Abstract
Both the nonlinear energy sink (NES) and the inerters have received extensive attention in the field of vibration control. In this study, we propose a dual-stage inerter-enhanced NES (IE-NES) to be an enhanced for substantial transmissibility reduction with tunable performance. The harmonic balance method and the Runge–Kutta method are employed to obtain the system responses. Computational results demonstrate good agreement between the analytical and numerical solutions. Parametric studies suggest that the inertance of inerters attached to the different NES masses has diverse effects on the vibration mitigation capacity of the IE-NES system. All the simulations are implemented in the vicinity of 1:1 resonance. It is found that the IE-NES improves the target energy transfer efficiency with proper inertance, leading to high-efficient vibration suppression. In addition, the inerter-induced new dynamics properties such as the transition among different response regimes are investigated. The study on the influence of the initial conditions and global bifurcation is exerted to reveal the complex dynamic behaviour of the IE-NES under various working conditions. The results show that such a type of NES paves a new road for advanced NES design.
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References
Cheng, Z.B., Palermo, A., Shi, Z.F., Marzani, A.: Enhanced tuned mass damper using an inertial amplification mechanism. J. Sound Vib. 475, 115267 (2020)
Pietrosanti, D., De Angelis, M., Basili, M.: A generalized 2-DOF model for optimal design of MDOF structures controlled by tuned mass damper inerter (TMDI). Int. J. Mech. Sci. 185, 105849 (2020)
Zhao, F., Cao, S.Q., Luo, Q.T., Li, L.Q., Ji, J.C.: Practical design of the QZS isolator with one pair of oblique bars by considering pre-compression and low-dynamic stiffness. Nonlinear Dyn. 108, 3313–3330 (2022)
Zhao, F., Ji, J.C., Luo, Q.T., Cao, S.Q., Chen, L.M., Du, W.L.: An improved quasi-zero stiffness isolator with two pairs of oblique springs to increase isolation frequency band. Nonlinear Dyn. 104, 349–365 (2021)
Zhao, F., Ji, J.C., Ye, K., Luo, Q.T.: An innovative quasi-zero stiffness isolator with three pairs of oblique springs. Int. J. Mech. Sci. 192, 106903 (2021)
Vakakis, A.F.: Inducing passive nonlinear energy sinks in vibrating systems. J. Vib. Acoust. 123, 324–332 (2001)
Vakakis, A.F., Gendelman, O.V., Bergman, L.A., McFarland, D.M., Kerschen, G., Lee, Y.S.: Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems, pp. 161–229. Springer, Berlin (2008)
Gendelman, O.V.: Targeted energy transfer in systems with external and self-excitation. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 225, 2007–2043 (2011)
Qiu, D.H., Seguy, S., Paredes, M.: Tuned nonlinear energy sink with conical spring: design theory and sensitivity analysis. J. Mech. Des. 140, 011404 (2017)
Vakakis, A.F., Gendelman, O.V.: Energy pumping in nonlinear mechanical oscillators: part II—resonance capture. J. Appl. Mech. 68, 42–48 (2001)
Ding, H., Chen, L.Q.: Designs, analysis, and applications of nonlinear energy sinks. Nonlinear Dyn. 100, 3061–3107 (2020)
Li, J.J., He, X.F., Yang, X.K., Liu, Y.F.: A consistent geometrically nonlinear model of cantilevered piezoelectric vibration energy harvesters. J. Sound Vib. 486, 115614 (2020)
Ghayesh, M.H., Farokhi, H.: Nonlinear broadband performance of energy harvesters. Int. J. Eng. Sci. 147, 103202 (2020)
