Nonlinear standing and resonantly forced oscillations in a tube with slowly changing length (Q2783743)

The paper deals with the oscillations of a gas contained in a tube partially closed at one end and driven by a piston located at the other end. Two problems arise: the first problem involves piston motions that generate slow compression or expansion of the gas, and the second problem deals with resonance oscillations obtained by adding an additional high-frequency component to the slow piston motion. The authors reduce these problems to mappings in dynamical systems and generalize these mappings. They examine oscillations forced at fundamental and half-fundamental frequencies. In both cases, the solution describing the passage through the resonance exhibits decaying shocks transported through the resonant band.