Ray shooting, eigenray search, and complex resonances for submerged structures

The general theory of a ray-mode approach for time-harmonic responses and a wavefront-resonant approach for transient responses of submerged structures [I-T. Lu, J. Acoust. Soc. Am. 99, 114–132 (1996)] is applied to a prototype structure consisting of a cylindrical pipe, hemispherical endcaps, a bulkhead, and a rib. The acoustic scattering returns are synthesized systematically in terms of angular spectra of surface modes of the structural elements where bookkeeping of various spectral objects such as ray, collective ray, modes, ray mode, resonance, etc. can be maintained. Ray shooting and eigenray searching procedures for the guided modes of structural elements are derived. An approximate solution for the resonances of the global submerged structure is also obtained. Numerical examples of typical ray trajectories of these guided modes, travel times of wavefronts, and complex frequencies of resonances are presented.