Resonant three-wave interactions in non-linear hyper-elastic fluid-filled tubes |
| |
Authors: | Gordon E Swaters |
| |
Institution: | (1) Applied Mathematics Institute, Dept. of Mathematics, University of Alberta, T6G 2C1 Edmonton, Alberta, Canada |
| |
Abstract: | A multiple-scales method is used to derive the Three-Wave Interaction (TWI) equations describing resonantly interacting triads in nonlinear hyper-elastic fluid-filled tubes. The tube wall is assumed to be an axially-tethered nonlinear membraneous cylindrical shell for which the resultant stresses can be determined by a strain-energy functional. The fluid within the tube is assumed to be two-dimensional, axi-symmetric and inviscid. We show that small-but-finite amplitude strongly dispersive pressure wave packets can continuously exchange energy in a resonant triad while conserving total energy. For a Mooney-Rivlin shell wall the theory presented predicts a short wavelength cutoff on the order of the tube radius. Thus pressure pulses containing wavelengths on the order of the tube radius and longer may contain resonantly interacting modes. Special solutions are presented: temporally developing modes, pump-wave approximations and explosively unstable steadily-traveling wave packets. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|