Diffraction of Plane Sound Waves by a Rigid Circular Cylindrical Cavity with an Acoustically Absorbing Internal Surface

Abstract

Diffraction of sound waves from a rigid circular cylindrical cavity with an acoustically absorbing internal surface is investigated rigorously by a modified version of the Wiener‐Hopf technique. The solution involves a set of infinitely many expansion coefficients satisfying an infinite system of linear algebraic equations. The numerical solution of this system is obtained for different parameters of the problem such as the cavity radius, cavity depth, cavity internal surface impedance, and their effects on the diffraction phenomenon are shown graphically.

Diffraction of sound waves by a rigid cylindrical cavity of finite length with an internal impedance surface

“…Demir ZAMP ing the admittance of the internal lateral surface of the cavity. The results are also compared with those reported in [8]and it is observed that the diffracted field exhibit a more oscillatory behavior in the present case. This is due to the interferences resulting from the interactions between the mouth of the cavity and its rear end.…”

“…In Fig.8, the solid line shows the results related to the semi-infinite geometry while the dashed line corresponds to those of the corresponding finite cavity. We observe that the diffracted field obtained in [8] is almost constant (no resonance effects) while the graph pertaining to the present solution exhibits an oscillatory behavior. This is due to the interferences caused by the interaction of the fields diffracted by the rim and the rear end of the finite cavity.…”

“…In what follows, the results obtained in this work will be compared with the previously obtained ones related to a cavity in a semi-infinite cylindrical waveguide shown in Fig.7 [8]. Fig.8 and Fig.9 show the influence of the cavity depth kl on the diffraction phenomenon.…”

“…This work is a generalization of the geometry treated recently by Bykaksoy, Demir and Polat [8] which consists of a cavity formed by a semi-infinite cylindrical Vol. 56 (2005) Diffraction of sound waves by a rigid cylindrical cavity 695 Figure 1.…”

Propagation of Waves in a Bifurcated Cylindrical Waveguide With Wall Impedance Discontinuity

“…Therefore, a hybrid method of formulation consisting of expressing the field in the region a < ρ < b, z < 0 in terms of normal waveguide modes and using the Fourier transform technique elsewhere may be adopted. The use of this hybrid method results in a single modified Wiener-Hopf equation involving infinitely many unknown expansion coefficients satisfying an infinite system of linear algebraic equations [7]. An alternative approach would be the very well known mode matching technique.…”