New Green functions for nearfield acoustical holography in aircraft fuselages

Abstract

This paper presents a new set of Neumann Green functions for the interior of a cylindrical cavity which are based on evanescent wave expansions instead of the usual normal mode expansions. The new expansion capitalizes on the known physics of the shellfluid interaction providing terms which decay exponentially from the surface of the fuselage when the vibration these is subsonic. Due to this decay the convergence of the new Green functions is much faster than the conventional Neumann Green function. Furthermore, these evanescent Green 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 fuselage velocity from a measurement of the pressure in the interior. Simulations of nearfield acoustical holography (NAH) are carried out using the evanescent Green functions, with inversion provided by the singular value decomposition technique applied to the resulting matrix relating the interior pressure to the surface velocity. After demonstrating the accuracy of the velocity reconstruction, we reconstruct the complete interior acoustic intensity to demonstrate another useful tool resulting from this technique.