Energy Flow Theory of Nonlinear Dynamical Systems with by Jing Tang Xing

By Jing Tang Xing

This monograph develops a generalised strength movement concept to enquire non-linear dynamical structures ruled via usual differential equations in section house and infrequently met in numerous technological know-how and engineering fields. vital nonlinear phenomena similar to, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding strength circulate behaviors are printed utilizing the proposed power move technique. As examples, the typical nonlinear dynamical structures, similar to, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, and so on, are mentioned. This monograph lighting fixtures a brand new strength stream study course for nonlinear dynamics. A generalised Matlab code with person Manuel is equipped for readers to behavior the strength movement research in their nonlinear dynamical structures. through the monograph the writer constantly returns to a few examples in each one bankruptcy to demonstrate the functions of the mentioned idea and ways. The booklet can be utilized as an undergraduate or graduate textbook or a complete resource for scientists, researchers and engineers, delivering the assertion of the artwork on power stream or strength move conception and methods.

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Another approach is to use nonlinear springs with a variable dynamic stiffness. For ground vibration tests of aircrafts, a nonlinear supporting system was proposed and used (Molyneux 1958; Xing 1975) to obtain a very low supporting frequency. 6 Short Review on Current State of PFA 37 on designs, practical techniques and performance of nonlinear suspension systems were reported quite late, see, for example, Alabuzhev et al (1989), Platus (1992), Zhang et al (2004), Carrela, Brennan & Waters (2007), Carrela et al (2008), Kovaic, Brennan & Waters (2008), Ahn (2008), Cao et al (2008ab), Liu, Chen & Cao (2010).

By conducting power flow analysis, the power flow transmissions from a machine into the base structure can be identified, which is a more appropriate indictor of isolation performance than the traditional force or displacement transmissibility. For this reason, many researches focused their attentions on the analysis and control of vibrational power flows of dynamical systems (see, for example, Pinnington 1987; Pinnington & White 1981; Pan, Pan & Hansen 1992; Gardonio, Elliott & Pinnington 1997ab; Mahajan & Redfield 1998; Li & Lavrich 1999; Xiong, Xing & Price 2000c, 2003).

Another approach is to use nonlinear springs with a variable dynamic stiffness. For ground vibration tests of aircrafts, a nonlinear supporting system was proposed and used (Molyneux 1958; Xing 1975) to obtain a very low supporting frequency. 6 Short Review on Current State of PFA 37 on designs, practical techniques and performance of nonlinear suspension systems were reported quite late, see, for example, Alabuzhev et al (1989), Platus (1992), Zhang et al (2004), Carrela, Brennan & Waters (2007), Carrela et al (2008), Kovaic, Brennan & Waters (2008), Ahn (2008), Cao et al (2008ab), Liu, Chen & Cao (2010).

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