Complex dynamics of a harmonically excited structure coupled with a nonlinear energy sink 
期刊名称Acta Mechanica Sinica
作者Jian Zang; Li-Qun Chen
摘要Nonlinear behaviors are investigated for a structure coupled with a nonlinear energy sink. The structure is linear and subject to a harmonic excitation, modeled as a forced single-degree-of-freedom oscillator. The nonlinear energy sink is modeled as an oscillator consisting of a mass, a nonlinear spring, and a linear damper. Based on the numerical solutions, global bifurcation diagrams are presented to reveal the coexistence of periodic and chaotic motions for varying nonlinear energy sink mass and stiffness. Chaos is numerically identified via phase trajectories, power spectra, and Poincaré maps. Amplitude-frequency response curves are predicted by the method of harmonic balance for periodic steady-state responses. Their stabilities are analyzed. The Hopf bifurcation and the saddle-node bifurcation are determined. The investigation demonstrates that a nonlinear energy sink may create dynamic complexity.
关键词Nonlinear energy sink; Global bifurcation; Chaos; Harmonic balance method; Stability
参考文献1. Vakakis, A. F.:Inducing passive nonlinear energy sink in vibrating systems. J. Vib. Acoust. 123, 324-332 (2001)  
2. Gendelman, O., Manevitch, L. I., Vakakis, A. F., et al.:Energy pumping in nonlinear mechanical oscillators:part I-dynamics of the underlying hamiltonian systems. J. Appl. Mech. 68, 34-41 (2001)  
3. Lee, Y. S., Vakakis, A. F., Bergman, L. A., et al.:Passive non-linear targeted energy transfer and its applications to vibration absorption:a review. Proc. IMechE Part K J. Multi-body Dyn. 222, 77-134 (2008)
4. Vakakis, A. F., Gendelman, O. V., Bergman, L. A., et al.:Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems. Springer, Dordrecht (2009)
5. Jiang, X., McFarland, D. M., Bergman, L. A., et al.:Steady state passive nonlinear energy pumping in coupled oscillators:theoretical and experimental results. Nonlinear Dyn. 33, 87-102 (2003)  
6. Gendelman, O. V., Lamarque, C. H.:Dynamics of linear oscillator coupled to strongly nonlinear attachment with multiple states of equilibrium. Chaos Solitons Fractals 24, 501-509 (2005)  
7. Gendelman, O. V., Gourdon, E., Lamarque, C. H.:Quasiperiodic energy pumping in coupled oscillators under periodic forcing. J. Sound Vib. 294, 651-662 (2006)  
8. Malatkar, P., Nayfeh, A. H.:Steady-State dynamics of a linear structure weakly coupled to an essentially nonlinear oscillator. Nonlinear Dyn. 47, 167-179 (2006)  
9. 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 (2007)  
10. Starosvetsky, Y., Gendelman, O. V.:Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. b:optimization of a nonlinear vibration absorber. Nonlinear Dyn. 51, 47-57 (2007)
11. Starosvetsky, Y., Gendelman, O. V.:Response regimes of linear oscillator coupled to nonlinear energy sink with harmonic forcing and frequency detuning. J. Sound Vib. 315, 746-765 (2008)  
12. Starosvetsky, Y., Gendelman, O. V.:Strongly modulated response in forced 2DOF oscillatory system with essential mass and potential asymmetry. Phys. D Nonlinear Phenom. 237, 1719-1733 (2008)  
13. Starosvetsky, Y., Gendelman, O. V.:Vibration absorption in systems with a nonlinear energy sink:nonlinear damping. J. Sound Vib. 324, 916-939 (2009)  
14. Ture Savadkoohi, A., Manevitch, L. I., Lamarque, C. -H.:Analysis of the transient behavior in a two dof nonlinear system. Chaos Solitons Fractals 44, 450-463 (2011)  