Kerschen, G., Peeters, M., Golinval, J.C., Vakakis, A.F.: Nonlinear normal modes, Part I: a useful framework for the structural dynamicist. Mech. Syst. Signal Process 23, 170–194 (2009)
Peeters, M., Viguié, R., Sérandour, G., Kerschen, G., Golinval, J.C.: Nonlinear normal modes, part II: toward a practical computation using numerical continuation techniques. Mech. Syst. Signal Process 23, 195–216 (2009)
Vakakis, A.F., Rand, R.H.: Normal modes and global dynamics of a two-degree-of-freedom non-linear system—I. low energies. Int. J. Non Linear Mech. 27, 861–874 (1992)
Vakakis, A.F.: Non-similar normal oscillation in a strongly non-linear discrete system. J. Sound Vib. 158, 341–361 (1992)
Happawana, G.S., Bajaj, A.K.: An analytical solution to non-linear normal modes in a strongly non-linear discrete system. J. Sound Vib. 183, 361–367 (1995)
Aubrecht, J., Vakakis, A.F., Tsao, T.C., Bentsman, J.: Experimental of non-linear transient motion confinement in a system of coupled beams. J. Sound Vib. 195, 629–648 (1996)
Klimenko, A.A., Mikhlin, Y.V., Awrejcewicz, J.: Nonlinear normal modes in pendulum systems. Nonlinear Dyn. 70, 797–813 (2012)
Kerschen, G., Peeters, M., Golinval, J.C., Stephen, C.: Nonlinear modal analysis of a full-scale aircraft. J. Aircr 50, 1409–1419 (2014)
Erdogen, Y.S.: A study on the crack detection in beams using linear and nonlinear normal modes. Adv. Struct. Eng. 23, 1305–1321 (2019)
Zulli, D., Luongo, A.: Nonlinear energy sink to control vibrations of an internally nonresonant elastic string. Meccanica 50, 781–794 (2015)
Fang, Z.W., Zhang, Y.W., Li, X., Ding, H., Chen, L.Q.: Integration of a nonlinear energy sink and a giant magnetostrictive energy harvester. J. Sound Vib. 391, 35–49 (2016)
Geng, X.F., Ding, H.: Two-modal resonance control with an encapsulated nonlinear energy sink. J. Sound Vib. 520, 116667 (2022)
Yang, T.Z., Liu, T., Tang, Y., Hou, S., Lv, X.F.: Enhanced targeted energy transfer for adaptive vibration suppression of pipes conveying fluid. Nonlinear Dyn. 97, 1937–1944 (2019)
Dang, W.H., Wang, Z.H., Chen, L.Q., Yang, T.Z.: A high-effificient nonlinear energysink with a one-way energy converter. Nonlinear Dyn. 109, 2247–2261 (2022)
Zang, J., Cao, R.Q., Zhang, Y.W., Fang, B., Chen, L.Q.: A lever-enhanced nonlinear energy sink absorber harvesting vibratory energy via giant magnetostrictive-piezoelectricity. Commun. Nonlinear Sci. Numer. Simul. 95, 105620 (2021)
Zang, J., Yuan, T.C., Lu, Z.Q., Zhang, Y.W., Ding, H., Chen, L.Q.: A lever-type nonlinear energy sink. J. Sound Vib. 437, 119–134 (2018)
Geng, X.F., Ding, H.: Theoretical and experimental study of an enhanced nonlinear energy sink. Nonlinear Dyn. 104, 3269–3291 (2021)
Yao, H.L., Cao, Y.B., Wang, Y.W., Wen, B.C.: A tri-stable nonlinear energy sink with piecewise stiffness. J. Sound Vib. 463, 114971 (2019)
Li, X.L., Liu, K.F., Xiong, L.Y., Tang, L.H.: Development and validation of a piecewise linear nonlinear energy sink for vibration suppression and energy harvesting. J. Sound Vib. 503, 116104 (2021)
Wang, J.J., Zhang, C., Li, H.B., Liu, Z.B.: Experimental and numerical studies of a novel track bistable nonlinear energy sink with improved energy robustness for structural response mitigation. Eng. Struct. 237, 112184 (2021)
Lynch, J.P., Wang, Y., Swartz, R.A., Lu, K.C., Loh, C.H.: Implementation of a closed-loop structural control system using wireless sensor networks. Struct. Control Health Monit. 15, 518–239 (2008)
Yang, T.Z., Hou, S., Qin, Z.H., Ding, Q., Chen, L.Q.: A dynamic reconfifigurable nonlinear energy sink. J. Sound Vib. 494, 115629 (2019)
