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Multi-valued responses and dynamic stability of a nonlinear vibro-impact system with a unilateral non-zero offset barrier

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Chinese Physics B 2016年第3期25卷 91-99页

作者：徐伟黄冬梅谢文贤 Department of Applied Mathematics Northwestern Polytechnical UniversityXi'an 710072China Department of Civil and Environmental Engineering Rice UniversityHouston 77005USA

In this paper, multi-valued responses and dynamic properties of a nonlinear vibro-impact system with a unilateral nonzero offset barrier are studied. Based on the Krylov-Bogoliubov averaging method and Zhuravlev non-smooth trans- formation, the frequency response, stability conditions, and the equation of backbone curve are derived. Results show that in some conditions impact system may have two or four steady-state solutions, which are interesting and not mentioned for a vibro-impact system with the existence of frequency island phenomena. Then, the classification of the steady-state solutions is discussed, and it is shown that the nontrivial steady-state solutions may lose stability by saddle node bifurcation and Hopf bifurcation. Furthermore, a criterion for avoiding the jump phenomenon is derived and verified. Lastly, it is found that the distance between the system＇s static equilibrium position and the barrier can lead to jump phenomenon under hardening type of nonlinearity stiffness.

关键词： vibro-impact system multi-valued response frequency island stability

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Principal resonance response of a stochastic elastic impact oscillator under nonlinear delayed state feedback

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Chinese Physics B 2015年第4期24卷 90-99页

作者：黄冬梅徐伟谢文贤韩群 Department of Applied Mathematics Northwestern Polytechnical University Department of Civil and Environmental Engineering Rice University

In this paper, the principal resonance response of a stochastically driven elastic impact （El） system with time-delayed cubic velocity feedback is investigated. Firstly, based on the method of multiple scales, the steady-state response and its dynamic stability are analyzed in deterministic and stochastic cases, respectively. It is shown that for the case of the multi- valued response with the frequency island phenomenon, only the smallest amplitude of the steady-state response is stable under a certain time delay, which is different from the case of the traditional frequency response. Then, a design criterion is proposed to suppress the jump phenomenon, which is induced by the saddle-node bifurcation. The effects of the feedback parameters on the steady-state responses, as well as the size, shape, and location of stability regions are studied. Results show that the system responses and the stability boundaries are highly dependent on these parameters. Furthermore, with the purpose of suppressing the amplitude peak and governing the resonance stability, appropriate feedback gain and time delay are derived.

关键词： elastic impact system time delay frequency island jump avoidance

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Study of response and transmissibility of a viscoelastic isolation system with a power-form restoring force under delayed feedback control

Study of response and transmissibility of a viscoelastic iso...

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第十届动力学与控制学术会议

作者： HUANG Dong-me Department of Applied Mathematics Northwestern Polytechnical University

In this paper, combination of cubic nonlinearity and time delay is designed to improve the performance of a viscoelastic isolation system with a power-form restoring force. Based on the method of multiple scales, the frequency response and stability are considered. The viscoelastic damping coefficient is shown to induce multi-valued responses and frequency island phenomenon. Then, equivalent damping and jump avoidance condition are proposed to interpret the effect of feedback control loop on dynamic behaviors. Furthermore, the effects of time delays on frequency response and performance of controllers are presented. With the purpose of improving the stability and reducing the vibration, suitable feedback parameter pairs are determined. Last, the effects of the system parameters on the energy transmissibility is investigated.

关键词： Delayed feedback control frequency island dynamic vibration isolator multivalued response transmissibility

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