×

Nonlinear dynamics analysis of a bi-state nonlinear vibration isolator with symmetric permanent magnets. (English) Zbl 1430.70024

Summary: This paper proposes a novel bi-state nonlinear vibration isolator (BS-NVI) consisting of a linear mass-spring-damper and several permanent magnets (PMs). The working state of the BS-NVI can be monostable or bistable depending on the relative position of the PMs. The theoretical model of the BS-NVI is established. The transmissibility of the BS-NVI is derived according to the harmonic balance method. Both the simulation and experimental efforts are performed to study the nonlinear dynamics and vibration isolation performance of the BS-NVI. The results demonstrate that the monostable isolator acts like a quasi-zero-stiffness isolator and exhibits the hardening-spring-liked characteristic. With the change in the relative position of the PMs, the transmissibility and the peak frequency are decreased. However, the bistable isolator undergoes the interwell and intrawell oscillations with the change in the excitation amplitude and frequency. The motion of the bistable isolator can be periodic or chaotic. Due to the snap-through action, the transmissibility of the bistable isolator could be smaller than 1 in part of the resonance region.

MSC:

70E55 Dynamics of multibody systems
70K20 Stability for nonlinear problems in mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Yan, B., Zhang, X.N., Niu, H.P.: Design and test of a novel isolator with negative resistance electromagnetic shunt damping. Smart Mater. Struct. 21(3), 035003 (2012). https://doi.org/10.1088/0964-1726/21/3/035003 · doi:10.1088/0964-1726/21/3/035003
[2] Yan, B., Wang, K., Kang, C.X., Zhang, X.N., Wu, C.Y.: Self-sensing electromagnetic transducer for vibration control of space antenna reflector. IEEE/ASME Trans. Mechatron. 22(5), 1944-1951 (2017). https://doi.org/10.1109/Tmech.2017.2712718 · doi:10.1109/Tmech.2017.2712718
[3] Laalej, H., Lang, Z.Q., Daley, S., Zazas, I., Billings, S.A., Tomlinson, G.R.: Application of non-linear damping to vibration isolation: an experimental study. Nonlinear Dyn. 69(1), 409-421 (2012). https://doi.org/10.1007/s11071-011-0274-1 · doi:10.1007/s11071-011-0274-1
[4] Mokni, L., Belhaq, M., Lakrad, F.: Effect of fast parametric viscous damping excitation on vibration isolation in SDOF systems. Commun. Nonlinear Sci. Numer. Simul. 16(4), 1720-1724 (2011). https://doi.org/10.1016/j.cnsns.2010.08.031 · Zbl 1221.74040 · doi:10.1016/j.cnsns.2010.08.031
[5] Ho, C., Lang, Z.-Q., Billings, S.A.: A frequency domain analysis of the effects of nonlinear damping on the Duffing equation. Mech. Syst. Signal Process. 45(1), 49-67 (2014). https://doi.org/10.1016/j.ymssp.2013.10.027 · doi:10.1016/j.ymssp.2013.10.027
[6] Virgin, L.N., Santillan, S.T., Plaut, R.H.: Vibration isolation using extreme geometric nonlinearity. J. Sound Vib. 315(3), 721-731 (2008). https://doi.org/10.1016/j.jsv.2007.12.025 · doi:10.1016/j.jsv.2007.12.025
[7] Huang, X.C., Liu, X.T., Sun, J.Y., Zhang, Z.Y., Hua, H.X.: Effect of the system imperfections on the dynamic response of a high-static-low-dynamic stiffness vibration isolator. Nonlinear Dyn. 76(2), 1157-1167 (2014). https://doi.org/10.1007/s11071-013-1199-7 · doi:10.1007/s11071-013-1199-7
[8] Hao, Z., Cao, Q.J., Wiercigroch, M.: Nonlinear dynamics of the quasi-zero-stiffness SD oscillator based upon the local and global bifurcation analyses. Nonlinear Dyn. 87(2), 987-1014 (2016). https://doi.org/10.1007/s11071-016-3093-6 · doi:10.1007/s11071-016-3093-6
