Non-linear wave propagation in acoustically lined circular ducts

✍ Scribed by Ali H. Nayfeh; M.-S. Tsai

• Publisher: Elsevier Science
• Year: 1974
• Tongue: English
• Weight: 604 KB
• Volume: 36
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(74)80344-5

✦ Synopsis

A second-order uniformly valid expansion is obtained by using the method of multiple scales for the 'non-linear wave propagation in a circular duct whose walls are lined with a non-linear acoustic material. The acoustic material is characterized by an empirical, non-linear impedance in which the instantaneous resistance is a non-linear function of the acoustic velocity while the instantaneous reactance is a non-linear function of both the frequency and the acoustic velocity. The results show that there exist frequency bandwidths around the resonant frequencies in which the non-linearity decreases the attenuation rate and outside which the non-linearity increases the attenuation rate, in qualitative agreement with experimental observations. Moreover, the effect of the gas non-linearity increases with increasing sound frequency, whereas the effect of the material non-linearity decreases with increasing sound frequency.