Energetics and conserved quantity of an axially moving string undergoing three-dimensional nonlinear vibration

• 来源期刊: 力学学报（英文版）
• 年，卷（期）: 2008,（2）
• 页码范围: 215-221
• 页数: 7页
• 语种: 英文
• DOI: 10.1007/s10409-008-0110-5

摘要

Nonlinear three-dimensional vibration of axially moving strings is investigated in the view of energetics. The governing equation is derived from the Eulerian equation of motion of a continuum for axially accelerating strings. The time-rate of the total mechanical energy associated with the vibration is calculated for the string with its ends moving in a prescribed way. For a string moving in a constant axial speed and constrained by two fixed ends, a conserved quan-tity is proved to remain unchanged during three-dimensional vibration, while the string energy is not conserved. An approximate conserved quantity is derived from the con-served quantity in the neighborhood of the straight equilib-rium configuration. The approximate conserved quantity is applied to verify the Lyapunov stability of the straight equi-librium configuration. Numerical simulations are performed for a rubber string and a steel string. The results demonstrate the variation of the total mechanical energy and the invari-ance of the conserved quantity.