Vibration Characteristics of the Axially Moving Continuum with Time-Varying Length: Spagetti Problem

축방향으로 이동하며 길이가 변하는 연속체의 진동특성: 스파게티 문제에 응용

Time-dependent frequency and energy of free vibration of the Spagetti problem, that is the axially moving continuum with time-varying length, are investigated. Exact expressions for the natural frequency and time-varying vibration energy are derived by dealing with traveling waves. When the string length is increased, the vibration period increases, but the free vibration energy varies as a function of both translating velocity and boundary velocity of the continuum. However, when the string undergoes retraction, the vibration energy increases with time, String tension together with non-zero instantaneous velocity at the moving boundary results in energy variation.