A resonance shift prediction based on the Boltzmann-Ehrenfest principle for cylindrical cavities with a rigid sphere

An investigation on the resonance frequency shift for a plane-wave mode in a cylindrical
cavity produced by a rigid sphere is reported in this paper. This change of the resonance
frequency has been previously considered as a cause of oscillational instabilities in singlemode
acoustic levitation devices. It is shown that the use of the Boltzmann-Ehrenfest
principle of adiabatic invariance allows the derivation of an expression for the resonance
frequency shift in a simpler and more direct way than a method based on a Green’s function
reported in the literature. The position of the sphere can be any point along the axis of the
cavity. Obtained predictions of the resonance frequency shift with the deduced equation
agree quite well with numerical simulations based on the Boundary Element Method. The
results are also confirmed by experiments. The equation derived from the Boltzman-
Ehrenfest principle appears to be more general, and for large spheres, it gives a better
approximation than the equation previously reported.