The dynamics of the pendulum suspended on the forced Duffing oscillator

TL;DR

This paper analyzes the complex dynamics of a pendulum attached to a forced Duffing oscillator, focusing on bifurcation behavior and attractor coexistence, with implications for practical mass absorption systems.

Contribution

It provides a detailed bifurcation analysis in two parameters, revealing the coexistence of multiple attractors and their impact on system stability and applications.

Findings

Identified regions with low attractor coexistence.

Mapped bifurcation structures in amplitude and frequency.

Discussed implications for tuned mass absorber design.

Abstract

We investigate the dynamics of the pendulum suspended on the forced Duffing oscillator. The detailed bifurcation analysis in two parameter space (amplitude and frequency of excitation) which presents both oscillating and rotating periodic solutions of the pendulum has been performed. We identify the areas with low number of coexisting attractors in the parameter space as the coexistence of different attractors has a significant impact on the practical usage of the proposed system as a tuned mass absorber.