In this article, a novel vibration control scheme of suspension systems is proposed. It combines the advantages of quasi-zero stiffness isolator, nonlinear energy sink absorber, and inerter. This proposed scheme can achieve low transmissibility, low amplitude, and low additional weight and resolve the conflict between riding comfort and handling stability. Strong nonlinear vibration equations of a quarter-vehicle suspension system are established. It also presents the detailed process of high-order harmonic approximation to obtain steady-state responses. Moreover, approximate solutions are validated by a numerical method. Furthermore, based on riding comfort and handling stability, the following four suspension systems are evaluated and compared, namely, 2-degree-of-freedom quarter-vehicle model, 2-degree-of-freedom quarter-vehicle with quasi-zero stiffness isolator, 2-degree-of-freedom quarter-vehicle with inerter-nonlinear energy sink absorber, and 2-degree-of-freedom quarter-vehicle integrated control scheme with quasi-zero stiffness and inerter-nonlinear energy sink. It is found that the integrated control scheme with quasi-zero stiffness and inerter-nonlinear energy sink can significantly improve the riding comfort and handling stability at the same time. In addition, the effects of system parameters are studied carefully. The results show that based on the reasonable design of the control system parameters, better riding comfort and handling stability can be obtained. In short, this article provides a theoretical basis for integrating quasi-zero stiffness isolators and inerter-nonlinear energy sink absorbers to improve the riding comfort and handling stability.
AbbasiAKhademSEBabS, et al. (2016) Vibration control of a rotor supported by journal bearings and an asymmetric high-static low-dynamic stiffness suspension. Nonlinear Dynamics85: 525–545.
2.
Al-ShudeifatMA. (2014) Highly efficient nonlinear energy sink. Nonlinear Dynamics76: 1905–1920.
3.
Al-ShudeifatMAWierschemNEBergmanLA, et al. (2016) Numerical and experimental investigations of a rotating nonlinear energy sink. Meccanica52: 763–779.
4.
AlexanderNASchilderF (2009) Exploring the performance of a nonlinear tuned mass damper. Journal of Sound and Vibration319: 445–462.
5.
AnubiOMCraneC (2015) A new semiactive variable stiffness suspension system using combined skyhook and nonlinear energy sink-based controllers. IEEE Transactions on Control Systems Technology23: 937–947.
6.
AvramovKVGendelmanOV (2009) On interaction of vibrating beam with essentially nonlinear absorber. Meccanica45: 355–365.
7.
BabSKhademSMahdiabadiM, et al. (2015a) Vibration mitigation of a rotating beam under external periodic force using a nonlinear energy sink (NES). Journal of Vibration and Control23: 1001–1025.
8.
BabSKhademSEShahgholiM (2015b) Vibration attenuation of a rotor supported by journal bearings with nonlinear suspensions under mass eccentricity force using nonlinear energy sink. Meccanica50: 2441–2460.
9.
BergeotBBellizziSCochelinB (2017) Passive suppression of helicopter ground resonance using nonlinear energy sinks attached on the helicopter blades. Journal of Sound and Vibration392: 41–55.
10.
CarrellaABrennanMJWatersTP (2007) Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. Journal of Sound and Vibration301: 678–689.
11.
ChenH-YMaoX-YDingH, et al. (2020) Elimination of multimode resonances of composite plate by inertial nonlinear energy sinks. Mechanical Systems and Signal Processing135: 106383.
12.
ChenMPapageorgiouCScheibeF, et al. (2009) The missing mechanical circuit element. IEEE Circuits and Systems Magazine9: 10–26.
13.
DingHChenL-Q (2018) Nonlinear vibration of a slightly curved beam with quasi-zero-stiffness isolators. Nonlinear Dynamics95: 2367–2382.
14.
DingHJiJChenL-Q (2019) Nonlinear vibration isolation for fluid-conveying pipes using quasi-zero stiffness characteristics. Mechanical Systems and Signal Processing121: 675–688.
15.
DuRQiuGGaoK, et al. (2020) Abnormal road surface recognition based on smartphone acceleration sensor. Sensors20: 451.
16.
