Presents a systematic view of vibro-impact dynamics based on the nonlinear dynamics analysis Comprehensive understanding of any vibro-impact system is critically impeded by the lack of analytical tools viable for properly characterizing grazing bifurcation. The authors establish vibro-impact dynamics as a subset of the theory of discontinuous systems, thus enabling all vibro-impact systems to be explored and characterized for applications. Vibro-impact Dynamics presents an original theoretical way of analyzing the behavior of vibro-impact dynamics that can be extended to discontinuous dynamics. All topics are logically integrated to allow for vibro-impact dynamics, the central theme, to be presented. It provides a unified treatment on the topic with a sound theoretical base that is applicable to both continuous and discrete systems Vibro-impact Dynamics: <ul>
<li>Presents mapping dynamics to determine bifurcation and chaos in vibro-impact systems</li> <li>Offers two simple vibro-impact systems with comprehensive physical interpretation of complex motions</li> <li>Uses the theory for discontinuous dynamical systems on time-varying domains, to investigate the Fermi-oscillator</li> </ul>
Essential reading for graduate students, university professors, researchers and scientists in mechanical engineering.

Vibro-impact Dynamics

Science & Math

Guo, Yu

Luo, Albert C.J.

Physics

wiley

The inherent complex dynamics of a parametrically excited pendulum is of great interest in nonlinear dynamics, which can help one better understand the complex world. Even though the parametrically excited pendulum is one of the simplest nonlinear systems, until now, complex motions in such a parametric pendulum cannot be achieved. In this book, the bifurcation dynamics of periodic motions to chaos in a damped, parametrically excited pendulum is discussed. Complete bifurcation trees of periodic motions to chaos in the parametrically excited pendulum include: <ul> <li>period-1 motion (static equilibriums) to chaos, and</li> <li>period- motions to chaos ( = 1, 2, ---, 6, 8, ---, 12).</li> </ul> The aforesaid bifurcation trees of periodic motions to chaos coexist in the same parameter ranges, which are very difficult to determine through traditional analysis. Harmonic frequency-amplitude characteristics of such bifurcation trees are also presented to show motion complexity and nonlinearity in such a parametrically excited pendulum system. The non-travelable and travelable periodic motions on the bifurcation trees are discovered. Through the bifurcation trees of travelable and non-travelable periodic motions, the travelable and non-travelable chaos in the parametrically excited pendulum can be achieved. Based on the traditional analysis, one cannot achieve the adequate solutions presented herein for periodic motions to chaos in the parametrically excited pendulum. The results in this book may cause one rethinking how to determine motion complexity in nonlinear dynamical systems.

Bifurcation Dynamics of a Damped Parametric Pendulum (Synthesis Lectures on Mechanical Engineering, 22)

Morgan & Claypool Publishers

Bifurcation Dynamics of a Damped Parametric Pendulum (Synthesis Lectures on Mechanical Engineering)

Springer

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