Nonlinear response of a multidirectional negative-stiffness isolation system via semirecursive multibody dynamic approach

Abstract

This paper investigates an innovative negative-stiffness device (NSD) that modifies the apparent stiffness of the supported structure for seismic isolation. The NSD comprises a lower base on the bottom and a cap on the top, together with a connecting rod, vertical movable wall, and compressed elastic spring, as well as circumferentially arranged, pretensioned external ropes, and inclined shape memory wires. This configuration can deliver negative stiffness and energy dissipation in any direction within the horizontal plane. A numerical model of the device is developed through a two-step semirecursive method to obtain the force–displacement characteristic relationship. Such a model is first validated through comparison with the results obtained via the commercial software ADAMS. Finally, a large parametric study is performed to assess the role and the influence of each design variable on the overall response of the proposed device. Useful guidelines are drawn from this analysis to guide the system design and optimization.

Keywords

multibody system / negative stiffness / semirecursive approach / seismic protection / vibration isolation

References

[1] Buckle IG, Mayes RL. Seismic isolation: history, application, and performance—a world view. Earthq Spectra. 1990;6(2):161-201.

[2] Jangid R, Datta T. Seismic behaviour of base-isolated buildings: a state-of-the-art review. Proc Inst Civ Eng Struct Build. 1995;110(2):186-203.

[3] Calvi PM, Calvi GM. Historical development of friction-based seismic isolation systems. Soil Dyn Earthq Eng. 2018;106:14-30.

[4] Makris N. Seismic isolation: early history. Earthq Eng Struct Dyn. 2019;48(2):269-283.

[5] De Luca A, Guidi LG. State of art in the worldwide evolution of base isolation design. Soil Dyn Earthq Eng. 2019;125:105722.

[6] Erdik M, Ülker Ö, Şadan B, Tüzün C. Seismic isolation code developments and significant applications in Turkey. Soil Dyn Earthq Eng. 2018;115:413-437.

[7] Nakamura Y, Okada K. Review on seismic isolation and response control methods of buildings in Japan. Geoenv Dis. 2019;6(1):1-10.

[8] Clemente P, Martelli A. Seismically isolated buildings in Italy: state-of-the-art review and applications. Soil Dyn Earthq Eng. 2019;119:471-487.

[9] Hogg SJ, Elliott DA, Maley T, Broglio S, Holden T, Giorgini S. Case studies on the practical application of resilient building technologies applied in New Zealand. Struct Eng Int. 2020;30(2):232-241.

[10] Xu G, Guo T, Li A, et al. Seismic resilience enhancement for building structures: a comprehensive review and outlook. Structures. 2024;59:105738.

[11] Taylor AW, Lin AN, Martin JW. Performance of elastomers in isolation bearings: a literature review. Earthq Spectra. 1992;8(2):279-303.

[12] Buckle I, Nagarajaiah S, Ferrell K. Stability of elastomeric isolation bearings: experimental study. J Struct Eng. 2002;128(1):3-11.

[13] Mazza F, Mazza M. Nonlinear modelling of HDRBs in the seismic analysis of retrofitted and new base-isolated RC buildings. Structures. 2021;33:4148-4161.

[14] Mokha A, Constantinou M, Reinhorn A, Zayas VA. Experimental study of friction-pendulum isolation system. J Struct Eng. 1991;117(4):1201-1217.

[15] Almazán JL, De La Llera JC, Inaudi JA. Modelling aspects of structures isolated with the frictional pendulum system. Earthq Eng Struct Dyn. 1998;27(8):845-867.

[16] Fenz DM, Constantinou MC. Behaviour of the double concave friction pendulum bearing. Earthq Eng Struct Dyn. 2006;35(11):1403-1424.

[17] Castaldo P, Palazzo B, Della Vecchia P. Seismic reliability of base-isolated structures with friction pendulum bearings. Eng Struct. 2015;95:80-93.

[18] Zhou S, Liu Y, Jiang Z, Ren Z. Nonlinear dynamic behavior of a bio-inspired embedded X-shaped vibration isolation system. Nonlinear Dyn. 2022;110(1):153-175.

[19] Zhou S, Hou B, Zheng L, Xu P, Yu T, Ren Z. Nonlinear property and dynamic stability analysis of a novel bio-inspired vibration isolation-absorption structure. Nonlinear Dyn. 2024;112(2):887-902.

[20] Ou H, Sun X, Wu Q, et al. A novel bio-inspired kangaroo leg structure for low-frequency vibration isolation. Nonlinear Dyn. 2024;112(3):1797-1814.

[21] Pu H, Liu J, Wang M, et al. Bio-inspired quasi-zero stiffness vibration isolator with quasilinear negative stiffness in full stroke. J Sound Vib. 2024;574:118240.

