TRAPPED MODES IN CYLINDRICAL WAVE-GUIDES

We prove the existence of trapped modes in the presence of two classes of obstacles in cylindrical acoustic waveguides. First we prove that trapped modes exist whenever the obstacle is thin and has a normal whi ch is everywhere perpendicular to the generators of the cylinder. Seco ndly we prove that for the case of a circular cylindrical guide contai ning an axisymmetric obstacle, an infinite sequence of trapped modes e xists, the frequency of the modes tending to infinity. In each case we consider an example where the trapped mode frequencies can be calcula ted numerically using the residue calculus method.