Improved efficiency of vibration-based sound power computation through multi-layered radiation resistance matrix symmetry.

Computing sound power using complex-valued surface velocities involves using a geometry-dependent acoustic radiation resistance matrix multiplied by a velocity vector to compute sound power for a given frequency range. Using a laser scan grid with constant spacing and a scalar radiator area approximation, a multi-layered Toeplitz symmetry exists in the radiation resistance matrix. An innovative approach was developed to exploit this Toeplitz symmetry. This approach preserved accuracy and resulted in a maximum of ∼1300% computation time reduction for curved plate calculations and a ∼9600% computation time reduction for cylindrical shell sound power calculations.