Bandgap formation under temperature-induced quasi-periodicity in an acoustic duct with flexible walls

This paper is concerned with the acoustic bandgap formation in a duct with periodically flush-mounted flexible walls, subject to a stream-wise temperature variation. A numerical model, based on a piecewise treatment of the arbitrary temperature gradient, is proposed for the accurate prediction of sound propagation in a complex thermal environment. Effects of the system quasi-periodicity due to the temperature change on the bandgap formation, as well as possible mitigation measures through parameter tuning, are revealed. It is shown that, on the top of the resonance bandgap, Bragg reflection bandgap can still be created despite the system quasi-periodicity. In addition to an alteration to the bandgap central frequency due to the temperature-induced acoustic wavelength changes inside the duct, the bandwidths of the bandgaps are also adversely affected, especially when the temperature gradient is large. Numerical analyses show the possibility of tuning and customizing the bandgap formation through a proper selection of the lattice distance and the structural parameters. A combined tuning strategy would warrant a merging of the bandgaps, adjustment of their central frequencies as well as an enlargement of the bandwidth for a given temperature variation range through creating a favorable coupling between the Bragg reflections and the local resonances of the flexible walls.