Weakly nonlinear oscillations of gas column driven by self-sustained sources

Czech Technical University in Prague, Faculty of Electrical Engineering, Technická 2, 166 27 Prague 6, Czech Republic

^* e-mail: viktor.hruska@fel.cvut.cz

Abstract

Self-sustained sources coupled to some sort of resonator have drawn attention recently as a subject of nonlinear dynamics with many practical applications as well as interesting mathematical problems from the chaos theory and the theory of synchronizations. In order to mimic the self-sustainability arising from physical background the van der Pol equation is commonly used as a model (e.g. vortex induced noise, flowstructure interactions, vocal folds motion etc.). In many cases the sound field inside the resonator is strong enough for weakly nonlinear formulation based on the Kuznetsov model equation to be employed. An array of sources governed by the inhomogeneous van der Pol equation coupled to the nonlinear acoustic wave equation is studied. The one dimensional constant cross-section open resonator with zero radiation impedance is assumed. The focus is on the main features such as mode-locking, harmonics generation and build-up from infinitesimal fluctuations.