Nonlinear resonant oscillations of a gas in a tube under the action of a periodically varying pressure
One-dimensional nonlinear motions of an ideal gas in a tube are considered. The tube is closed at one end, and the pressure, periodically varying with time, is specified at the other end. Nonlinear asymptotic equations controlling the periodic oscillation of the gas are obtained for the frequency range close to the resonance frequencies. The complete problem of integrating the system of partial differential equations of gas dynamics is reduced to finding the solution of a single functional equation. Two different solutions exist, one smooth, and another containing strong discontinuities.
frequency range close to the resonance frequencies
scientific article; zbMATH DE number 3917972