GattiG (2017) Fundamental insight on the performance of a nonlinear tuned mass damper. Meccanica53: 111–123.
17.
GattiGBrennanMJ (2017) Inner detached frequency response curves: an experimental study. Journal of Sound and Vibration396: 246–254.
18.
GengXDingHWeiK, et al. (2020) Suppression of multiple modal resonances of a cantilever beam by an impact damper. Applied Mathematics and Mechanics41: 383–400.
19.
GiaralisAPetriniF (2017) Wind-induced vibration mitigation in tall buildings using the tuned mass-damper-inerter. Journal of Structural Engineering143: 04017127.
20.
GiaralisATaflanidisAA (2018) Optimal tuned mass-damper-inerter (TMDI) design for seismically excited MDOF structures with model uncertainties based on reliability criteria. Structural Control and Health Monitoring25: e2082.
21.
HanYCaoQJiJ (2015) Nonlinear dynamics of a smooth and discontinuous oscillator with multiple stability. International Journal of Bifurcation and Chaos25: 1530038.
22.
HuYChenMZQSunY (2017) Comfort-oriented vehicle suspension design with skyhook inerter configuration. Journal of Sound and Vibration405: 34–47.
23.
JiangXMcfarlandDMBergmanLA, et al. (2003) Steady state passive nonlinear energy pumping in coupled oscillators: theoretical and experimental results. Nonlinear Dynamics33: 87–102.
24.
KremerDLiuK (2014) A nonlinear energy sink with an energy harvester: transient responses. Journal of Sound and Vibration333: 4859–4880.
25.
KuetherRJRensonLDetrouxT, et al. (2015) Nonlinear normal modes, modal interactions and isolated resonance curves. Journal of Sound and Vibration351: 299–310.
26.
LazarIFNeildSAWaggDJ (2014) Using an inerter-based device for structural vibration suppression. Earthquake Engineering & Structural Dynamics43: 1129–1147.
27.
LeTDAhnKK (2011) A vibration isolation system in low frequency excitation region using negative stiffness structure for vehicle seat. Journal of Sound and Vibration330: 6311–6335.
28.
LiCLiangMWangY, et al. (2011) Vibration suppression using two-terminal flywheel. Part II: application to vehicle passive suspension. Journal of Vibration and Control18: 1353–1365.
29.
LiXZhangY-WDingH, et al. (2018) Dynamics and evaluation of a nonlinear energy sink integrated by a piezoelectric energy harvester under a harmonic excitation. Journal of Vibration and Control25: 851–867.
30.
LiuXHuangXHuaH (2013) On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector. Journal of Sound and Vibration332: 3359–3376.
31.
LuZ-QDingHChenL-Q (2019) Resonance response interaction without internal resonance in vibratory energy harvesting. Mechanical Systems and Signal Processing121: 767–776.
32.
LuoACJHuangJ (2013) Analytical solutions for asymmetric periodic motions to chaos in a hardening Duffing oscillator. Nonlinear Dynamics72: 417–438.
33.
PapageorgiouCSmithMC (2006) Positive real synthesis using matrix inequalities for mechanical networks: application to vehicle suspension. IEEE Transactions on Control Systems Technology14: 423–435.
34.
PuHYuanSPengY, et al. (2019) Multi-layer electromagnetic spring with tunable negative stiffness for semi-active vibration isolation. Mechanical Systems and Signal Processing121: 942–960.
35.
QinYXiangCWangZ, et al. (2017) Road excitation classification for semi-active suspension system based on system response. Journal of Vibration and Control24: 2732–2748.
36.
SmithMC (2002) Synthesis of mechanical networks: the inerter. IEEE Transactions on Automatic Control47: 1648–1662.
37.
SmithMCWangF-C (2004) Performance benefits in passive vehicle suspensions employing inerters. Vehicle System Dynamics42: 235–257.
38.
WangF-CLiaoM-KLiaoB-H, et al. (2006) The performance improvements of train suspension systems with mechanical networks employing inerters. Vehicle System Dynamics47: 805–830.
39.
