Geometrical effects in resonant gas oscillations

It is known that the response of a cylindrical acoustic resonator to excitation by an oscillating piston can contain shock waves if the detuning is sufficiently small. However, the response of a spherical annular resonator is continuous, with an amplitude that depends on the detuning in the same way as does a Duffing equation. This paper discusses the response in resonators that deviate from being cylindrical and shows that, in general, the detuning range in which shocks are possible decreases as the geometrical imperfection increases.