ACOUSTIC SCATTERING OF A PLANE-WAVE BY 2 SPHERICAL ELASTIC SHELLS ABOVE THE COINCIDENCE FREQUENCY

The acoustic scattering by two fluid-filled spherical elastic shells i n close proximity to each other and insonified by plane waves at arbit rary angles of incidence is analyzed exactly in the frequency range th at includes the midfrequency or coincidence enhancement region of the backscattered echoes. The incident and scattered wave fields are expan ded in terms of the classical modal series and the addition theorem fo r the spherical wave functions is used to determine the exact expressi on for the sound fields scattered by each spherical elastic shell in t he presence of the other, referred to coordinate systems at the center s of either spherical shell. The solution to the scattering problem is found by simultaneously solving the Helmholtz equations governing the wave motion in the fluid medium in which the two shells are submerged as well as in the fluid media contained in the shells, together with the two sets of equations of motion of the two elastic shells obtained from the complete three-dimensional elasticity theory after satisfyin g the boundary conditions at all fluid-shell interfaces as well as the far-held radiation condition. Again, the numerical computation of the scattered pressure wave involves the solution of a truncated ill-cond itioned complex matrix system the size of which depends on how many te rms of the modal series are required for convergence. This in turn dep ends on the value of the frequency, and on the proximity of the two sp herical elastic shells. The ill-conditioned matrix equation is solved using the Gauss-Seidel iteration method. Backscattered and bistatic ec hoes from two identical spherical elastic shells are extensively calcu lated. The result also exhibits the large enhancement present in the b ackscattered echoes for the endfire situation after the midfrequency o r coincidence enhancement has taken place. This can be attributed to t he effects of focusing by the front elastic shell and to the reflectio n and refocusing by the back elastic shell of the a(0) Lamb wave rerad iation in the observer's direction.