Numerical study of the mechano-acoustic coupled resonance of a tube-membrane system

The acoustic behaviour of a tube is well known since antiquity, nevertheless, differences appear when a flexible element interferes this behaviour. The tube acoustic resonance is altered by the mechanic resonance of this element due to complex mechano-acoustic effects. In this paper, an experiment is designed to evaluate the response of a tube with a membrane at the end, subject to sound pressure at the open side of the tube. A baffle isolates both sides of the tube. A comprehensive numerical study is made to understand the behaviour of different parameter of the system as the tube length and those related with the membrane stiffness and mass. A proper numerical methodology has been developed and is described and justified. The study of the simple tube system is also accomplished finding that results match with the theoretical expected values with an effective length correction. Regarding the behaviour of the tube-membrane system, it is found that the membrane is not a transparent element, but its contribution as closing element is limited to a 10 dB sound pressure drop compared with the absence of membrane. The acoustic resonance of the tube is affected by the membrane resonance but a general pattern similar to the open-closed case is observed. No presence of the open-open case is found.