Malcolm J. Crocker

Prediction of transmission loss in mufflers by the finite−element method

A numerical technique based on the finite−element method has been developed for analyzing the performance of systems of acoustic elements including expansion chambers in mufflers. The theories developed are, firstly, the variational formulation of the acoustic field existing in the system and, secondly, the finite−element approximate solutions of the variational problems. The predictions of transmission loss are then made by forming the equivalent acoustic four−terminal transmission network in which the acoustic four−pole constants are calculated from the finite−element method. As used, the finite−element approach is perfectly general and may be applied to any system component with arbitrary boundary geometry provided this may be realized by an assembly of rectangular elements. The method is applied to simple expansion chamber models because the results are tractable and theoretical results from acoustic filter theory are available for comparison purposes. The comparison brings out an important fact: the ...

Acoustical source characterization studies on a multi-cylinder engine exhaust system

Abstract It is well known that the characterization of the acoustic source in an exhaust muffler system is of utmost importance in the proper evaluation of the acoustic performance of the muffler. However, in the literature, there are very few experimental studies on source characterization of a multi-cylinder internal combustion engine. This paper describes the use of a transfer function method (with a random excitation source) for measurement of the internal source impedance of an eight-cylinder engine under running conditions. The results obtained agree well with those obtained by the standing wave method by earlier investigators. The studies include the effect on the measured internal source impedance caused by variation of engine speed and load. The source impedance results obtained for the engine in operation are compared with those for the engine not in operation. The use of these results in the overall modeling of the exhaust system is described in an accompanying paper.

Theory and Measurement of Modal Spectra in Hard‐Walled Cylindrical Ducts

The propagation and interaction of acoustic modes in ducts is of importance for the measurement and control of sound generated by ducted fans and compressors. A method is presented by which the modal spectra (pressure and power spectral densities) for the first nine cross modes can be determined from pressure cross‐spectrum measurements in the duct. The flow noise, a potential source of errors, is suppressed by placing the two microphones sufficiently far apart in the duct. The modal spectra and some of the modal interaction terms (modal correlations) for a number of fans are presented. The method should have many applications in verifying modal propagation, absorption of linings, and scattering of modes as well as in identifying sound sources.

STUDIES OF ACOUSTICAL PERFORMANCE OF A MULTI-CYLINDER ENGINE EXHAUST MUFFLER SYSTEM

Abstract Among the various descriptors of a multi-cylinder engine exhaust muffler system performance, it is evident that insertion loss and radiated sound pressure are the most useful. Insertion loss depicts the effectiveness of a muffler, whereas radiated sound pressure level is the design criterion used to meet the noise regulations. The main difficulty in prediction of these descriptors is the characterization of the source. In addition, both flow and temperature gradient effects have to be included in the modeling. This paper describes a theoretical acoustical model to predict insertion loss and radiated sound pressure level, in which the source impedance is obtained from measurement (see the accompanying paper) and from which the source strength is estimated. Also, both flow and temperature gradient effects are included in the analysis. The implications due to the various assumptions for the source impedance in the modeling have been investigated. The studies are carried out on two exhaust system configurations. Good agreement is obtained provided the measured impedance is used and also if mean flow and temperature gradient effects are included in the theoretical model.

Multimode Response of Panels to Normal and to Traveling Sonic Booms

A detailed theoretical study of the response of a uniform flat rectangular panel to a sonic boom (or “N” wave) is presented. Both cases, where the N wave arrives normal to the panel surface and where the shock front arrives at any angle of incidence and crosses the panel parallel to one side, are considered. Closed‐form solutions (for individual modes) are given for the cases of simply supported panel response to normal and traveling N waves; an approximate solution is presented for the response of a panel with fully fixed edges to a normal N wave. The Duhamel integral method used gives panel displacement‐, strain‐, and stress‐time histories for any point on the panel. The analyses derived have engineering applications in the computation of window or wall‐panel response to sonic boom. Some comparison made between theory and experiment. Good agreement is shown to exist between measured and predicted strain maxima and fair agreement to exist between the early parts of the strain‐time histories, despite some differences between the experimental and theoretical models. The necessity to include the contributions due to the higher modes is clearly borne out in theory and experiment, particularly for accuracy in strain‐time histories.