[22] Meng Q, Hou L, Lin R, et al. Accurate nonlinear dynamic characteristics analysis of quasi-zero-stiffness vibration isolator via a modified incremental harmonic balance method. Nonlinear Dyn. 2024;112(1):125-150.

[23] Xu J, Jing J. Nonlinear behavior of quasi-zero stiffness nonlinear torsional vibration isolator. Nonlinear Dyn. 2024;112:2545-2568.

[24] Zhao F, Ji J, Cao S, Ye K, Luo Q. QZS isolators with multi-pairs of oblique bars for isolating ultralow frequency vibrations. Nonlinear Dyn. 2024;112(3):1815-1842.

[25] Liu C, Zhang W, Yu K, Liu T, Zheng Y. Quasi-zero-stiffness vibration isolation: designs, improvements and applications. Eng Struct. 2024;301:117282.

[26] Li H, Li Y, Li J. Negative stiffness devices for vibration isolation applications: a review. Adv Struct Eng. 2020;23(8):1739-1755.

[27] Chai Y, Bian J, Li M. A novel quasi-zero-stiffness isolation platform via tunable positive and negative stiffness compensation mechanism. Nonlinear Dyn. 2024;112(1):101-123.

[28] Niu MQ, Chen LQ. Analysis on nonlinear stiffness isolators revealing damping thresholds. Commun Nonlinear Sci Numer Simul. 2024;128:107536.

[29] Molyneux W. Supports for vibration isolation. ARC/CP-322. Aeronautical Research Council.

[30] Lee CM, Goverdovskiy V, Temnikov A. Design of springs with “negative” stiffness to improve vehicle driver vibration isolation. J Sound Vib. 2007;302(4-5):865-874.

[31] Tu L, Ning D, Sun S, et al. A novel negative stiffness magnetic spring design for vehicle seat suspension system. Mechatronics. 2020;68:102370.

[32] Shi X, Shi W, Xing L. Performance analysis of vehicle suspension systems with negative stiffness. Smart Struct Syst. 2019;24(1):141-155.

[33] Suman S, Balaji P, Selvakumar K, Kumaraswamidhas L. Nonlinear vibration control device for a vehicle suspension using negative stiffness mechanism. J Vib Eng Technol. 2021;9:957-966.

[34] Shi X, Zhu S, Ni YQ, Li J. Vibration suppression in high-speed trains with negative stiffness dampers. Smart Struct Syst. 2018;21(5):653-668.

[35] Hua Y, Zhu S, Shi X. High-performance semiactive secondary suspension of high-speed trains using negative stiffness and magnetorheological dampers. Veh Syst Dyn. 2022;60(7):2290-2311.

[36] Sarlis AA, Pasala DTR, Constantinou M, Reinhorn A, Nagarajaiah S, Taylor D. Negative stiffness device for seismic protection of structures. J Struct Eng. 2013;139(7):1124-1133.

[37] Sarlis A, Pasala D, Constantinou MC, Reinhorn AM, Nagarajaiah S, Taylor DP. Negative stiffness device for seismic protection of structures: shake table testing of a seismically isolated structure. J Struct Eng. 2016;142(5):04016005.

[38] Cimellaro GP, Domaneschi M, Warn G. Three-dimensional base isolation using vertical negative stiffness devices. J Earthq Eng. 2020;24(12):2004-2032.

[39] Alhan C, Öncü-Davas S. Performance limits of seismically isolated buildings under near-field earthquakes. Eng Struct. 2016;116:83-94.

[40] Güneş N. Effects of near-fault pulse-like ground motions on seismically isolated buildings. J Build Eng. 2022;52:104508.

[41] Quaranta G, Mollaioli F. On the use of the equivalent linearization for bilinear oscillators under pulse-like ground motion. Eng Struct. 2018;160:395-407.

[42] Quaranta G, Angelucci G, Mollaioli F. Near-fault earthquakes with pulse-like horizontal and vertical seismic ground motion components: analysis and effects on elastomeric bearings. Soil Dyn Earthq Eng. 2022;160:107361.

[43] Chen P, Wang B, Dai K, Li T. Analytical and numerical investigations of base isolation system with negative stiffness devices. Eng Struct. 2022;268:114799.

[44] Cao S, Ozbulut OE, Shi F, Deng J. An SMA cable-based negative stiffness seismic isolator: development, experimental characterization, and numerical modeling. J Intell Mater Syst Struct. 2022;33(14):1819-1833.

[45] Moghadam SR, Konstantinidis D. Finite element study of the effect of support rotation on the horizontal behavior of elastomeric bearings. Comp Struct. 2017;163:474-490.

[46] Vaiana N, Spizzuoco M, Serino G. Wire rope isolators for seismically base-isolated lightweight structures: experimental characterization and mathematical modeling. Eng Struct. 2017;140:498-514.

