Radiation by a submerged cylindrical shell in response to an external non-stationary acoustic pulse - Iakovlev, Serguei (Canadian Acoustics, 2007)
A mixed analytical-numerical solution has been developed, where the separation of variables was used in combination with the Laplace transform technique to obtain the diffraction and radiation pressure in modal form, and the finite differences were employed to obtain the harmonics of the shell surface displacements, with subsequent coupling of the two parts. A steel shell submerged into water was considered, and its thickness and radius were assumed to be 0.005 m and 0.5 m. The fluid is assumed to be irrotational, inviscid, and linearly compressible, and is therefore governed by the wave equation. The motion of the fluid is coupled to that of the shell through the dynamic boundary condition on the interface. The images of the radiated field taken during the late interaction allow one to see the entire evolution of the dynamics of the process in a single shot, which makes them a very useful analysis tool.