UCLA

Prior resonator research is first over-viewed. Galerkin analysis applied to a perturbedthin ring yields intuition and motivation for the primary contributions, described below.

The first contribution is a fully fleshed novel method to derive the empirical frequencyresponse by extracting a state space model from transient data through a Hankel matrix based approach. This method has the advantage of not containing feed-through parasitic capacitance present in frequency responses derived from conventional methods. Furthermore, a zoom method is described to reduce the computational cost associated with extracting the state space based model.

The second contribution is the use of the aforementioned empirical state space modelto fit a second order mechanistic model that accurately predicts changes in resonator dynamics after a mass and/or stiffness perturbation has been applied. This model is a better alternative to older predictive models because it includes a stiffness energy component. In addition, this new model gives the added tool of a predictive system frequency response, which conventional models do not have. In general it is found that, especially as the modes are close to degenerate, using lower sensitivity point masses in the outermost ring layers optimizes the predictive power of the new model. Furthermore, predicting for the effects of as few point masses as possible limits the model due to point mass variance and higher harmonic radial velocity components creating model prediction error.

The third contribution is in the design, building, and testing of a stiff, piezoelectric 6degree of freedom force/torque transducer to measure and inform modeling techniques for coupling between a resonator and its base affixed center stem. A simple lightweight steel tuning fork attached to this transducer confirms the latter’s efficacy.