Nonlinear standing and resonantly forced oscillations in a tube with slowly changing length

摘要

Gas oscillations in a piston driven tube form the setting for two problems: The first problem involves piston motions that generate slow compression or expansion of the gas, and the second problem involves resonance oscillations obtained by adding an additional high frequency component to the slow piston motion. The slow component then detunes the physical system through resonance. We examine oscillations forced at the fundamental and the half fundamental frequencies. In both cases, the solution to the partial differential equation describing the passage through resonance exhibits decaying shocks transported through the resonant band. [References: 20]