15. Luongo, A., Zulli, D.:Dynamic analysis of externally excited NEScontrolled systems via a mixed Multiple Scale/Harmonic Balance algorithm. Nonlinear Dyn. 70, 2049-2061 (2012)  
16. Gourc, E., Michon, G., Seguy, S., et al.:Experimental investigation and design optimization of targeted energy transfer under periodic forcing. J. Vib. Acoust. 136, 21021 (2014)  
17. Ture Savadkoohi, A., Lamarque, C. -H., Dimitrijevic, Z.:Vibratory energy exchange between a linear and a nonsmooth system in the presence of the gravity. Nonlinear Dyn. 70, 1473-1483 (2012)  
18. Weiss, M., Chenia, M., Ture Savadkoohi, A., et al.:Multi-scale energy exchanges between an elasto-plastic oscillator and a light nonsmooth system with external pre-stress. Nonlinear Dyn. 83, 109-135 (2016)  
19. Lamarque, C. -H., Ture Savadkoohi, A., Charlemagne, S., et al.:Nonlinear vibratory interactions between a linear and a non-smooth forced oscillator in the gravitational field. Mech. Syst. Signal Process. 89, 131-148 (2017)  
20. Ahmadabadi, Z. N., Khadem, S. E.:Annihilation of high-amplitude periodic responses of a forced two degrees-of-freedom oscillatory system using nonlinear energy sink. J. Vib. Control 19, 2401-2412 (2013)  
21. Bellizzi, S., Côte, R., Pachebat, M.:Responses of a two degree-offreedom system coupled to a nonlinear damper under multi-forcing frequencies. J. Sound Vib. 332, 1639-1653 (2013)  
22. Yang, K., Zhang, Y. -W., Ding, H., et al.:The transmissibility of nonlinear energy sink based on nonlinear output frequency-response functions. Commun. Nonlinear Sci. Numer. Simul. 44, 184-192 (2017)  
23. Yang, K., Zhang, Y. -W., Ding, H., et al.:Nonlinear energy sink for whole-spacecraft vibration reduction. J. Vib. Acoust. 139, 21011 (2017)  
24. Luongo, A., Zulli, D.:Nonlinear energy sink to control elastic strings:the internal resonance case. Nonlinear Dyn. 81, 425-435 (2015)  
25. Zulli, D., Luongo, A.:Nonlinear energy sink to control vibrations of an internally nonresonant elastic string. Meccanica 50, 781-794 (2015)  
26. Parseh, M., Dardel, M., Ghasemi, M. H.:Performance comparison of nonlinear energy sink and linear tuned mass damper in steadystate dynamics of a linear beam. Nonlinear Dyn. 81, 1981-2002 (2015)  
27. Parseh, M., Dardel, M., Ghasemi, M. H.:Investigating the robustness of nonlinear energy sink in steady state dynamics of linear beams with different boundary conditions. Commun. Nonlinear Sci. Numer. Simul. 29, 50-71 (2015)  
28. Taghipour, J., Dardel, M.:Steady state dynamics and robustness of a harmonically excited essentially nonlinear oscillator coupled with a two-DOF nonlinear energy sink. Mech. Syst. Signal Process. 62-63, 164-182 (2015)
29. Ding, H., Zu, J. W.:Steady-state responses of pulley-belt systems with a one-way clutch and belt bending stiffness. J. Vib. Acoust. 136, 41006 (2014)  
30. Ding, H.:Periodic responses of a pulley-belt system with one-way clutch under inertia excitation. J. Sound Vib. 353, 308-326 (2015)  
作者地址1 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
2 Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai 200072, China;
3 Department of Mechanics, Shanghai University, Shanghai 200444, China

版权所有 中国力学学会 | 网站内容未经许可,不得转载。 | 京ICP备05039218号-1, 审核日期:2014年2月26日
北京市北四环西路15号  邮政编码:100190  联系电话:+86-10-82543905  传真:+86-10-82543907  电子邮箱:
总访问量: 212424