Acoustic diffraction by a variable thickness fluid layer

The effect of a variable thickness, cylindrical, fluid layer on the directional response patterns of a particular acoustic source distribution is investigated. The source consists of an array of parallel line sources on a rigid cylindrical baffle surrounded by a constant thickness cylindrical fluid layer. Located off center of these two cylinders is a third cylinder of a second fluid, which has a variable thickness because it is nonconcentric with the other two. The outer cylinder is surrounded by an infinite medium of the same fluid as the inner cylindrical layer. An analytical solution for the acoustic field is obtained by writing appropriate expressions for the pressure in each region, and applying the boundary conditions between the regions to solve for the unknown modal coefficients in these expressions. The translational addition theorem for cylindrical wavefunctions is used to simplify the matching of boundary conditions on the nonconcentric cylinders. The expression for the farfield pressure is used to produce numerical results for variations of some of the many parameters of the problem.