The dynamics and vibration reduction performance of bistable nonlinear energy sink (BNES) are studied in this paper. First, the negative stiffness of BNES is realized by geometric nonlinearity, and the dynamics model of the system is established. The slow flow equation of the system under 1:1 main resonance is analyzed based on the complexification-averaging (CX-A) method, and the boundary conditions of saddle node bifurcation and Hopf bifurcation are analyzed. Second, the slow invariant manifold (SIM) of the BNES is studied based on multiscale analysis, and the excitation threshold of strongly modulated response (SMR) is analyzed; the analysis results are verified by the numerical method. The results show that the analytical solution is highly consistent with the numerical solution, and the error is less than 1%. Finally, the influence of structural parameters on the vibration reduction performance is analyzed and optimized. The vibration reduction performance of BNES and CNES is compared, and the results show that the BNES has better vibration reduction performance in the full frequency band.
AlisverisciGFBayirogluHFelixJLP, et al. (2016) A nonlinear electromechanical pendulum arm with a nonlinear energy sink control (NES) approach. Journal of Theoretical and Applied Mechanics54(3): 975–986. DOI: 10.15632/jtam-pl.54.3.975.
3.
BarbaraciG. Axial active magnetic bearing design[J]. Journal of Vibration and Control, 2016, 22(5): 1190-1197. DOI: 10.1177/1077546314534720
4.
BekMAAmerTSSirwahMA, et al. (2020) The vibrational motion of a spring pendulum in a fluid flow. Results in Physics19: 103465. DOI: 10.1016/j.rinp.2020.103465.
5.
BekMAAmerTSAlmahalawyA, et al. (2021) The asymptotic analysis for the motion of 3DOF dynamical system close to resonances. Alexandria Engineering Journal60(4): 3539–3551. DOI: 10.1016/j.aej.2021.02.017.
6.
BorosonEMissoumSMatteiPO, et al. (2017) Optimization under uncertainty of parallel nonlinear energy sinks. Journal of Sound and Vibration394: 451–464. DOI: 10.1016/j.jsv.2016.12.043.
7.
ChenJEZhangWYaoMH, et al. (2017) Vibration suppression for truss core sandwich beam based on principle of nonlinear targeted energy transfer. Composite Structures171: 419–428. DOI: 10.1016/j.compstruct.2017.03.030.
8.
ChenJZhangWLiuJ, et al. (2021) Vibration absorption of parallel-coupled nonlinear energy sink under shock and harmonic excitations. Applied Mathematics and Mechanics42(8): 1135–1154. DOI: 10.1007/s10483-021-2757-6.
9.
DingHChenLQ (2020) Designs, analysis, and applications of nonlinear energy sinks. Nonlinear Dynamics100(4): 3061–3107. DOI: 10.1007/s11071-020-05724-1.
10.
FasihiAShahgholiMGhahremaniS (2022) The effects of nonlinear energy sink and piezoelectric energy harvester on aeroelastic instability of an airfoil. Journal of Vibration and Control28(11–12): 1418–1432. DOI: 10.1177/1077546321993585.
LiXZhangYWDingH, et al. (2019) Dynamics and evaluation of a nonlinear energy sink integrated by a piezoelectric energy harvester under a harmonic excitation. Journal of Vibration and Control25(4): 851–867. DOI: 10.1177/1077546318802456.
13.
LiSWuHChenJ (2022) Global dynamics and performance of vibration reduction for a new vibro-impact bistable nonlinear energy sink. International Journal of Non-Linear Mechanics139: 103891. DOI: 10.1016/j.ijnonlinmec.2021.103891.
QiuD (2018) Theoretical and Experimental Study of Tuned Nonlinear Energy Sink: Application to Passive Vibration control[D]. INSA de Toulouse. https://tel.archives-ouvertes.fr/tel-02083714/
16.
RenBLiuLZhangX, et al. (2017) Dynamic characteristics and parametric influences of nonlinear vibration absorbers based on bi-stable power generation. J], Jornal of Vibration and Shock (In Chinese)36(17): 220–230. http://dx.chinadoi.cn/10.13465/j.cnki.jvs.2017.17.033
17.
RobersonRE (1952) Synthesis of a nonlinear dynamic vibration absorber. Journal of the Franklin Institute254: 205–220. DOI: 10.1016/0016-0032(52)90457-2.
18.
SavadjiiguATVaurigaudBLamarqueCH, et al. (2012) Targeted energy transfer with parallel nonlinear energy sinks. Part II: theory and experiments. Nonlinear Dynamics67(1): 37–46. DOI: 10.1007/s11071-011-9955-z.
19.
SongWLiuLuZCLiY, et al. (2020) Research on vibration reduction performance of dynamic vibration absorber based on damping characteristic of a new material. Advances in Mechanical Engineering12(11): 168781402096159. DOI: 10.1177/168781402096159.
20.
SongWLiuZLuC, et al. (2022) Analysis of vibration suppression performance of parallel nonlinear energy sink[J]. Journal of Vibration and Control: 10775463221085867. Online ahead of print. DOI: 10.1177/1077546322108586.
21.
StarosvetskyYGendelmanOV (2009) Vibration absorption in systems with a nonlinear energy sink: nonlinear damping. Journal of Sound and Vibration324(3–5): 916–939. DOI: 10.1016/j.jsv.2009.02.052.
WeizhiSZhienLChihuaL, et al. (2022) Analysis of vibration suppression performance of nonlinear energy sink with negative stiffness. Journal of Vibration Engineering & Technologies10: 1481–1493. DOI: 10.1007/s42417-022-00462-7.
24.
WuWChenXShanY (2014) Analysis and experiment of a vibration isolator using a novel magnetic spring with negative stiffness. Journal of Sound and Vibration333(13): 2958–2970. DOI: 10.1016/j.jsv.2014.02.009.
25.
YaoHCaoYWangY, et al. (2019) A tri-stable nonlinear energy sink with piecewise stiffness. Journal of Sound and Vibration463: 114971. DOI: 10.1016/j.jsv.2019.114971.
YaohuiSYeweiZHuD, et al. (2018) Nonlinear energy sink for a flywheel system vibration reduction. Journal of Sound and Vibration429: 305–324. DOI: 10.1016/j.jsv.2018.05.025.
28.
ZangJZhangYWDingH, et al. (2019) The evaluation of a nonlinear energy sink absorber based on the transmissibility. Mechanical Systems and Signal Processing125: 99–122. DOI: 10.1016/j.ymssp.2018.05.061.
29.
ZengYDingHDuRH, et al. (2022) A suspension system with quasi-zero stiffness characteristics and inerter nonlinear energy sink. Journal of Vibration and Control28(1–2): 143–158. DOI: 10.1177/1077546320972904.
30.
ZhangXHeLZhouW (2016) Theoretical design of a low frequency vibration isolation platform based on permanent magnet negative-stiffness device. [J] Jornal of Vibration and Shock (In Chinese)35(15): 184–189. http://dx.chinadoi.cn/10.13465/j.cnki.jvs.2016.15.031
31.
ZhangYKongXYueC, et al. (2021) Dynamic analysis of 1-dof and 2-dof nonlinear energy sink with geometrically nonlinear damping and combined stiffness. Nonlinear Dynamics105(1): 167–190. DOI: 10.1007/s11071-021-06615-9.
