Abstract
A common phenomenon observed in dynamic mechanical systems is the presence of selfexcited vibrations under normal operating conditions. A classic example of this phenomenon can be seen on electrical power transmission lines that is commonly referred to as transmission line gallop. Transmission lines have been known to ”gallop”, oscillate up and down, with the oscillation increasing in magnitude until mechanical failure of the system occurs. The type of vibration that is occurring is classified as a self-excited vibration and is an example of a system that is dynamically unstable. In his classic text book, Mechanical Vibrations, J.P. Den Hartog presented this phenomena and described the dynamics of the phenomena in great detail. In addition, he proposed an apparatus that clearly and simply illustrates this phenomena to the reader. This apparatus is a simple massspring system that can be constructed and used to demonstrate the self-excited vibrations with the use of a small desk fan. This thesis will cover the theory and derivation of a proposed control method to settle the self-excited vibrating system. The approach for quenching the vibrations will utilize the theory of applying a controlled periodic force that mimics the forces created by a tuned mass damper. In addition to developing a control method, the thesis will also look at the development of the apparatus proposed by Den Hartog as well as implement the proposed control method and evaluate its effectiveness in canceling the self-excited vibration. And finally, in the development of this apparatus and control system, efforts will be made to utilize simple low cost micro-controller (Arduino) and hobbyist hardware (servos and springs) with the intention that this system could be easily constructed by students and educators in the future. The goal of this thesis was to develop a control method and test the theory for effectiveness after constructing the aforementioned apparatus. The results of this research activity have the potential to be extended and adapted for many applications where self-excited vibrations may occur. In addition, the platform that was developed to to test the theories in this thesis could be extended to further research and demonstration purposes.