Macromechanical Parametric Amplification

Parametric amplification is obtained by adding parametric excitation to direct (externally driven) excitation for boosting near-resonant oscillations. It is utilized for mass and force sensing, switching and signal processing, filtering, timing, signal amplification, and appears promising for energy harvesting. Using analytical, numerical, and experimental methods, the thesis focuses on superthreshold pumping (above the systems parametric instability threshold), nonlinear effects, frequency response backbones, and frequency detuning effects for parametric amplifiers.
Part one of the thesis covers superthreshold pumping and nonlinear effects. Superthresh-old pumping produces some useful characteristics. For instance, strong superthreshold pumping yields a high gain even though nonlinear effects tend to reduce it. In addition, a narrower excitation phase range is realized for which attenuation occurs. It is demonstrated that stronger nonlinear effects can cause jumps and bistability in the amplitude-phase characteristics, which in turn enrich the dynamic response of the system.
Part two shows that mixed quadratic and cubic nonlinearities may generate additional amplitude-frequency solutions, as compared to a system where only cubic nonlinearities are considered. When these effects cancel out, a significantly increased response is obtained, as compared to the case with pure quadratic or pure cubic nonlinearity.
Part three investigates frequency response backbones. An undamped but parametrically excited frequency response backbone is proposed instead of the classic unforced and undamped backbone. With the modified and more general backbone, it is shown how the response of a superthreshold pumped amplifier is related to respectively the pure directly and pure parametrically excited response. Benefits of superthreshold parametric pumping, as compared to pure direct or pure parametric excitation, are given.
The last part examines frequency detuning effects. In addition to being relevant for most applications in itself, frequency detuning yields some interesting and useful features. Some of the characteristics of, respectively, a pure directly excited system and a pure parametrically excited system can simultaneously be utilized or avoided in a frequency detuned parametric amplifier. Moreover, parts of the amplitude-frequency curves can collapse, and the frequency separation between the two peaks can be altered. The first experimental bistable amplified steady-state responses are also reported.
The derived analytical models and experimental setups can readily be extended to investigate other factors. Some of the results are also applicable to the more general field of systems subjected to combined parametric and direct excitation.