Analytical Study of Quasilinear Self-Oscillations in the Helmholtz Resonator

A quasilinear model of the self-oscillations in the Helmholtz resonator is developed. The conditions of existence, uniqueness, and stability of periodic solutions are determined using the Lyapunov-Poincaré, local integral manifold, and averaging methods. In the first approximation, the basic parameters of the self-oscillations are calculated and their qualitative features are studied. A thermodynamic interpretation of the gas self-oscillations in the resonator is given.