A unified model for the dynamics of driven ribbon with strain and magnetic order parameters

TL;DR

This paper presents a comprehensive model for the complex driven dynamics of magnetostrictive ribbons with strain and magnetic order parameters, explaining various routes to chaos and symmetry phenomena observed experimentally.

Contribution

The authors introduce a unified mathematical framework that captures diverse dynamical behaviors in driven magnetostrictive and martensitic ribbons, extending understanding of their nonlinear responses.

Findings

Demonstrates period doubling and quasiperiodic routes to chaos.

Shows influence of near resonant fields on chaos suppression and induction.

Identifies symmetry restoring crisis with an exponent close to unity.

Abstract

We develop a unified model to explain the dynamics of driven one dimensional ribbon for materials with strain and magnetic order parameters. We show that the model equations in their most general form explain several results on driven magnetostrictive metallic glass ribbons such as the period doubling route to chaos as a function of a dc magnetic field in the presence of a sinusoidal field, the quasiperiodic route to chaos as a function of the sinusoidal field for a fixed dc field, and induced and suppressed chaos in the presence of an additional low amplitude near resonant sinusoidal field. We also investigate the influence of a low amplitude near resonant field on the period doubling route. The model equations also exhibit symmetry restoring crisis with an exponent close to unity. The model can be adopted to explain certain results on magnetoelastic beam and martensitic ribbon under sinusoidal driving conditions. In the latter case, we find interesting dynamics of a periodic one orbit switching between two equivalent wells as a function of an ac magnetic field that eventually makes a direct transition to chaos under resonant driving condition. The model is also applicable to magnetomartensites and materials with two order parameters.