Gendelman, O.V., Sapsis, T., Vakakis, A.F., Bergman, L.A.: Enhanced passive targeted energy transfer in strongly nonlinear mechanical oscillators. J. Sound Vib. 330, 1–8 (2011)
Grinberg, I., Lanton, V., Gendelman, O.V.: Response regimes in linear oscillator with 2DOF nonlinear energy sink under periodic forcing. Nonlinear Dyn. 69, 1889–1902 (2012)
Smith, M.C.: Synthesis of mechanical networks: the inerter. IEEE Trans. Automat. Contr. 47, 1648–1662 (2002)
Ikago, K., Saito, K., Inoue, N.: Seismic control of single-degree-of-freedom structure using tuned viscous mass damper. Earthq. Eng. Struct. Dyn. 41, 453–474 (2012)
Giaralis, A., Petrini, F.: Wind-induced vibration mitigation in tall buildings using the tuned mass-damper-inerter. J. Struct. Eng. 143, 08217004 (2018)
Sun, L.M., Hong, D.X., Chen, L.: Cables interconnected with tuned inerter damper for vibration mitigation. Eng. Struct. 151, 57–67 (2017)
Xu, K., Bi, K.M., Han, Q., Li, X.P., Du, X.L.: Using tuned mass damper inerter to mitigate vortex-induced vibration of long-span bridges: analytical study. Eng. Struct. 182, 101–111 (2019)
Chen, H.Y., Mao, X.Y., Ding, H., Chen, L.Q.: Elimination of multimode resonances of composite plate by inertial nonlinear energy sinks. Mech. Syst. Signal Process 135, 106383 (2020)
Zhang, Z., Ding, H., Zhang, Y.W., Chen, L.Q.: Vibration suppression of an elastic beam with boundary inerter-enhanced nonlinear energy sinks. Acta Mech. Sin. 37, 387–401 (2021)
Yang, K., Zhang, Y.W., Ding, H., Chen, L.Q.: The transmissibility of nonlinear energy sink based on nonlinear output frequency-response functions. Commun. Nonlinear Sci. Numer. Simul. 44, 184–192 (2017)
Luo, A.C.J., Huang, J.Z.: Approximate solutions of periodic motions in nonlinear systems via a generalized harmonic balance. J. Vib. Control 18, 1661–1674 (2011)
Starosvetsky, Y., Gendelman, O.V.: Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. II: optimization of a nonlinear vibration absorber. Nonlinear Dyn. 51, 47–57 (2008)
Guo, H.L., Yang, T.Z., Chen, Y.S., Chen, L.Q.: Singularity analysis on vibration reduction of a nonlinear energy sink system. Mech. Syst. Signal Process 173, 109074 (2022)
Starosvetsky, Y., Gendelman, O.V.: Strongly modulated response in forced 2DOF oscillatory system with essential mass and potential asymmetry. Physica D 237, 1719–1733 (2008)
Gendelman, O.V., Starosvetsky, Y., Feldman, M.: Attractors of harmonically forced linear oscillator with attached nonlinear energy sink I: description of response regimes. Nonlinear Dyn. 51, 31–46 (2008)
Deng, S.N., Ji, J.C., Wen, G.L., Xu, H.D.: Two-parameter dynamics of an autonomous mechanical governor system with time delay. Nonlinear Dyn. 107, 641–663 (2022)
Acknowledgements
This work was supported by the Natural Science Foundation of China [Grant Numbers 1207221, 12232014], the Fundamental Research Funds for the Central Universities [Grant Number 2013017] and the Ten Thousand Talents Program.
Funding
This work was supported by the Natural Science Foundation of China [Grant Numbers 1207221 and 12232014], the Fundamental Research Funds for the Central Universities [Grant Number 2013017] and the Ten Thousand Talents Program.
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Dang, W., Liu, S., Chen, L. et al. A dual-stage inerter-enhanced nonlinear energy sink. Nonlinear Dyn 111, 6001–6015 (2023). https://doi.org/10.1007/s11071-022-08183-y
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DOI: https://doi.org/10.1007/s11071-022-08183-y