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Over 30 years ago, A. H. Vincent of Westland Helicopters demonstrated that if a structure is excited harmonically, the response at another position (at a fixed frequency) will trace a circle in the complex plane as a result of a dynamic stiffness modification between two points. As either the real or imaginary part of an introduced dynamic stiffness is varied from minus infinity to plus infinity, the structural or acoustic response on any position will map a circle in the complex plane. This paper reviews the basis for this little known principle for vibro-acoustics problems and illustrates the viability for a cantilevered plate example. The applicability of the method is then considered for strictly acoustic systems like intake and exhaust systems. Specifically, it is shown that the response traces a circle in the complex plane if either the real or imaginary parts of the source or termination impedance are varied from minus to plus infinity.

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.

The theory of patch (or panel) contribution analysis is first reviewed and then applied to a motorcycle engine on a test stand. The approach is used to predict the sound pressure in the far field and the contribution from different engine components to the sound pressure at a point. First, the engine is divided into a number of patches. The transfer functions between the sound pressure in the field and the volume velocity of each patch were determined by taking advantage of vibro-acoustic reciprocity. An inexpensive monopole source is placed at the receiver point and the sound pressure is measured at the center of each patch. With the engine idling, a p-u probe was used to measure particle velocity and sound intensity simultaneously on each patch. The contribution from each patch to the target point is the multiplication of the transfer function and the volume velocity, which can be calculated from particle velocity or sound intensity. There were two target points considered.