Mechanical Domain Parametric Amplification

Abstract

Though utilized for more than 50years in a variety of power and communication systems, parametric amplification, the process of amplifying a harmonic signal with a parametric pump, has received very little attention in the mechanical engineering community. In fact, only within the past 15–20years has the technique been implemented in micromechanical systems as a means of amplifying the output of resonant microtransducers. While the vast potential of parametric amplification has been demonstrated, to date, in a number of micro- and nanomechanical systems (as well as a number electrical systems), few, if any, macroscale mechanical amplifiers have been reported. Given that these amplifiers are easily realizable using larger-scale mechanical systems, the present work seeks to address this void by examining a simple representative example: a cantilevered beam with longitudinal and transverse base excitations. The work begins with the systematic formulation of a representative system model, which is used to derive a number of pertinent metrics. A series of experimental results, which validate the work’s analytical findings, are subsequently examined, and the work concludes with a brief look at some plausible applications of parametric amplification in macroscale mechanical systems.

In-Plane Nonlinear Dynamics of Wind Turbine Blades

“…As such, a linear system excited both parametrically and directly at the same frequency can exhibit a superharmonic resonance. This complements linear primary resonance phenomena and linear subharmonic resonances exploited in parametric amplification [12,13].…”

“…They have identified systems with direct and parametric excitation and studied their behavior. Experimental results that demonstrate exploitation of parametric amplification [13]. Other work has been on forced and unforced parametrically excited systems with van der Pol, Rayleigh and Duffing nonlinearities.…”

An experimentally validated parametrically excited vibration energy harvester with time-varying stiffness

“…Parametric amplification has been studied for different applications in macro scale devices. 14,30,31 For the system introduced here, the parametric amplitude δ is a function of AC current and the sooner the system becomes parametric and reaches the instability threshold, the lower the power consumed by the parametrically excited energy harvester. The experimental results for the transition curve when the stable responses are captured shows the system has potential to generate the steady-state responses inside the transition curve plotted in Fig.…”

“…The free response study of the nonlinear parametrically excited system has been mentioned in few work, although the forced responses were explained in several publications. [14][15][16] The voltage across the optimum resistive load parallel with the piezoelectric sensor is measured to find the average dissipated power. The Root Mean Square power (RMS power) for a parametrically excited harvester at different frequency is compared.…”

Mass-modulation schemes for a class of wave energy converters: Experiments, models, and efficacy

“…The goal of this variation is to increase the velocity of the relative heaving motion of the system thereby improving energy harvesting. Part of the inspiration for the method came from the response amplification observed in the resonant behavior of parametrically excited systems (see, e.g., Rhoads et al (2008); Rugar and Grütter (1991); Wirkus et al (1998)). …”