Influence of boundary restraint on sound attenuation performance of a duct-membrane silencer

• The TL of duct-membrane silencer is predicted by a modified Fourier series method.
• Energy principle is employed for the modeling of structural-acoustic interaction.
• Reliability of this model is verified through comparison with those in literature.
• Boundary restraint has an important influence on the TL of duct-membrane silencer.

Low frequency noise in duct is a challenge for the traditional passive noise control techniques. Recently, a so-called duct-membrane silencer has attracted much research attention due to its simple configuration and potential application, however, the current studies are merely limited to the cases in which just the classical boundary conditions are considered. Actually, as an important factor affecting the modal characteristics of the membrane, and the existing studies are not enough to fully understand the vibro-acoustic characteristics of such silencer with complicated boundary conditions. Motivated by this, in this paper, the structural–acoustic coupling model of duct-membrane system is established by a modified Fourier series method in combination with Rayleigh–Ritz procedure, in which the transverse elastic boundary restraints are taken into account. Energy principle is formulated for the vibro-acoustic coupling of such duct-membrane silencer to obtain the system matrix equation. Numerical results are then presented to validate the proposed model, and the influence of boundary restraining stiffness on sound attenuation performance is also studied. To the best of authors’ knowledge, this work represents the first time that the elastic boundary restraints have been considered for such duct-membrane silencing system.