Development of Particle Velocity Transfer Path Analysis

The transfer path analysis (TPA) in terms of sound pressure has been implemented for decades in many application areas, such as car, train and construction machine. In this article, we propose a transfer path analysis where particle velocity is employed as the measure of TPA. Sound pressure is a scalar quantity, while particle velocity, which is the other fundamental quantity of sound, is a vector quantity. The phase differences among particle velocity vector components have to be generally considered. For TPA, not only the six degrees-of-freedom of each path motion, but also the three degrees-of-freedom of the particle velocity at the receiver location have to be considered together for an effective path rank ordering. We first propose the formulation of the particle velocity transfer path analysis where the same formulation of the standard sound pressure transfer path analysis is assumed to hold true for each direction of particle velocity. In order to verify the proposed particle velocity transfer path analysis, we carry out an experiment using a simple test box structure. As a result we have found that the error in the particle velocity vector synthesis is acceptably small, and is as small as the error in the standard sound pressure synthesis, which indicates that the same synthesis method can be employed. We then perform rank ordering of the particle velocity transmission paths. Here, a simple method of path rank ordering is applied. Lastly, we briefly discuss sound energy as a measure of TPA.