Static Nodes of an Axially Moving String With Time-Varying Supports

Abstract

By investigating the transverse vibrations of an axially moving string with time-varying supports, the existence and the pattern of static nodes are studied based on the assumed mode method and the linear superposition method. The explicit expressions for the response of the system with five different boundary conditions are illustrated. Traditional excited static strings show nodes when resonance occurs. However, it is found in this study that the static nodes of axially moving strings appear under arbitrary frequency even far away from resonance, if the excitation frequency is higher than the fundamental frequency. The varying nodes and frequencies under different time-varying supports are revealed.