Coupled nonlinear oscillators: metamorphoses of amplitude profiles for the approximate effective equation - the case of 1:3 resonance

TL;DR

This paper analyzes how the amplitude response of two coupled nonlinear oscillators, modeled as a vibration absorber, changes with parameters during 1:3 resonance, revealing metamorphoses in amplitude profiles.

Contribution

It investigates the metamorphoses of amplitude profiles in coupled oscillators during 1:3 resonance using an approximate effective equation.

Findings

Amplitude profiles exhibit significant metamorphoses with parameter changes.

The study provides detailed characterization of these metamorphoses.

Results enhance understanding of nonlinear resonance behaviors in coupled systems.

Abstract

We study dynamics of two coupled periodically driven oscillators. An important example of such a system is a dynamic vibration absorber which consists of a small mass attached to the primary vibrating system of a large mass. Periodic solutions of the approximate effective equation (derived in our earlier papers) are determined within the Krylov-Bogoliubov-Mitropolsky approach to compute the amplitude profiles $A(\Omega)$. In the present paper we investigate metamorphoses of the function $A(\Omega)$ induced by changes of the control parameters in the case of 1:3 resonances.