A. F. Seybert

A Review of Current Techniques for Measuring Muffler Transmission Loss

The most common approach for measuring the transmission loss of a muffler is to determine the incident power by decomposition theory and the transmitted power by the plane wave approximation assuming an anechoic termination. Unfortunately, it is difficult to construct a fully anechoic termination. Thus, two alternative measurement approaches are considered, which do not require an anechoic termination: the two load method and the two-source method. Both methods are demonstrated on two muffler types: (1) a simple expansion chamber and (2) a double expansion chamber with an internal connecting tube. For both cases, the measured transmission losses were compared to those obtained from the boundary element method. The measured transmission losses compared well for both cases demonstrating that transmission losses can be determined reliably without an anechoic termination. It should be noted that the two-load method is the easier to employ for measuring transmission loss. However, the two-source method can be used to measure both transmission loss and the four-pole parameters of a muffler.

A New Look at the High Frequency Boundary Element and Rayleigh Integral Approximations

This paper revisits the popular Rayleigh integral approximation, and also considers a second approximation, the high frequency boundary element method which is similar to the Rayleigh integral. Both methods are approximations to the boundary integral equation, and can solve problems in a fraction of the time required by the conventional boundary element method. The development of both methods from the Helmholtz integral equation is demonstrated and the differences between the two methods are delineated. Both methods were compared on practical examples including a running engine, gearbox, and construction cab. It was concluded that both methods can reliably predict the sound power for many problems but are inaccurate for sound pressure computations.

An efficient boundary element algorithm for multi‐frequency acoustical analysis

In this article, a new boundary element algorithm in acoustics is proposed. This new algorithm uses a so‐called ‘‘Green’s function interpolation technique’’ so that it is ideally suited to a multi‐frequency analysis. In the numerical implementation of this new algorithm, the Green’s function used in the boundary integral equation is interpolated by a set of shape functions. Numerical integration is then confined to a frequency‐independent part only, and hence, is carried out only once at the first frequency of a multi‐frequency run. At subsequent frequencies, only the nodal values of the Green’s function have to be re‐calculated for the formation of the boundary element coefficient matrices. Compared to the recently developed ‘‘frequency interpolation technique,’’ this new algorithm requires much less disk space and can be easily extended to half‐space problems and problems with planes of symmetry.

SELECTING MEASUREMENT LOCATIONS TO MINIMIZE RECONSTRUCTION ERROR USING THE INVERSE BOUNDARY ELEMENT METHOD

This paper details an approach to select measurement point locations for the inverse boundary element method. An accurate reconstruction of the vibration requires a well conditioned acoustic transfer matrix, which depends on measurement point selection. Matrix techniques can be used to regularize the solution though they often lead to poor reconstruction rank. A technique to determine the number of measurement points required, and their placement, prior to measurement has been developed using three criteria: uniqueness, completeness, and measurement point density. With this technique, the reconstruction error and the number of measurements can be minimized.

Practical Considerations in Reconstructing the Surface Vibration Using Inverse Numerical Acoustics

This paper explores the use of inverse numerical acoustics to reconstruct the surface vibration of a noise source. Inverse numerical acoustics is mainly used for source identification. This approach uses the measured sound pressure at a set of field points and the Helmholtz integral equation to reconstruct the normal surface velocity. The number of sound pressure measurements is considerably less than the number of surface vibration nodes. A brief guideline on choosing the number and location of the field points to provide an acceptable reproduction of the surface vibration is presented. The effect of adding a few measured velocities to improve the accuracy will also be discussed. Other practical considerations such as the shape of the field point mesh and effect of experimental errors on reconstruction accuracy will be presented. Examples will include a diesel engine and a transmission housing.

Measuring Bulk Properties of Sound-Absorbing Materials using the Two-Source Method

The two-source method was used to measure the bulk properties (complex characteristic impedance and complex wavenumber) of sound -absorbing materials, and results were compared to those obtained with the more commonly used two-cavity method. The results indicated that the two-source method is superior to the two-cavity method for materials having low absorption. Several applications using bulk properties are then presented. These include: (1) predicting the absorptive properties of an arbitrary thickness absorbing material or (2) layered material and (3) using bulk properties for a multi -domain boundary element analysis.

Accurate Measurement of Small Absorption Coefficients

In this paper procedures for estimating the sound absorption coefficient when the specimen has inherently low absorption are discussed. Examples of this include the measurement of the absorption coefficient of pavements, closed cell foams and other barrier materials whose absorption coefficient is nevertheless required, and the measurement of sound absorption of muffler components such as perforates. The focus of the paper is on (1) obtaining an accurate phase correction and (2) proper correction for tube attenuation when using impedance tube methods. For the latter it is shown that the equations for tube attenuation correction in the standards underestimate the actual tube attenuation, leading to an overestimate of the measured absorption coefficient. This error could be critical, for example, when one is attempting to qualify a facility for the measurement of pass-by noise. In this paper we propose a remedy – to measure the actual tube attenuation and to use this value, as opposed to the value recommended by the standards, to correct the measured sound absorption. We also recommend an alternative way to determine the microphone phase error.

Structural Acoustics Applications of the BEM and the FEM

In this paper we discuss how the boundary element method (BEM) may be used by itself or in conjunction with the finite element method (FEM) for the solution of problems in structural acoustics. Problems in this category include: the scattering of sound from an elastic solid or shell submerged in a heavy fluid such as sea water, and the sound field generated within a vehicle passenger compartment or aircraft cabin due to vibration of the surrounding structure. In the latter case, the modes of the structure and the acoustic fluid may be coupled even if the fluid is air. Two approaches to structural acoustics modeling are considered. In one approach, the BEM is used to model both the elastic and the acoustic parts of the problem. In the second approach, the FEM is used to model the structure, while the BEM is used to model the fluid.

Case study evaluation of the Rayleigh integral method

The Rayleigh integral is based on the assumption that the vibrating surface is flat and part of an infinite rigid baffle. Though approximate, the Rayleigh integral can evaluate the sound power radiated by a vibrating surface in a fraction of the time required by the boundary element method. Three case studies were conducted to evaluate the reliability of the Rayleigh integral. Specifically, the Rayleigh integral was used to predict the sound power from a wheel‐rail structure, a gearbox, and an engine. In each case, Rayleigh integral results were compared with boundary element results. The results indicated that sound power compared well with that obtained using the boundary element method. The differences were less than 5 dB except at low frequencies. However, the Rayleigh integral did not accurately predict the sound pressures at field points. The results suggested that the Rayleigh integral could be used in place of the more time intensive boundary element method for sound power calculations.

Energy source superposition technique for solving two‐dimensional acoustic problems

An energy source superposition technique has been developed to determine sound energy and intensity. Using this method, the intensity along the boundary is approximated by superimposing energy sources placed outside the acoustic domain. The unknown amplitudes of these sources are found using a linear least squares, then these energy sources may be superimposed to approximate the sound energy. Several tests were performed to evaluate the approach. First, it was demonstrated that the energy sources could be superimposed if the interference pattern between propagating waves was neglected. This was demonstrated for plane waves, cylindrical waves, and spherical waves. Two‐dimensional energy results were then compared for the few cases where a closed form solution could be obtained like the pulsating cylinder and the one‐dimensional duct. Finally, results were compared to acoustic boundary element solutions with good agreement. [Work supported by the University of Kentucky Center for Computational Sciences.]