Coupled nonlinear oscillators: metamorphoses of amplitude profiles. The case of the approximate effective equation

TL;DR

This paper investigates the complex amplitude responses of two coupled nonlinear oscillators, such as vibration absorbers, revealing new nonlinear phenomena through analysis of approximate effective equations and their metamorphoses.

Contribution

It introduces an analysis of amplitude profile metamorphoses in coupled oscillators using the Krylov-Bogoliubov-Mitropolsky approach, highlighting complex behaviors beyond single oscillator models.

Findings

Amplitude profiles exhibit complex metamorphoses with parameter changes.

New nonlinear phenomena are identified in coupled oscillator dynamics.

Dependence of amplitude on frequency is more intricate than in single Duffing oscillators.

Abstract

We study dynamics of two coupled periodically driven oscillators. 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 are determined within the Krylov-Bogoliubov-Mitropolsky approach to get the amplitude profiles $AOmega) $. Dependence of the amplitude $A$ of nonlinear resonances on the frequency $ \Omega $ is much more complicated than in the case of one Duffing oscillator and hence new nonlinear phenomena are possible. In the present paper we study metamorphoses of the function $A(\Omega) $ induced by changes of the control parameters.