Modal analysis of a drumlike silencer

Abstract

Low-frequency duct noise is difficult to deal with by passive methods such as porous duct lining. Reactive methods like expansion chamber are rather bulky, while compact resonators are too narrow banded. This study shows that a suitably stretched thin membrane backed by a slender cavity can achieve a satisfactory performance from low to medium frequencies over an octave band. The present paper focuses on the details of the modal behavior of the fully coupled membrane-cavity system, and examples are given with parameters set in a practical range. Typically, the membrane has a structure to air mass ratio of unity, and is stretched towards the elastic stress limit for a material like aluminum. The backing cavity has a depth equal to the duct height and a length five times the duct height. Three resonant peaks are found in the low to medium frequency range while the transmission loss between adjacent peaks remain above 10 dB. For the first peak, almost complete sound reflection occurs as a result of an out-of-phase combination of the first and second in vacuo modes of simply supported membranes. The second peak is solely contributed to by the first mode, while the third peak features mainly the second mode vibration.