Work

Dynamic Patterns and Self-Knotting of a Driven Hanging Chain

Year: 2001

Type: article

Abstract: When shaken vertically, a hanging chain displays a startling variety of distinct behaviors. We find experimentally that instabilities occur in tonguelike bands of parameter space, to swinging or rotating pendular motion, or to chaotic states. Mathematically, the dynamics are described by a nonlinear wave equation. A linear stability analysis predicts instabilities within the well-known resonance tongues; their boundaries agree very well with experiment. Full simulations of the 3D dynamics reproduce and elucidate many aspects of the experiment. The chain is also observed to tie knots in itself, some quite complex. This is beyond the reach of the current analysis and simulations.

Source: Physical Review Letters

DOI: 10.1103/physrevlett.87.114301

Authors: Andrew Belmonte, Michael J. Shelley, Shaden T. Eldakar, Chris H. Wiggins

Institutions: Pennsylvania State University, Courant Institute of Mathematical Sciences, New York University

Language: English

Topic: Vibration and Dynamic Analysis

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, U.S. Department of Energy, Alfred P. Sloan Foundation

OpenAlex ID: W2168855222

FWCI: 4.258

Cites: 27

Cited by: 75

Related to: 10