Modeling of restoring force characteristics of rubber bearings under multi-axial loading

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The present study investigates an alternative remedy to control self-excited oscillation of slender structures by transferring energy from lower modes of vibration to higher modes. In a theoretical approach based on simplified models, various passive and semi-active devices are proposed and compared. The first chapter introduces the principle and the background of this study. In chapter two and three, a self-excited two-degree-of-freedom model with a passive magnetic device is considered. The presence of the device induces a strong non-linearity in the system. The analysis is based on energy considerations and finds that, depending on the setting of the device, the system can have either one or two stable steady states. The existence of two families of steady states is an obstacle for an optimal design of a passive magnetic device. To ensure that the system stays at the steady state with the lowest amplitude of oscillation, semi-active devices are proposed and analyzed in chapter four. It is found that the efficiency and robustness is greatly improved. Results of simulation showing good agreements with the analysis are also presented. The second part of this study is concerned with continuous structures. In chapter five, the galloping wind model is formulated and chapter six deals with the implementation of a passive magnetic device on a cable. Finally, the passive magnetic device and the semi-active devices are tested on a cable via simulation. The results, presented in chapter seven, are similar to those obtained in two degrees of freedom and demonstrates the potential of using these control schemes in practical applications on slender structures : energy input through the building up of unstable lower modes is transferred to stable higher modes and then dissipated by the decay of high frequency vibration.