Analytical coupled vibro-acoustic modeling of a cavity-backed duct-membrane system with uniform mean flow

Sound propagation in a flow duct is a complex and technically challenging problem. The presence of flexible vibrating walls inside the duct creates additional difficulties to the problem due to the complex vibro-acoustic and aero-acoustic couplings involved in the system. An accurate prediction of the coupled system response is of great importance for a good understanding of the underlying physics as well as the optimal design of relevant noise suppression devices. In the present work, a unified energy formulation is proposed for the fully coupled structural-acoustic modelling of a duct-mounted membrane backed by an acoustic cavity with a grazing flow. Sufficiently smoothed admissible functions, taking the form of a combination of Fourier series and supplementary polynomials, are constructed to overcome the differential discontinuities for various boundary and/or coupling conditions. The formulation allows the obtention of all relevant vibro-acoustic field information in conjunction with the generalized Lighthill equation and Rayleigh-Ritz procedure. The validation and convergence studies show the accuracy and the efficiency of the proposed model. Results show the strong structural-acoustic interaction in such a duct-membrane-cavity system, and the flow affects resonant amplitude of membrane-dominant modes significantly. Some cross-zones can be observed for the membrane kinetic energy frequency response with low Mach number cases, especially when a higher tension is applied to the membrane. Analyses on the structural-acoustic coupling strength indicate that the coupling between the odd-even structural modes becomes more significant at a higher Mach number compared with odd-odd and even-even mode pairs. It is also shown that adjusting the boundary constraint of the membrane or imposing a higher tensile force allows impairing the adverse influence of the flow in the duct on sound attenuation.