[9] Wang, X.L., Zhou, J.X., Xu, D.L., Ouyang, H.J., Duan, Y.: Force transmissibility of a two-stage vibration isolation system with quasi-zero stiffness. Nonlinear Dyn. 87(1), 633-646 (2016). https://doi.org/10.1007/s11071-016-3065-x · doi:10.1007/s11071-016-3065-x
[10] Wang, Y., Li, S., Neild, S.A., Jiang, J.Z.: Comparison of the dynamic performance of nonlinear one and two degree-of-freedom vibration isolators with quasi-zero stiffness. Nonlinear Dyn. 88(1), 635-654 (2016). https://doi.org/10.1007/s11071-016-3266-3 · doi:10.1007/s11071-016-3266-3
[11] Esin, M., Pasternak, E., Dyskin, A.V.: Stability of chains of oscillators with negative stiffness normal, shear and rotational springs. Int. J. Eng. Sci. 108, 16-33 (2016). https://doi.org/10.1016/j.ijengsci.2016.08.002 · Zbl 1423.70023 · doi:10.1016/j.ijengsci.2016.08.002
[12] Liu, C.R., Yu, K.P.: A high-static-low-dynamic-stiffness vibration isolator with the auxiliary system. Nonlinear Dyn. (2018). https://doi.org/10.1007/s11071-018-4441-5 · doi:10.1007/s11071-018-4441-5
[13] Ding, H., Chen, L.Q.: Nonlinear vibration of a slightly curved beam with quasi-zero-stiffness isolators. Nonlinear Dyn. (2018). https://doi.org/10.1007/s11071-018-4697-9 · Zbl 1432.74109 · doi:10.1007/s11071-018-4697-9
[14] Ding, H., Ji, J., Chen, L.Q.: Nonlinear vibration isolation for fluid-conveying pipes using quasi-zero stiffness characteristics. Mech. Syst. Signal Process. 121, 675-688 (2019). https://doi.org/10.1016/j.ymssp.2018.11.057 · doi:10.1016/j.ymssp.2018.11.057
[15] Carrella, A., Brennan, M.J., Waters, T.P.: Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. J. Sound Vib. 301(3-5), 678-689 (2007). https://doi.org/10.1016/j.jsv.2006.10.011 · doi:10.1016/j.jsv.2006.10.011
[16] Carrella, A., Brennan, M.J., Kovacic, I., Waters, T.P.: On the force transmissibility of a vibration isolator with quasi-zero-stiffness. J. Sound Vib. 322(4-5), 707-717 (2009). https://doi.org/10.1016/j.jsv.2008.11.034 · doi:10.1016/j.jsv.2008.11.034
[17] Carrella, A., Brennan, M.J., Waters, T.P., Lopes, V.: Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness. Int. J. Mech. Sci. 55(1), 22-29 (2012). https://doi.org/10.1016/j.ijmecsci.2011.11.012 · doi:10.1016/j.ijmecsci.2011.11.012
[18] Kovacic, I., Brennan, M.J., Waters, T.P.: A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic. J. Sound Vib. 315(3), 700-711 (2008). https://doi.org/10.1016/j.jsv.2007.12.019 · doi:10.1016/j.jsv.2007.12.019
[19] Kovacic, I., Brennan, M.J., Lineton, B.: Effect of a static force on the dynamic behaviour of a harmonically excited quasi-zero stiffness system. J. Sound Vib. 325(4), 870-883 (2009). https://doi.org/10.1016/j.jsv.2009.03.036 · doi:10.1016/j.jsv.2009.03.036
[20] Gatti, G., Kovacic, I., Brennan, M.J.: On the response of a harmonically excited two degree-of-freedom system consisting of a linear and a nonlinear quasi-zero stiffness oscillator. J. Sound Vib. 329(10), 1823-1835 (2010). https://doi.org/10.1016/j.jsv.2009.11.019 · doi:10.1016/j.jsv.2009.11.019
[21] Tang, B., Brennan, M.J.: On the shock performance of a nonlinear vibration isolator with high-static-low-dynamic-stiffness. Int. J. Mech. Sci. 81, 207-214 (2014). https://doi.org/10.1016/j.ijmecsci.2014.02.019 · doi:10.1016/j.ijmecsci.2014.02.019
[22] Lan, C.C., Yang, S.A., Wu, Y.S.: Design and experiment of a compact quasi-zero-stiffness isolator capable of a wide range of loads. J. Sound Vib. 333(20), 4843-4858 (2014). https://doi.org/10.1016/j.jsv.2014.05.009 · doi:10.1016/j.jsv.2014.05.009
