On the combustion experimental platform of high temperature and pressure

the thermoacoustic system with a concentric stratified swirl-stabilized partially premixed-prevaporized flame with self-excited response was excited by external-excited signal with frequency ff of 78-716Hz and amplitude A of 0.026-0.629

and its nonlinear dynamic responses were studied. It was found that the system self-excited frequency fn was 366.85Hz; when the ratio of external-excited frequency to self-excited frequency was 1.022 and amplitude A was 0.629; the flame was dominated by the harmonic frequency and its state trajectory was dense in a very narrow closed zone. When the ratio of external-excited frequency to self-excited frequency and A was in other ranges

the flame responded not only at ff and fn

but also at the harmonic

combining and divided frequencies. It showed that when amplitude A was large enough and external-excited frequency was close to the self-excited frequency

the flame was phase-locked. When the flame was not phase-locked

the nonlinear responses of the harmonic

combining and divided frequencies appeared

and the flame oscillated quasi-periodically. Forced van Der Pol oscillator model can predict phase-locked

odd harmonic frequencies and combining frequencies 2fn±ff.