Fala Akustyczna w Cylindrze Odkształconym w Sposób Skończony

A hollow circular cylinder is subject to a finite inflation. Assuming the cylinder to be made of the Mooney material, the state of stress is determined. The propagation of an axi-symmetric acoustic wave propagating in the direction of the axis is considered. A nonlinear differentia equation for the discontinuity surface is obtained. Two first approximations of the surface and the propagation velocity are calculated by means of the perturbation method. It is shown that when the radius of the cylinder increases (decreases) in the process of initial deformation, the cylinder behaves as a convergent (divergent) lens.
On the basis of the theory of small deformations superposed on finite deformations, the equations of bicharacteristics and the acoustic radii are found, and the phase and radial velocities are determined. Certain modes of dispersive vibrations are also derived.