Spherical transfer matrix method for assessment of sound emission from elastic structures

This paper presents the Spherical Transfer Matrix (STM) method, a reduced-order modeling approach for linear time-harmonic acoustic prediction of far-field sound power emitted from elastic structures such as centrifugal pumps or turbo-machinery. Structures of this type are subject to internally distributed pressure pulsations, and their vibration-induced emission of airborne sound corresponds to light fluid loading conditions. The STM method leverages quasi-isometric mapping to decompose excitation inputs and response outputs into a spatially varying, frequency-independent spherical harmonic basis, enabling the formulation of a transfer matrix that relates internal pressure excitations to external surface normal velocities. This mapping requires both the internal pressure-loaded surface and external sound-emitting surface to be genus-0, i.e., water-tight. From here, far-field sound power is efficiently approximated using analytical solutions to the canonical acoustic Neumann problem in spherical coordinates. The STM method thus allows far-field sound power radiation to be approximated through simple matrix/vector multiplication. The computational efficiency of the STM method is particularly significant in iterative design processes (where multiple excitation conditions must be evaluated) due to pre-computing the transfer matrix for a fixed structural geometry. The STM method offers significant time savings compared to conventional finite element-based methods, which require re-computation for each new excitation, while maintaining comparable accuracy. Additionally, the STM method puts significantly lower requirements on computational hardware compared with full acoustic simulations using, e.g., the finite element method.