google Scholar 

  138. Wu, W., Chen, X., Shan, Y.: Analysis and experiment of a vibration isolator using a novel magnetic spring with negative stiffness. J. Sound Vib. 333(13), 2958–2970 (2014)

    Google Scholar 

  139. Di Matteo, A., Masnata, C., Pirrotta, A.: Simplified analytical solution for the optimal design of tuned mass damper inerter for base isolated structures. Mech. Syst. Signal Process. 134, 106337 (2019)

    Google Scholar 

  140. Menga, N., Bottiglione, F., Carbone, G.: Nonlinear viscoelastic isolation for seismic vibration mitigation. Mech. Syst. Signal Process. 157, 107626 (2021)

    Google Scholar 

  141. Djedoui, N., Ounis, A.: Tuned mass damper for base isolated structures. Sci. Technol. B Sci. de l’ingénieur 29–34 (2014)

  142. Jangid, R.: Optimum tuned inerter damper for base-isolated structures. J. Vib. Eng. Technol. 9(7), 1483–1497 (2021)

    Google Scholar 

  143. Marian, L., Giaralis, A.: Optimal design of a novel tuned mass-damper-inerter (TMDI) passive vibration control configuration for stochastically support-excited structural systems. Probab. Eng. Mech. 38, 156–164 (2014)

  144. Deringöl, A.H., Güneyisi, E.M.: Influence of nonlinear fluid viscous dampers in controlling the seismic response of the base-isolated buildings. In: Structures, vol. 34, pp. 1923–1941. Elsevier (2021)

  145. Pietrosanti, D., De Angelis, M., Giaralis, A.: Experimental seismic performance assessment and numerical modelling of nonlinear inerter vibration absorber (IVA)-equipped base isolated structures tested on shaking table. Earthq. Eng. Struct. Dyn. 50(10), 2732–2753 (2021)

    Google Scholar 

  146. Wang, J., Li, H., Wang, B., Liu, Z., Zhang, C.: Development of a two-phased nonlinear mass damper for displacement mitigation in base-isolated structures. Soil Dyn. Earthq. Eng. 123, 435–448 (2019)

    Google Scholar 

  147. Wongprasert, N., Symans, M.D.: Seismic response control of nonlinear base-isolated structures using variable fluid dampers. In: Smart Structures and Materials 2001: Smart Systems for Bridges, Structures, and Highways, vol. 4330, pp. 333–344. SPIE (2001)

  148. Chowdhury, S., Banerjee, A., Adhikari, S.: The optimal design of dynamic systems with negative stiffness inertial amplifier tuned mass dampers. Appl. Math. Model. (2022)

  149. Chowdhury, S., Banerjee, A.: The exact closed-form equations for optimal design parameters of enhanced inerter-based isolation systems. J. Vib. Control 10775463221133428 (2022)

  150. Chopra, A.K.: Dynamics of structures, Pearson Education India (2007)

  151. Chowdhury, S., Banerjee, A., Adhikari, S.: Optimal design of inertial amplifier base isolators for dynamic response control of multi-storey buildings. Int. J. Struct. Stab. Dyn. 0 (ja) (0) null. https://doi.org/10.1142/S0219455423500475

  152. Banerjee, A., Chanda, A., Das, R.: Seismic analysis of a curved bridge considering deck-abutment pounding interaction: an analytical investigation on the post-impact response. Earthq. Eng. Struct. Dyn. 46(2), 267–290 (2017)

    Google Scholar 

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Funding

The authors would like to acknowledge the Inspire faculty grant, grant number DST/INSPIRE/04/2018/000052, for partial financial support for the project. SC would like to acknowledge the MHRD grant received from IIT Delhi during the period of this research work.

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    Sudip Chowdhury & Arnab Banerjee

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Chowdhury, S., Banerjee, A. The nonlinear dynamic analysis of optimum nonlinear inertial amplifier base isolators for vibration isolation. Nonlinear Dyn 111, 12749–12786 (2023). https://doi.org/10.1007/s11071-023-08599-0

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