| The subject of this study is the dynamic analysis of linear, multi-degree-of-freedom structures with closely spaced natural frequencies. Such structures appear in complex civil, mechanical, and aerospace systems.; The study begins with non-classical damping, where the undamped modes are strongly coupled by structural damping. Both modal and frequency response approaches are used. Closed-form solutions of the eigen-properties are obtained by a generalized perturbation technique. The results show that even small damping terms can result in significant changes in the modal properties of structures with closely spaced natural frequencies.; The results of the non-classical damping study are then used to develop two vibration control methods. The first involves tuned mass dampers (TMD's). The conventional TMD design uses a single oscillator attached to a relatively large structure. Herein, a new concept is developed where the single TMD is replaced by multiple TMD's. The theoretical foundation and an optimal design strategy for multiple TMD's is derived using the impedance concept and asymptotic techniques. It is found that multiple TMD's can be more robust and more effective than a single TMD of the same total mass.; The last part of thesis discusses active control of structures with closely spaced natural frequencies. In this case, the control input acts to couple the equations of motion in a more general manner than found in non-classical damping. Three well-known control algorithms, velocity feedback, pole allocation, and optimal control, are examined. It is found that if only a single controller is used to control two modes with closely spaced natural frequencies, then all of the control algorithms will have an upper bound of effectiveness. A study of robustness indicates that the closed-loop system can become unstable even with small errors in the spacing of the natural frequencies. |
