ON GREENS-FUNCTIONS FOR A CYLINDRICAL CAVITY

This paper presents a set of Green's functions for Neumann and Dirichl et boundary conditions for the Helmholtz equation applied to the inter ior of a cylindrical cavity which are based on evanescent wave expansi ons instead of the usual normal mode expansions. The evanescent expans ion capitalizes on the known physics of the shell-fluid interaction, g iven a cavity with flexible walls, providing a pressure field which de cays exponentially (in the Limit of small wavelength) into the interio r of the cavity when the wall vibration is subsonic, Due to this decay the evanescent Green's functions converge much faster than the conven tional Green's functions which are built up out of the interior eigenm odes of a rigid (or pressure release) cavity. Furthermore, these evane scent Green's functions can be inverted in a fairly straightforward wa y to provide the foundations for solving the inverse holography proble m, that is, the reconstruction of the normal surface velocity from a m easurement of the pressure in tile interior. [S0001-4966(97)05012-1].