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

本文研究了一种控制细长结构自激振动的方法，即通过将低阶振动的能量转移到高阶振动的能量。在简化模型的基础上的理论方法，提出了各种无源和半有源器件和比较。第一章介绍了本文的研究背景和研究原则。第二章和第三章考虑了带被动磁装置的自激二自由度模型。设备的存在在系统中引起强非线性。分析是基于能量的考虑，并发现，根据设备的设置，系统可以有一个或两个稳定的稳态。两族稳态的存在是无源磁器件优化设计的一个障碍。为了保证系统在稳态时具有最小的振荡幅度，第四章提出并分析了半主动装置。实验结果表明，该算法的效率和鲁棒性得到了很大的提高.仿真结果与分析结果吻合较好。本研究的第二部分涉及连续结构。第五章建立了驰振风的数学模型，第六章讨论了在电缆上安装被动磁装置的方法。最后，通过仿真，在电缆上对无源磁器件和半有源磁器件进行了测试。在第七章中给出的结果与在两个自由度中得到的结果相似，并且展示了在细长结构的实际应用中使用这些控制方案的潜力：通过建立不稳定的低阶模态输入的能量被转移到稳定的高阶模态，然后通过高频振动的衰减被耗散。

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.