The energetics and the stability of axially moving Kirchhoff strings (L)

The energetics and the stability of free transverse vibration of an axially moving string are investigated based on the Kirchhoff nonlinear model. The model is derived in a physically meaningful manner. The time-rate of the total mechanical energy associated with the vibration is calculated to show that the energy is not conserved. It is proved that there exists a conserved quantity that remains a constant during the nonlinear vibration. The conserved quantity is applied to verify the Lyapunov stability of the axially moving Kirchhoff string.