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

Calculating sound power using complex-valued surface velocities is becoming an established practice in structural acoustics with rising optimism about this method’s potential versatility compared to traditional pressure-based methods. One approach involves using a geometry-dependent acoustic radiation resistance matrix multiplied by a velocity vector to compute sound power for a given frequency range. At scale, the computational costs incurred through this calculation limits the application of this method. Given a discretized surface with constant spacing and using a well-informed average radiator area approximation, a multilayered Toeplitz symmetry exists in the radiation resistance matrix. This symmetry, its origins and necessary assumptions are explored. By exploiting the Toeplitz symmetry, computationally expensive mathematical operations that used to be performed on the entire radiation resistance matrix, can be performed on a single row of the matrix, and then expanded using the pattern that will be presented. This approach preserves accuracy and greatly accelerates the processing, as evidenced through experimental data. The approach resulted in a maximum of ∼1300% computation time reduction for single radius curved plate calculations and a ∼9,600% computation time reduction for cylindrical shell calculations. [Funding for this work was provided by the National Science Foundation (NSF).]