WangJWierschemNEWangB, et al. (2019a) Multi‐objective design and performance investigation of a high‐rise building with track nonlinear energy sinks. The Structural Design of Tall and Special Buildings29: e1692.
40.
WangXZhouJXuD, et al. (2016) Force transmissibility of a two-stage vibration isolation system with quasi-zero stiffness. Nonlinear Dynamics87: 633–646.
41.
WangQZhouJXuD, et al. (2020) Design and experimental investigation of ultra-low frequency vibration isolation during neonatal transport. Mechanical Systems and Signal Processing139: 106633.
42.
WangYJingXDaiH, et al. (2019b) Subharmonics and ultra-subharmonics of a bio-inspired nonlinear isolation system. International Journal of Mechanical Sciences152: 167–184.
43.
WangYJingXGuoY (2018a) Nonlinear analysis of a bio-inspired vertically asymmetric isolation system under different structural constraints. Nonlinear Dynamics95: 445–464.
44.
WangYLiSChengC, et al. (2018b) Adaptive control of a vehicle-seat-human coupled model using quasi-zero-stiffness vibration isolator as seat suspension. Journal of Mechanical Science and Technology32: 2973–2985.
45.
WierschemNEHubbardSALuoJ, et al. (2017) Response attenuation in a large-scale structure subjected to blast excitation utilizing a system of essentially nonlinear vibration absorbers. Journal of Sound and Vibration389: 52–72.
46.
XueJZhangYDingH, et al. (2019) Vibration reduction evaluation of a linear system with a nonlinear energy sink under a harmonic and random excitation. Applied Mathematics and Mechanics41: 1–14.
47.
YanBMaHJianB, et al. (2019a) Nonlinear dynamics analysis of a bi-state nonlinear vibration isolator with symmetric permanent magnets. Nonlinear Dynamics97: 2499–2519.
48.
YanBMaHZhengW, et al. (2019b) Nonlinear electromagnetic shunt damping for nonlinear vibration isolators. IEEE/ASME Transactions on Mechatronics24: 1851–1860.
49.
YangKZhangY-WDingH, et al. (2017) Nonlinear energy sink for whole-spacecraft vibration reduction. Journal of Vibration and Acoustics139: 021011.
50.
YangT-ZYangX-DLiY, et al. (2013) Passive and adaptive vibration suppression of pipes conveying fluid with variable velocity. Journal of Vibration and Control20: 1293–1300.
51.
YeKJiJCBrownT (2020) Design of a quasi-zero stiffness isolation system for supporting different loads. Journal of Sound and Vibration471: 115198.
52.
ZangJYuanT-CLuZ-Q, et al. (2018) A lever-type nonlinear energy sink. Journal of Sound and Vibration437: 119–134.
53.
ZhangQXiaSXuD, et al. (2019a) A torsion-translational vibration isolator with quasi-zero stiffness. Nonlinear Dynamics99: 1467–1488.
54.
ZhangY-WSuCNiZ-Y, et al. (2019b) A multifunctional lattice sandwich structure with energy harvesting and nonlinear vibration control. Composite Structures221: 11087.
55.
ZhangY-WZhouLWangS, et al. (2019c) Vibration power flow characteristics of the whole-spacecraft with a nonlinear energy sink. Journal of Low Frequency Noise, Vibration and Active Control38: 341–351.
56.
ZhangYFangBChenY (2011) Vibration isolation performance evaluation of the discrete whole-spacecraft vibration isolation platform for flexible spacecrafts. Meccanica47: 1185–1195.
57.
ZhangYLuYChenL (2019d) Energy harvesting via nonlinear energy sink for whole-spacecraft. Science China Technological Sciences62: 1483–1491.
58.
ZhangZLuZ-QDingH, et al. (2019e) An inertial nonlinear energy sink. Journal of Sound and Vibration450: 199–213.
59.
ZhangX-JAhmadianMGuoK-H (2012) On the benefits of semi-active suspensions with inerters. Shock and Vibration19: 257–272.
60.
ZulliDLuongoA (2014) Nonlinear energy sink to control vibrations of an internally nonresonant elastic string. Meccanica50: 781–794.
