Devil’s staircases in a thermoacoustic system with sinusoidal excitations
School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, P.R. China
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Received in final form: 24 January 2019
Published online: 25 September 2019
The influences of sinusoidal excitations on a Rijke tube system through the introduction of nonlinear dynamics are investigated in detail. The system is governed by one-dimensional partial differential equations, which are addressed by means of the Galerkin procedure and analysed from the viewpoint of nonlinear dynamics. The results show a rich variety of behaviours in the system, including subcritical bifurcation, hysteresis and phase locking. In certain parameter ranges, the solution switches between periodic and quasi-periodic. These ranges mainly depend on the intensity of the heat source in the tube. The phase-locking intervals that correspond to periodic solutions compose a devil’s staircase, whose Lebesgue measure increases as the amplitude of the excitation increases.
© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature, 2019