Synchronous motion of two vertically excited planar elastic pendula

TL;DR

This paper investigates the synchronized oscillatory and rotational behaviors of two elastic pendula on a horizontally excited platform, revealing stable in-phase and anti-phase states and their bifurcations.

Contribution

It provides a comprehensive analysis of the bifurcation scenarios and robustness of synchronous states in coupled elastic pendula systems.

Findings

Stable in-phase and anti-phase synchronous states coexist.

Bifurcation scenarios from synchronous to asynchronous motion are mapped.

Synchronization persists over a wide range of parameters.

Abstract

The dynamics of two planar elastic pendula mounted on the horizontally excited platform have been studied. We give evidence that the pendula can exhibit synchronous oscillatory and rotation motion and show that stable in-phase and anti-phase synchronous states always co-exist. The complete bifurcational scenario leading from synchronous to asynchronous motion is shown. We argue that our results are robust as they exist in the wide range of the system parameters.