Analytical, numerical and experimental investigation of a tunable, nonlinear multi-degree-of-freedom parametrically excited amplifier

TL;DR

This paper presents a comprehensive study of a tunable, nonlinear multi-degree-of-freedom parametric amplifier, combining analytical, numerical, and experimental methods to demonstrate its ability to shift weak signals to higher frequencies.

Contribution

It introduces a novel tunable amplifier design with a detailed analytical model, numerical simulations, and experimental validation, advancing the understanding of nonlinear parametric amplification.

Findings

Analytical solutions match numerical simulations.

Preliminary experiments show favorable agreement with theory.

The device effectively shifts weak signals to higher frequencies.

Abstract

A tunable, multi-degree-of-freedom, parametrically excited amplifier is introduced as an apparatus capable of shifting slow, weak signals to higher frequencies, by exploiting the amplifier natural resonances via controlled parametric excitation and nonlinear feedback. This device can find use as a signal amplifier and as a spectrum control device. A tuned dual-frequency signal is created to parametrically excite (pump) the system and produce the desired energy shift. The pump signal is applied by a controlled electromechanical actuator, and is modified in-situ according to the slow frequency signal and the desired response. A three DOF model is introduced, and the governing nonlinear EOM are derived and solved analytically via asymptotic methods and verified with numerical simulations. A parametric design of an experimental rig was carried out, and the importance of experimental calibration and system identification is emphasized. Some preliminary experimental results are provided with favorable agreement with the theory.