[47] De Domenico D, Ricciardi G, Benzoni G. Analytical and finite element investigation on the thermo-mechanical coupled response of friction isolators under bidirectional excitation. Soil Dyn Earthq Eng. 2018;106:131-147.

[48] Bianco V, Monti G, Pio Belfiore N, Vailati M. Multibody kinematics of the double concave curved surface sliders: from supposed compliant sliding to suspected stick-slip. Pract Period Struct Des Constr. 2021;26(3):04021024.

[49] Mezghani F, Rincónd AF, Fernandez PG, Juan dA, Sanchez-Espiga J, Rueda FV. Effectiveness study of wire mesh vibration damper for sensitive equipment protection from seismic events. Mech Syst Signal Process. 2022;164:108160.

[50] Wang Q, Zeng J, Wei L, Zhu B. Carbody vibrations of high-speed train caused by dynamic unbalance of underframe suspended equipment. Adv Mech Eng. 2018;10(12):1687814018818969.

[51] Mahalingam I, Padmanabhan C. A novel alternate multibody model for the longitudinal and ride dynamics of a tracked vehicle. Veh Syst Dyn. 2021;59(3):433-457.

[52] Roupa I, Gonçalves SB, Silva dMT. Kinematics and dynamics of planar multibody systems with fully Cartesian coordinates and a generic rigid body. Mech Mach Theory. 2023;180:105134.

[53] Dopico Dopico D, López Varela Á, Luaces Fernández A. Augmented Lagrangian index-3 semi-recursive formulations with projections: kinematics and dynamics. Multibody Syst Dyn. 2021;52:377-405.

[54] Khadim Q, Kaikko EP, Puolatie E, Mikkola A. Targeting the user experience in the development of mobile machinery using real-time multibody simulation. Adv Mech Eng. 2020;12(6):1687814020923176.

[55] Rodríguez AJ, Sanjurjo E, Pastorino R, Naya MÁ. State, parameter and input observers based on multibody models and Kalman filters for vehicle dynamics. Mech Syst Signal Process. 2021;155:107544.

[56] Yu X, Mikkola A, Pan Y, Escalona JL. The explanation of two semi-recursive multibody methods for educational purpose. Mech Mach Theory. 2022;175:104935.

[57] Bae DS, Haug EJ. A recursive formulation for constrained mechanical system dynamics: part II. Closed loop systems. J Struct Mech. 1987;15(4):481-506.

[58] García Jalón dJ, Álvarez E, De Ribera F, Rodríguez I, Funes F. A fast and simple semi-recursive formulation for multi-rigid-body systems. In: JA Ambrósio, ed. Advances in Computational Multibody Systems. Springer;2005:1-23.

[59] Salvatore A, Carboni B, Lacarbonara W. Multidirectional hysteretic damper with negative stiffness. Italian Patent N 102021000025130 (2021-09-30), PCT/IB2022/059325 (2022-09-30) (e0141674); 2021.

[60] Salvatore A, Carboni B, Lacarbonara W. Nonlinear dynamic response of an isolation system with superelastic hysteresis and negative stiffness. Nonlinear Dyn. 2022;107:1765-1790.

[61] Wieleba W. The statistical correlation of the coefficient of friction and wear rate of PTFE composites with steel counterface roughness and hardness. Wear. 2002;252(9-10):719-729.

[62] Shabana AA. Dynamics of Multibody Systems. Cambridge University Press; 2020.

[63] Pan Y, Dai W, Xiong Y, Xiang S, Mikkola A. Tree-topology-oriented modeling for the real-time simulation of sedan vehicle dynamics using independent coordinates and the rod-removal technique. Mech Mach Theory. 2020;143:103626.

[64] Jalón dJG. Twenty-five years of natural coordinates. Multibody Syst Dyn. 2007;18:15-33.

[65] Jalon GdJ, Callejo A, Hidalgo AF. Efficient solution of Maggi’s equations. J Comput Nonlinear Dyn. 2012;7:2.

[66] Callejo A, Pan Y, Ricón JL, Kövecses J, Jalón GdJ. Comparison of semirecursive and subsystem synthesis algorithms for the efficient simulation of multibody systems. J Comput Nonlinear Dyn. 2017;12(1):011020.

[67] Charalampakis AE, Tsiatas GC. A simple rate-independent uniaxial shape memory alloy (SMA) model. Front Built Environ. 2018;4:46.

[68] Carboni B, Lacarbonara W, Auricchio F. Hysteresis of multiconfiguration assemblies of nitinol and steel strands: experiments and phenomenological identification. J Eng Mech. 2015;141(3):04014135.

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2024 The Author(s). International Journal of Mechanical System Dynamics published by John Wiley & Sons Australia, Ltd on behalf of Nanjing University of Science and Technology.