Abstract
The Mathieu equation is known for its unique excitating scheme and great sensitivity to resonant conditions. However, due to the strong non-stationarity and non-linearity, its application to measurement has hardly been considered. In this paper, we formulate the Mathieu equation system based on the weighted integral method in time domain, and develop the parameter estimation method. Then, from the analysis of the statistical characteristics of the above method, we derive the optimal conditions for measuring the parameters with super-sensitivity, and propose a self-oscillatory measurement scheme in which target parameters are continuously captured in the measurable range with great sensitivity by controlling the excitation frequency toward the phase transition point of the Mathieu equation system. To verify the above, we fabricate an experimental equipment using the piezo actuator as the tension exciter of the phosphor bronze beam. We observe that the system can successfully follow the change of tension and viscous resistance with excellent sensitivity.