[23] Lu, Z.Q., Chen, L.Q., Brennan, M.J., Yang, T.J., Ding, H., Liu, Z.G.: Stochastic resonance in a nonlinear mechanical vibration isolation system. J. Sound Vib. 370, 221-229 (2016). https://doi.org/10.1016/j.jsv.2016.01.042 · doi:10.1016/j.jsv.2016.01.042
[24] Lu, Z.Q., Shao, D., Ding, H., Chen, L.Q.: Power flow in a two-stage nonlinear vibration isolation system with high-static-low-dynamic stiffness. Shock Vib. 2018, 1-13 (2018). https://doi.org/10.1155/2018/1697639 · doi:10.1155/2018/1697639
[25] Abbasi, A., Khadem, S.E., Bab, S., Friswell, M.I.: Vibration control of a rotor supported by journal bearings and an asymmetric high-static low-dynamic stiffness suspension. Nonlinear Dyn. 85(1), 525-545 (2016). https://doi.org/10.1007/s11071-016-2704-6 · doi:10.1007/s11071-016-2704-6
[26] Araki, Y., Asai, T., Kimura, K., Maezawa, K., Masui, T.: Nonlinear vibration isolator with adjustable restoring force. J. Sound Vib. 332(23), 6063-6077 (2013). https://doi.org/10.1016/j.jsv.2013.06.030 · doi:10.1016/j.jsv.2013.06.030
[27] Mofidian, S.M.M., Bardaweel, H.: Displacement transmissibility evaluation of vibration isolation system employing nonlinear-damping and nonlinear-stiffness elements. J. Vib. Control 24(18), 4247-4259 (2018). https://doi.org/10.1177/1077546317722702 · doi:10.1177/1077546317722702
[28] Zhou, J.X., Wang, X.L., Xu, D.L., Bishop, S.: Nonlinear dynamic characteristics of a quasi-zero stiffness vibration isolator with cam – roller – spring mechanisms. J. Sound Vib. 346, 53-69 (2015). https://doi.org/10.1016/j.jsv.2015.02.005 · doi:10.1016/j.jsv.2015.02.005
[29] Zhou, J.X., Xu, D.L., Bishop, S.: A torsion quasi-zero stiffness vibration isolator. J. Sound Vib. 338, 121-133 (2015). https://doi.org/10.1016/j.jsv.2014.10.027 · doi:10.1016/j.jsv.2014.10.027
[30] Zhou, J.X., Xiao, Q.Y., Xu, D.L., Ouyang, H.J., Li, Y.L.: A novel quasi-zero-stiffness strut and its applications in six-degree-of-freedom vibration isolation platform. J. Sound Vib. 394, 59-74 (2017). https://doi.org/10.1016/j.jsv.2017.01.021 · doi:10.1016/j.jsv.2017.01.021
[31] Sun, X.T., Jing, X.J., Xu, J., Cheng, L.: Vibration isolation via a scissor-like structured platform. J. Sound Vib. 333(9), 2404-2420 (2014). https://doi.org/10.1016/j.jsv.2013.12.025 · doi:10.1016/j.jsv.2013.12.025
[32] Huang, X.C., Liu, X.T., Sun, J.Y., Zhang, Z.Y., Hua, H.X.: 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). https://doi.org/10.1016/j.jsv.2013.10.026 · doi:10.1016/j.jsv.2013.10.026
[33] Carrella, A., Brennan, M.J., Waters, T.P., Shin, K.: On the design of a high-static-low-dynamic stiffness isolator using linear mechanical springs and magnets. J. Sound Vib. 315(3), 712-720 (2008). https://doi.org/10.1016/j.jsv.2008.01.046 · doi:10.1016/j.jsv.2008.01.046
[34] Robertson, W.S., Kidner, M.R.F., Cazzolato, B.S., Zander, A.C.: Theoretical design parameters for a quasi-zero stiffness magnetic spring for vibration isolation. J. Sound Vib. 326(1), 88-103 (2009). https://doi.org/10.1016/j.jsv.2009.04.015 · doi:10.1016/j.jsv.2009.04.015
[35] Zheng, Y.S., Zhang, X.N., Luo, Y.J., Yan, B., Ma, C.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). https://doi.org/10.1016/j.jsv.2015.09.019 · doi:10.1016/j.jsv.2015.09.019
[36] Zhou, N.B., Liu, K.F.: A tunable high-static-low-dynamic stiffness vibration isolator. J. Sound Vib. 329(9), 1254-1273 (2010). https://doi.org/10.1016/j.jsv.2009.11.001 · doi:10.1016/j.jsv.2009.11.001
[37] Wu, W.J., Chen, X.D., Shan, Y.H.: Analysis and experiment of a vibration isolator using a novel magnetic spring with negative stiffness. J. Sound Vib. 333(13), 2958-2970 (2014). https://doi.org/10.1016/j.jsv.2014.02.009 · doi:10.1016/j.jsv.2014.02.009
