Axisymmetric oscillations in open doubly – connected rotationally symmetric cavities with sound soft walls

A rigorous approach for analysis of wave scattering from acoustically soft rotationally symmetric cavities with two coaxial apertures is developed. The solution algorithm is based on the generalisation of the Method of Analytical Regularisation which has been previously applied to obtain the accurate solution of the wave scattering problem for open canonical objects. Distinctive features of the original method such as fast solution convergence and guaranteed desired accuracy are preserved. The spectrum of the axisymmetric complex oscillations is studied for four types of cylindrical cavities of finite length: closed, open, partially open (capped by circular annuli) and sinusoidally corrugated cylinders. After finding the complex eigenvalues the backscattering cross section in the resonance region is investigated.