The Mathematical model for elimination of resonance effect in the two-dimensional rigid fixed cylinder in arbitrary cross section

摘要

In this study, three different formulations are preented: 1) the single layer integral equation formulation, 2)the double layer integral equation formulation, and 3)the combined double and single layer integral equation formulation for solving acoustic scattering problems associated with two dimensional rigid cylinders of an arbitrary cross section. In particular, using the boundary conditions on the surface of the body and properly selecting the associated velocity potential for the problem, the three different formulations are derived. These equations are then solved by approximating the cylindrical cross section by linear segments and employing the method of moments. Further, it is shown that the moment matrices generated by the single layer and double layer integral equation formulations are ill-conditioned at the resonant frequencies of the cylinder; whereas, the combined layer integral equation formulation generates a well-conditioned matrix at all frequencies. This study offers a better mathematical model and solution for the calculation of acoustic scatter field.