[38] Zhou, J.X., Dou, L.L., Wang, K., Xu, D.L., Ouyang, H.J.: A nonlinear resonator with inertial amplification for very low-frequency flexural wave attenuations in beams. Nonlinear Dyn. 96(1), 647-665 (2019). https://doi.org/10.1007/s11071-019-04812-1 · Zbl 1437.74017 · doi:10.1007/s11071-019-04812-1
[39] Yan, B., Ma, H.Y., Zhao, C.X., Wu, C.Y., Wang, K., Wang, P.F.: A vari-stiffness nonlinear isolator with magnetic effects: theoretical modeling and experimental verification. Int. J. Mech. Sci. 148, 745-755 (2018). https://doi.org/10.1016/j.ijmecsci.2018.09.031 · doi:10.1016/j.ijmecsci.2018.09.031
[40] Harne, R.L., Wang, K.W.: A review of the recent research on vibration energy harvesting via bistable systems. Smart Mater. Struct. 22(2), 023001 (2013). https://doi.org/10.1088/0964-1726/22/2/023001 · doi:10.1088/0964-1726/22/2/023001
[41] Johnson, D.R., Thota, M., Semperlotti, F., Wang, K.W.: On achieving high and adaptable damping via a bistable oscillator. Smart Mater. Struct. 22(11), 115027 (2013). https://doi.org/10.1088/0964-1726/22/11/115027 · doi:10.1088/0964-1726/22/11/115027
[42] Shaw, A.D., Neild, S.A., Wagg, D.J., Weaver, P.M., Carrella, A.: A nonlinear spring mechanism incorporating a bistable composite plate for vibration isolation. J. Sound Vib. 332(24), 6265-6275 (2013). https://doi.org/10.1016/j.jsv.2013.07.016 · doi:10.1016/j.jsv.2013.07.016
[43] Johnson, D.R., Harne, R.L., Wang, K.W.: A disturbance cancellation perspective on vibration control using a bistable snap-through attachment. AMSE J. Vib. Acoust. 136(3), 031006 (2014). https://doi.org/10.1115/1.4026673 · doi:10.1115/1.4026673
[44] Yang, K., Harne, R.L., Wang, K.W., Huang, H.: Investigation of a bistable dual-stage vibration isolator under harmonic excitation. Smart Mater. Struct. 23(4), 045033 (2014). https://doi.org/10.1088/0964-1726/23/4/045033 · doi:10.1088/0964-1726/23/4/045033
[45] Yang, K., Harne, R.L., Wang, K.W., Huang, H.: Dynamic stabilization of a bistable suspension system attached to a flexible host structure for operational safety enhancement. J. Sound Vib. 333(24), 6651-6661 (2014). https://doi.org/10.1016/j.jsv.2014.07.033 · doi:10.1016/j.jsv.2014.07.033
[46] Wu, Z., Harne, R.L., Wang, K.W.: Excitation-induced stability in a bistable duffing oscillator: analysis and experiments. J. Comput. Nonlinear Dyn. 10(1), 011016 (2014). https://doi.org/10.1115/1.4026974 · doi:10.1115/1.4026974
[47] Chen, L.Q., Jiang, W.A.: Internal resonance energy harvesting. ASME J. Appl. Mech. 82(3), 031004 (2015). https://doi.org/10.1115/1.4029606 · doi:10.1115/1.4029606
[48] Benacchio, S., Malher, A., Boisson, J., Touzé, C.: Design of a magnetic vibration absorber with tunable stiffnesses. Nonlinear Dyn. 85(2), 893-911 (2016). https://doi.org/10.1007/s11071-016-2731-3 · doi:10.1007/s11071-016-2731-3
[49] 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). https://doi.org/10.1016/j.jsv.2011.07.039 · doi:10.1016/j.jsv.2011.07.039
[50] Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley, New York (1979) · Zbl 0418.70001
[51] Brennan, M.J., Kovacic, I., Carrella, A., Waters, T.P.: On the jump-up and jump-down frequencies of the Duffing oscillator. J. Sound Vib. 318(4), 1250-1261 (2008). https://doi.org/10.1016/j.jsv.2008.04.032 · doi:10.1016/j.jsv.2008.04.032
[52] Yan, B., Zhou, S.X., Litak, G.: Nonlinear analysis of the tristable energy harvester with a resonant circuit for performance enhancement. Int. J. Bifurc. Chaos 28(07), 1850092 (2018). https://doi.org/10.1142/s021812741850092x · Zbl 1395.34057 · doi:10.1142/s021812741850092x
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.