Computing Radiated Sound Power using Quadratic Power Transfer Vector (QPTV)

Pressure Acoustic Transfer Functions or Vectors (PATVs) relate the surface velocity of a structure to the sound pressure level at a field point in the surrounding fluid. These functions depend only on the structure geometry, properties of the fluid medium (sound speed and characteristic density), the excitation frequency and the location of the field point, but are independent of the surface velocity values themselves. Once the pressure acoustic transfer function is computed between a structure and a specified field point, we can compute pressure at this point for any boundary velocity distribution by simply multiplying the forcing function (surface velocity) with the acoustic transfer function. These PATVs are usually computed by application of the Reciprocity Principle, and their computation is well understood. In this work, we present a novel way to compute the Velocity Acoustic Transfer Vector (VATV) which is a relation between the surface velocity of the structure and fluid particle velocity at a field point. To our knowledge, the computation of the VATV is completely new and has not been published in earlier works. By combining the PATVs and VATVs at a number of field points surrounding the structure, we obtain the Quadratic Power Transfer Vector (QPTV) that allows us to compute the sound power radiated by a structure for ANY surface velocity distribution. This allows rapid computation of the sound power for an arbitrary surface velocity distributions and is useful in designing quiet structures by minimizing the sound power radiated.