Modeling dispersion of circumferential waves in underwater targets with spectral methods

The dispersion of circumferential waves propagating around cylindrical and spherical underwater targets with an arbitrary number of elastic and fluid layers is modeled using the spectral collocation method. The underlying differential equations are discretized by Chebyshev interpolation and the corresponding differentiation matrices, and the calculation of the dispersion curves is transformed into a generalized eigenvalue problem. Furthermore, for targets in infinite fluid, the perfect matched layer is used to emulate the Sommerfeld radiation condition. For solid targets, a transformation of potential functions, along with the corresponding boundary condition, is introduced to eliminate the singularity of the low-order modes at the origin. Numerical results are presented and compared with results obtained by the winding number integral method to verify the accuracy and efficiency of the approach.