Harmonic analysis of oscillators through standard numerical continuation tools

TL;DR

This paper introduces a numerical continuation method for harmonic analysis of nonlinear oscillators, applicable across various systems, and demonstrated through electronic and mechanical case studies.

Contribution

The paper presents a novel boundary value problem approach for harmonic analysis that integrates seamlessly with standard continuation software like AUTO.

Findings

Method effectively analyzes harmonic content of diverse oscillators.

Applicable to electronic, mechanical, and biochemical systems.

Facilitates oscillator analysis and design through constraint-following.

Abstract

In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard continuation package - without modification - such as AUTO, which we used. Our technique works for any kind of oscillator, including electronic, mechanical and biochemical systems. We provide two case studies. The first study concerns itself with the autonomous electronic oscillator known as the Colpitts oscillator, and the second one with a nonlinear damped oscillator, a non-autonomous mechanical oscillator. As shown in the case studies, the proposed technique can aid both the analysis and the design of the oscillators, by following curves for which a certain constraint, related to harmonic analysis, is fulfilled.