Wave propagation in a fluid filled rubber tube: Theoretical and experimental results for Korteweg's wave

In this paper, the interaction between the wall vibrations of a stretched elastic cylindrical membrane and the inner acoustic field is considered under plane wave approximation. Three waves exist at low frequencies for this coupled system. The first of these, called Korteweg's wave, propagates mainly within the fluid and corresponds to the acoustic plane wave which is closely coupled to the wall vibrations. The two other waves mostly propagate within the structure and correspond to coupled longitudinal/flexural motions: one corresponds to predominant longitudinal motions in the membrane and the other exists only when tension is applied to the membrane and is similar to a string bending wave. A model for the dispersion curves is presented and is experimentally validated. In particular, the model and experiments reveal that three frequency ranges exist for which the propagation of the Korteweg's wave is subsonic, evanescent and supersonic. The experimental validation is achieved using the acoustic impedance measurements for a stretched rubber membrane. Assuming that the vibratory and acoustic fields are dominated by one wave, the latter are described by using only one dispersive wave, in this case, of equivalent wave speed. The input acoustic impedance curve can be fitted using this expression which only requires one equivalent wave.