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This paper documents an inverse visible element Rayleigh integral (VERI) approach. The VERI is a fast though approximate method for predicting sound radiation that can be used in the place of the boundary element method. This paper extends the method by applying it to the inverse problem where the VERI is used to generate the acoustic transfer matrix relating the velocity on the surface to measurement points. Given measured pressures, the inverse VERI can be used to reconstruct the vibration of a radiating surface. Results from an engine cover and diesel engine indicate that the method can be used to reliably quantify the sound power and also approximate directivity.

The principle of vibro-acoustic reciprocity is reviewed and applied to model sound radiation from a shaker excited structure. Transfer functions between sound pressure at a point in the far field and the velocity of a patch were determined reciprocally both for the to-scale structure and also for a half-scale model. A point monopole source was developed and utilized for the reciprocal measurements. In order to reduce the measurement effort, the boundary element method (BEM) was used to determine the reciprocal transfer functions as an alternative to measurement. Acceleration and sound intensity were measured on patches of the vibrating structure. Reciprocally measured or BEM generated transfer functions were then used to predict the sound pressure in the far field from the vibrating structure. The predicted sound pressure compared favorably with that measured.

Numerical acoustics has traditionally been relegated to a prediction only role. However, recent work has shown that numerical acoustics techniques can be used to diagnose noise problems. The starting point for these techniques is the acoustic transfer vector (ATV). First of all, ATV's can be used to conduct contribution analyses which can assess which parts of a machine are the predominant noise sources. As an example, the sound power contribution and radiation efficiency from parts of a running diesel engine are presented in this paper. Additionally, ATV's can be used to reliably reconstruct the vibration on a machine surface. This procedure, commonly called inverse numerical acoustics (INA), utilizes measured sound pressures along with ATV's to reconstruct the surface velocity. The procedure is demonstrated on an engine cover for which the reconstructed vibration had excellent agreement with experimental results.