On Green’s functions for a cylindrical cavity

This paper presents a set of Green’s functions for Neumann and Dirichlet boundary conditions for the Helmholtz equation applied to the interior of a cylindrical cavity which are based on evanescent wave expansions instead of the usual normal mode expansions. The evanescent expansion capitalizes on the known physics of the shell–fluid interaction, given a cavity with flexible walls, providing a pressure field which decays exponentially (in the limit of small wavelength) into the interior of the cavity when the wall vibration is subsonic. Due to this decay the evanescent Green’s functions converge much faster than the conventional Green’s functions which are built up out of the interior eigenmodes of a rigid (or pressure release) cavity. Furthermore, these evanescent Green’s functions can be inverted in a fairly straightforward way to provide the foundations for solving the inverse holography problem, that is, the reconstruction of the normal surface velocity from a measurement of the pressure in the interior.