Abstract
This research investigates the nonlinear dynamics and performance enhancement of a suspension system using a diamond-shaped linkage with inerter (D-inerter). The proposed suspension system consists of two inerters embedded in a four-bar linkage mechanism connected with a spring and a damper. Both sinusoidal and random road profiles are considered as external excitation sources. The evaluation of vibration isolation and riding comfort performance is based on displacement transmissibility, acceleration amplitude, car body acceleration, suspension stroke, and dynamic tyre load. The results show that compared with a linear suspension system, the D-inerter has a broader bandwidth of enhanced isolation and lower resonant peak. It is found that a larger inertance value and initial length between the ends of inerter can effectively improve the suppression performance of the nonlinear suspension. The root mean square of vehicle body acceleration with the D-inerter is decreased by 21.5% at the speed of 30 m/s. Additionally, design guidance is provided to select optimal inertance values for improved suspension performance. The results demonstrate that the D-inerter is beneficial for enhancing the suspension structural stability, riding comfort, and vibration suppression, which can potentially be employed for vibration isolation in suspension systems.
Similar content being viewed by others
References
Hać, A.: Optimal linear preview control of active vehicle suspension. Veh. Syst. Dyn. 21(1), 167–195 (1992)
Roh, H.S., Park, Y.: Stochastic optimal preview control of an active vehicle suspension. J. Sound Vib. 220(2), 313–330 (1999)
Hu, Y., Chen, M.Z.Q., Hou, Z.: Multiplexed model predictive control for active vehicle suspensions. Int. J. Control 88(2), 347–363 (2015)
Wang, R., Ding, R., Chen, L.: Application of hybrid electromagnetic suspension in vibration energy regeneration and active control. J. Vib. Control 24(1), 223–233 (2018)
Yao, G.Z., Yap, F.F., Chen, G., Li, W.H., Yeo, S.H.: MR damper and its application for semi-active control of vehicle suspension system. Mechatronics 12(7), 963–973 (2002)
Shen, Y., Golnaraghi, M.F., Heppler, G.R.: Semi-active vibration control schemes for suspension systems using magnetorheological dampers. J. Vib. Control 12(1), 3–24 (2006)
Tseng, H.E., Hrovat, D.: State of the art survey: active and semi-active suspension control. Veh. Syst. Dyn. 53(7), 1034–1062 (2015)
Smith, M.C.: Synthesis of mechanical networks: the inerter. IEEE Trans. Autom. Control 47(10), 1648–1662 (2002)
Papageorgiou, C., Houghton, N.E., Smith, M.C.: Experimental testing and analysis of inerter devices. J. Dyn. Syst. Meas. Control 131(1), 011001 (2009)
Li, C., Liang, M., Wang, Y., Dong, Y.: Vibration suppression using two-terminal flywheel. Part I: modeling and characterization. J. Vib. Control 18(8), 1096–1105 (2012)
Swift, S.J., Smith, M.C., Glover, A.R., Papageorgiou, C., Gartner, B., Houghton, N.E.: Design and modelling of a fluid inerter. Int. J. Control 86(11), 2035–2051 (2013)
Liu, X., Jiang, J.Z., Titurus, B., Harrison, A.: Model identification methodology for fluid-based inerters. Mech. Syst. Signal Process. 106, 479–494 (2018)
Jiang, J.Z., Matamoros-Sanchez, A.Z., Goodall, R.M., Smith, M.C.: Passive suspensions incorporating inerters for railway vehicles. Veh. Syst. Dyn. 50(Suppl. 1), 263–276 (2012)
Wang, F.C., Hong, M.F., Chan, C.W.: Building suspensions with inerters. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 224(8), 1605–1616 (2010)
Lazar, I.F., Neild, S.A., Wagg, D.J.: Using an inerter-based device for structural vibration suspension. Earthq. Eng. Struct. Dyn. 43, 1129–1147 (2014)
Li, Y., Jiang, J.Z., Neild, S.A.: Inerter-based configurations for main-landing-gear shimmy suppression. J. Aircr. 54(2), 684–693 (2017)
Luo, J., Macdonald, J.H.G., Jiang, J.Z.: Identification of optimum cable vibration absorbers using fixed-sized-inerter layouts. Mech. Mach. Theory 140, 292–304 (2019)
Smith, M.C., Wang, F.C.: Performance benefits in passive vehicle suspensions employing inerters. Veh. Syst. Dyn. 42(4), 235–257 (2004)
Hu, Y., Chen, M.Z., Sun, Y.: Comfort-oriented vehicle suspension design with skyhook inerter configuration. J. Sound Vib. 405, 34–47 (2017)
Shen, Y., Chen, L., Yang, X., Shi, D., Yang, J.: Improved design of dynamic vibration absorber by using the inerter and its application in vehicle suspension. J. Sound Vib. 361, 148–158 (2016)
Wang, F.C., Su, W.J.: Impact of inerter nonlinearities on vehicle suspension control. Veh. Syst. Dyn. 46(7), 575–595 (2008)
