Quasilinear Self-Excited Oscillations of a Helmholtz Resonator

摘要

The thermal gas-dynamic model of self-excited oscillations of a Helmholtz resonator is analyzed. We introduce dimensionless variables and parameters that provide an adequate description of periodic motions by a third-order quasilinear system. The conditions of existence, uniqueness, and stability of the limiting cycles are ascertained. By the methods of local integral manifolds, averaging, and the Lyapunov-Poincare method, a first-approximation solution is constructed and basic qualitative and quantitative characteristics of self-excited oscillations of the Helmholtz resonator are established. This thermal-mechanical system has not yet been satisfactorily studied.