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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.

This paper considers the use of partial enclosures and absorbing materials inside those enclosures to dissipate energy. Several experiments were conducted where various parameters of an enclosure were altered and the effect on the noise radiating through the opening was measured. From these results, the parameters that play the most important role in sound radiation through the opening of an enclosure were determined. The two-point method and decomposition theory were used to calculate the transmission loss, which was used as the primary variable to analyze the enclosure's performance; the transmission loss is shown to be a better variable than sound pressure or output sound power for this purpose. Numerical simulations were conducted using the indirect boundary element method, and the results were compared with experimental results.

This paper considers two questions: how does one know when a boundary element mesh is reliable, and what are the advantages and potential pitfalls of various methods for sound radiation prediction. To answer the first question, a mesh checking method is used. With this method velocity boundary conditions are calculated on the nodes of the mesh using a point source or sources placed inside the mesh. A boundary element program is then used to calculate the sound power due to these boundary conditions. The result is compared to the known sound power of the point source or sources. This method has been used to determine the maximum frequency of a mesh, how many CHIEF points to use, etc. The second question is answered by comparing the results of several numerical methods to experimental results for a running diesel engine. The methods examined include the direct and indirect boundary element methods and the Rayleigh integral.

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.

This paper examines the feasibility of using the boundary element method (BEM) and the Rayleigh integral to assess the sound radiation from engine components such as oil pans. Two oil pans, one cast aluminum and the other stamped steel, are used in the study. All numerical results are compared to running engine data obtained for each of these oil pans on a Cummins engine. Measured running-engine surface velocity data are used as input to the BEM calculations. The BEM models of the oil pains are baffled in various ways to determine the feasibility of analyzing the sound radiated from the oil pan in isolation of the engine. Two baffling conditions are considered: an infinite baffle in which the edge of the oil pan are attached to an infinite, flat surface; and a closed baffle in which the edge of the oil pan is sealed with a rigid structure. It is shown that either of these methods gives satisfactory results when compared to experiment.

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.

An advanced computational method is presented for calculating the sound radiated by vibrating engine of arbitrary shape. The method is based on the numerical evaluation of the Helmholtz Integral Equation. In particular an isoparametric element formulation is introduced in which both the surface geometry and the acoustic variables on the surface of the vibrating body are represented by second order shape functions within the local coordinate system. The formulation includes the case where the surface may have a non-unique normal (e.g. at edges or corners). A general result for the surface and field velocity potential is derived. Test cases involving spherical geometry are given for a pulsating sphere and for an oscillating sphere in which the analytical solutions are known. Examples for bodies with edges and corners are shown for the problems of radiation from a circular cylinder and from a pulsating cube.

Helmholtz resonators are normally an afterthought in the design of mufflers to target a very specific low frequency, usually the fundamental firing frequency of the engine. Due to space limitations in a complex muffler design, a resonator may have to be built by punching a few small holes on a thin-walled tube to create a neck passage into a small, enclosed volume outside the tube. The short neck passage created by punching a few small holes on a thin-walled tube can pose a great challenge in numerical modeling, especially when the boundary element method (BEM) is used. In this paper, a few different BEM modeling approaches are compared to one another and to the finite element method (FEM). These include the multi-domain BEM implemented in a substructure BEM framework, modeling both sides of the thin-walled tube and the details of each small hole using the Helmholtz integral equation and the hypersingular integral equation, and modeling just the mid surface of the thin-walled tube.