He, H., Li, Y., Jiang, J.Z., Burrow, S., Neild, S., Conn, A.: Enhancing the trade-off between ride comfort and active actuation requirements via an inerter-based passive-active-combined automotive suspension. Veh. Syst. Dyn. (2023). https://doi.org/10.1080/00423114.2023.2184703
Kuznetsov, A., Mammadov, M., Sultan, I., Hajilarov, E.: Optimization of improved suspension system with inerter device of the quarter-car model in vibration analysis. Arch. Appl. Mech. 81, 1427–1437 (2011)
Wang, Y., Ding, H., Chen, L.-Q.: Averaging analysis on a semi-active inerter-based suspension system with relative-acceleration-relative-velocity control. J. Vib. Control 26(13–14), 1199–1215 (2020)
Ge, Z., Wang, W., Li, G., Rao, D.: Design, parameter optimisation, and performance analysis of active tuned inerter damper (TID) suspension for vehicle. J. Sound Vib. 525, 116750 (2022)
Yang, J., Jiang, J.Z., Neild, S.A.: Dynamic analysis and performance evaluation of nonlinear inerter-based vibration isolators. Nonlinear Dyn. 99, 1823–1839 (2020)
Dong, Z., Shi, B., Yang, J., Li, T.: Suppression of vibration transmission in coupled systems with an inerter-based nonlinear joint. Nonlinear Dyn. 107, 1637–1662 (2022)
Dai, W., Shi, B., Yang, J., Zhu, X., Li, T.: Enhanced suppression of longitudinal vibration transmission in propulsion shaft system using nonlinear tuned mass damper inerter. J. Vib. Control 29(11–12), 2528–2538 (2023)
Wang, Y., Li, H.-X., Cheng, C., Ding, H., Chen, L.-Q.: Dynamic performance analysis of a mixed-connected inerter-based quasi-zero stiffness vibration isolator. Struct. Control Health Monit. 27(10), e2604 (2020)
Wang, Y., Wang, P., Meng, H., Chen, L.-Q.: Nonlinear vibration and dynamic performance analysis of the inerter-based multi-directional vibration isolator. Arch. Appl. Mech. 92(12), 3597–3629 (2022)
Wang, Y., Li, H.-X., Jiang, W.-A., Ding, H., Chen, L.-Q.: A base excited mixed-connected inerter-based quasi-zero stiffness vibration isolator with mistuned load. Mech. Adv. Mater. Struct. 29(25), 4224–4242 (2022)
Sun, X., Jing, X.: Multi-direction vibration isolation with quasi-zero stiffness by employing geometrical nonlinearity. Mech. Syst. Signal Process. 62–63, 149–163 (2015)
Wang, Y., Jing, X.: Nonlinear stiffness and dynamical response characteristics of an asymmetric X-shaped structure. Mech. Syst. Signal Process. 125, 142–169 (2019)
Sun, X., Jing, X., Xu, J., Cheng, L.: Vibration isolation via a scissor-like structured platform. J. Sound Vib. 333(9), 2404–2420 (2014)
Shi, B., Dai, W., Yang, J.: Performance analysis of a nonlinear inerter-based vibration isolator with inerter embedded in a linkage mechanism. Nonlinear Dyn. 109, 419–442 (2022)
Smith, M.C.: The inerter: a retrospective. Ann. Rev. Control Robot. Auton. Syst. 3, 361–391 (2020)
Papalukopoulos, C., Natsiavas, S.: Nonlinear biodynamics of passengers coupled with quarter car models. J. Sound Vib. 304(1–2), 50–71 (2007)
Silveira, M., Wahi, P., Fernandes, J.C.M.: Effects of asymmetrical damping on a 2 DOF quarter-car model under harmonic excitation. Commun. Nonlinear Sci. Numer. Simul. 43, 14–24 (2017)
Wang, S., Hua, L., Yang, C., Zhang, Y., Tan, X.: Nonlinear vibrations of a piecewise-linear quarter-car truck model by incremental harmonic balance method. Nonlinear Dyn. 92(4), 1719–1732 (2018)
Xiao, Z., Jing, X.: Frequency-domain analysis and design of linear feedback of nonlinear systems and applications in vehicle suspensions. IEEE/ASME Trans. Mechatron. 21, 506–517 (2015)
Yuan, H., Li, Y., Jiang, J.Z., Al Sakka, M., Dhaens, M., Burrow, S., Gonzalez-Buelga, A., Clare, L., Mellor, P.: A design methodology for passive mechatronic vibration absorbers. Mech. Mach. Theory 167, 104523 (2022)
Sun, X., Cai, Y., Chen, L., Liu, Y., Wang, S.: Vehicle height and posture control of the electronic air suspension system using the hybrid system approach. Veh. Syst. Dyn. 54(3), 328–352 (2016)
Shen, Y., Liu, Y., Chen, L., Yang, X.: Optimal design and experimental research of vehicle suspension based on a hydraulic electric inerter. Mechatronics 61, 12–19 (2019)
Funding
This work was supported by the National Natural Science Foundation of China under Grant Numbers 12172185 and 12202152, by the Zhejiang Provincial Natural Science Foundation of China under Grant Number LY22A020006, and by Ningbo Municipal Natural Science Foundation of China under Grant Number 2022J174.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Shi, B., Dai, W. & Yang, J. Performance enhancement of vehicle suspension system with geometrically nonlinear inerters. Arch Appl Mech 94, 39–55 (2024). https://doi.org/10.1007/s00419-023-02502-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-023-02502-4