An overview of symmetry-based techniques used for sound power application with illustrative case studies

This work investigates the growing application of vibration-based sound power (VBSP) measurements in structural acoustics. The VBSP method involves multiplying a measured velocity vector by a geometry-dependent radiation resistance matrix to compute the frequency-dependent sound power. However, computational challenges arise during matrix construction, even for simple geometries. To address this, inherent symmetries in the radiation resistance matrix for both baffled and unbaffled geometries are exploited. Multi-layered Toeplitz symmetries emerge for baffled conditions, while centrosymmetric symmetries are manifest for unbaffled conditions. These symmetries enable an efficient compression and subsequent reconstruction of the resistance matrix. Simple case studies demonstrating the temporal costs for flat, curved, and arbitrarily curved plates in unbaffled conditions will be presented. [Funding for this work was partially provided by the National Science Foundation (NSF).]