| Elimination of unwanted vibrations is an important problem that engineers have been tackling for more than a hundred years. The most common method employed for minimization of unwanted vibrations is the mechanical vibration absorber. Vibration absorbers can be in different forms, such as mechanical mass-spring-dampers, as well as electro-mechanical and fluidic devices that resonate and dissipate energy. The main objective of this dissertation is to make fundamental contributions to the design theory of vibration absorbers, with specific applications to mechanical and electro-mechanical types.;Electro-mechanical vibration absorber design theory is relatively new compared to mechanical vibration absorber theory. In this study the electro-mechanical vibration absorber system under consideration is a piezoelectric patch, a simply supported plate, which is the main system to be controlled and a shunt circuit system across the piezoelectric patch. The classical vibration absorber theory (Den Hartog's method) is adapted to the electro-mechanical vibration absorber system. An alternative design method is introduced that accounts for the main system damping, multiple modal contributions and hysteretic non-linearity in the piezoelectric patch.;Mechanical vibration absorber theory is nearly a hundred years old. The most commonly used technique is based on Den Hartog's invariant points principle. However, this method is designed for single degree of freedom undamped main systems. It cannot account for multiple modal contributions and it cannot minimize a weighted linear summation of the coordinate or modal responses. Minimizing a weighted linear summation of coordinates is important when the acoustical properties of a system are to be minimized. A new method is introduced that extends Den Hartog's method to multi degree of freedom systems and this new method is capable of accounting for main system damping, multiple modal contributions and minimizing a weighted summation of coordinates or modal responses. |