Tubular windscreen design for microphones for in‐duct fan sound power measurements

The design of tubular windscreens (sometimes called sampling tubes) for in‐duct fan sound power measurements is described. Such sampling tubes might be used in the field, although the motive for the present study was the development of a windscreen (sampling tube) for use in an in‐duct fan sound power measurement standard. The head‐on frequency response, directivity, and turbulence rejection of several different designs of sampling tubes have been measured. A theory to predict head‐on frequency response and directivity of the sampling tube has been developed. The basic governing equations were derived from the conservation of mass and conservation of momentum with the assumption that the particular thermodynamic process is an adiabatic one. The theoretical results are in good agreement with the experimental results.

A scheme to predict the sound pressure radiated from an automotive exhaust system

A general scheme to predict the sound pressure radiated from an automotive exhaust system is presented. The scheme is demonstrated with a step‐wise computational procedure on a model system comprised of an electroacoustic driver source, an expansion chamber muffler, and a tailpipe radiating to free space. The predicted sound pressure level spectra agree well with the corresponding measured spectra for various test cases with zero mean flow. Also, studies are made of the theoretical effects of variations of the source impedance on the sound pressure radiated from the model system.

Acoustical analysts, testing, and design of flow‐reversing muffler chambers

The transmission loss characteristics of flow‐reversing muffler chambers were predicted by a numerical approach based on the finite‐element method. The theoretical model developed is described in this paper; its validity is established experimentally with a number of different chambers. The standing‐wave method was used to measure transmission loss and measurements were conducted with and without steady air flow. Depending on the inlet and outlet configurations, the flow‐reversing chambers have two completely different transmission loss characteristics: one is similar to that for two simple expansion chambers in series and the other is similar to that for a side‐branch resonator. Using the theoretical model developed, transmission loss curves were calculated for a large number of different flow‐reversing chamber dimensions. A summary of the transmission loss characteristics of flow‐reversing chambers is given for the assistance of muffler designers. [This work is a continuation of that reported by Young a...

Vibration analysis of hysteretically damped mass-loaded beams

Abstract A procedure for determining the dynamic displacement and dynamic strain of a hysteretically damped mass-loaded free-free beam, subjected to simple harmonic, half-sine pulse and white noise excitations, is presented. Although free-free beams are considered in the analysis, the same procedure could also be used for vibration analysis of mass-loaded beams with other end conditions. The mode shapes for free vibration, displacement and strain due to simple harmonic and half-sine pulse force excitation are presented in graphical form. The maximum mean square displacement and mean square strain are tabulated for Gaussian white noise excitation. The analysis is used to analyze a space structure, which was modelled as a mass-loaded free-free beam. An exhaustive optimization search was made to obtain a structure with minimum dynamic response, when it is subjected to simple harmonic and half-sine pulse force excitations and minimum mean square response when subjected to Gaussian white noise excitation.

Noise Source Identification on a V‐6 Diesel Engine by Means of the Coherence Function Method

Noise source identification on a V‐6 diesel engine has been performed by means of the “coherence function method.” The multiple coherence function between the cylinder pressure and the engine noise has been measured. Utilizing the measured coherence function, the engine “combustion noise” is separated from the mechanical impact noise. The frequency response function between the excitation (cylinder pressure) and the response (engine noise) has also been measured. Utilizing the measured frequency response, the engine “combustion noise” has been predicted for some specific cylinder pressure diagrams. A digital Fourier analyzer has been used for measuring the auto‐ and cross‐spectrum of the signals. Calibrations of the transducers and the instrumentation for this particular experiment are discussed. [Work performed under a grant from the National Science Foundation, Washington, D. C.]