Propagating stress-pulses and wiggling transition revealed in string dynamics

TL;DR

This paper explores the complex behaviors of flexible strings under different boundary motions, revealing stress pulse propagation and a wiggling transition, with analytical solutions and phase diagrams provided.

Contribution

It introduces the first analytical description of the wiggling transition and stress pulse propagation in string dynamics under specific boundary conditions.

Findings

Stress pulses propagate along the string under transverse harmonic motion.

The wiggling transition is analytically derived and characterized.

Phase diagrams illustrate different dynamic regimes.

Abstract

Understanding string dynamics yields insights into the intricate dynamic behaviors of various filamentary thin structures in nature and industry covering multiple length scales. In this work, we investigate the planar dynamics of a flexible string where one end is free and the other end is subject to transverse and longitudinal motions. Under transverse harmonic motion, we reveal the propagating pulse structure in the stress profile over the string, and analyze its role in bringing the system into a chaotic state. For a string where one end is under longitudinal uniform acceleration, we identify the wiggling transition, derive the analytical wiggling solution from the string equations, and present the phase diagram.