Parametric Resonance: Application on Low Noise Mechanical and Electromechanical Amplifiers

Due to the growing demand for low noise signal amplification, developing mechanical and electromechanical parametric amplifiers is a topic of interest. Parametric amplification in mechanical domain refers to the method for amplifying the dynamic response of a mechanical sensor by modulating system parameters such as effective stiffness. Most of the studies in this regard have been focused on truncating equation of motion such that only linear terms remain. In this chapter, mathematical models of mechanical and electromechanical parametric amplifiers in the literature are reviewed. Then, the effect of nonlinearity is investigated by including a cubic nonlinearity on the governing equation of a classical degenerate parametric amplifier. To this end, the method of multiple scales (perturbation) has been utilized to calculate steady state solution of the nonlinear Mathieu-type equation. In addition, by determining the nature of singular points, stability analysis over the steady state response is performed. All the frequency response curves demonstrate a Duffing-like trend near the primary resonance of the system; however, the number of stable solutions changes with the parameters of the system. Furthermore, performance metrics of the system is analyzed in the presence of nonlinearity. The findings indicate that even very small nonlinearity term can dramatically decrease system performance as well as changing the relative phase in which maximum gain occurs.

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