Power flow analysis of nonlinear dynamical systems

Abstract

The power flow analysis approach, which arose from high frequency vibration problems, has been developed into a powerful technique to characterise the dynamic behaviour of complex structures and coupled systems. It has been extensively used to study various linear systems. However, because of the complexity in modelling and simulation, the power flow behaviour of nonlinear dynamical systems remains largely unexplored. This thesis aims to develop power flow analysis approaches for nonlinear dynamical systems, to investigate the effects of damping and/or stiffness nonlinearities on their power flow behaviour, and to apply the findings to enhance the performance of energy harvesting devices as well as vibration control systems. Power flow characteristics of the Du?ng and the Van der Pol (VDP) oscillators are investigated to address the distinct power input and dissipation behaviour due to stiffness and damping nonlinearities, respectively. It is shown that in a nonlinear velocity response with multiple frequency signatures, only the in-phase component of the same frequency as the harmonic excitation contributes to the time-averaged input power. It is demonstrated that bifurcations can cause significant jumps of time-averaged power flows, whereas the associated time-averaged input power of a chaotic response is insensitive to the initial conditions but tends to an asymptotic value as the averaging time increases. It is also found that the time averaged input power of the unforced VDP oscillator can become negative in some ranges of excitation frequencies. Power flow behaviour of two degrees-of-freedom systems with nonlinear stiffness/- damping is also studied using the developed methods to enhance vibration isolation/absorption performance. It is demonstrated that the stiffness and damping nonlinearities in the system affects time-averaged power flows mainly in a narrow frequency range around resonance frequencies. The work described in this thesis provides new insights into power flow generation, transmission and dissipation mechanisms in nonlinear dynamical systems and facilitates more reliable and effective designs with improved dynamic performance. The ability of the VDP oscillator to extract external energy sheds light on energy harvesting using flow-induced vibrations of a nonlinear flapping foil system. A nonlinear isolator with a negative stiffness mechanism is proposed providing less input power in an enlarged frequency range. These studies thus yield an improved understanding of power flow behaviour in nonlinear dynamical systems.

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ORCID for Y.P. Xiong: orcid.org/0000-0002-0135-8464

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