Calculation Of Sound Power Research Articles

MODELLING THE VIBRATIONAL CHARACTERISTICS AND RADIATED SOUND POWER FOR A Y25-TYPE BOGIE AND WAGON

A theoretical investigation has considered the vibrational characteristics of the bogie and wagon to quantify the noise freight wagons. This study presents the analysis of the bogie by finite element methods (FEM) to cover the lower-frequency range. The wagon has been analyzed using a statistical energy analysis (SEA) approach. The accelerances on the bogie have been calculated and the sensitivity to excitation evaluated. The calculation of sound power for force inputs has also been determined. Complementary experimental results show the predictions to be in good agreement. The wagon has not been examined specifically to identify detailed response and radiated sound; instead it is possible to consider the response of larger identifiable structural areas such as the doors, walls, roof, etc. The response of these larger areas can also be used to predict the transfer functions from radiated sound power for forces applied at the connection points. Good agreement has been obtained with experimental measurements.

DETERMINATION OF THE MUTUAL RADIATION RESISTANCES OF A RECTANGULAR PLATE AND THEIR IMPACT ON THE RADIATED SOUND POWER

The mutual-radiation resistances resulting from cross-modal coupling have been mostly excluded from sound power calculations on the belief or premise that either for some reasons they have an insignificant impact on the power radiation or consideration of them can be an enormous computational burden. In this paper, the characteristics of the mutual-radiation resistances are investigated of a simply supported rectangular plate. It is shown that, once the self-radiation resistances (or the so-called modal-radiation efficiencies) have been calculated, the mutual-radiation resistances can be readily obtained at virtually no cost. Of equal importance, because no approximation is made, the present formulation is fully accurate in the entire frequency range. An asymptotic expression is also derived for large modal wavenumbers. Numerical results are presented to illustrate the spectral characteristics of the mutual-radiation resistances and the corresponding impact on the radiated sound power.

Determination of the airborne sound power radiated by structure-borne sound sources of arbitrary shape—First step of extension of the direct finite-element method to three-dimensional sources

The direct-finite-element method (DFEM) is an algorithm for calculation and measurement of airborne sound power radiated by structure-borne sources. Using a structure-borne source parameter directly means redundant intermediate sound field information such as sound pressure and sound intensity are not necessary. Previous investigation showed that for plane structure-borne sound sources, the DFEM can be derived from the Rayleigh description of sound radiation exactly. This paper deals with the extension of the DFEM for three-dimensional structure-borne sound sources. For these sound sources the DFEM algorithm as already used for plane structure-borne sound sources must be supplemented by a net of imaginary counter sources in order to meet the boundary condition of the arbitrarily shaped vibrating body. This supplement is described and discussed using some examples. Finally, measurement results are presented which are in good conformity with the theoretical results of the modified DFEM.

INVESTIGATION ON SOUND FIELD MODEL OF PROPELLER AIRCRAFT—THE EFFECT OF VIBRATING FUSELAGE BOUNDARY

The sound field model with multiple propeller noise sources and finite fuselage boundary developed for the prediction of propeller aircraft noise in reference [1] has been improved to take into consideration the effects of vibrating fuselage boundary. The model could be used to solve acoustic–elastic problems, such as calculating the added modal mass and loss factor induced by the interaction between the external sound field and fuselage structure. For demonstration of its application the intermodal coupling coefficients of a scaled fuselage model have been ascertained. For verification purposes the sound field radiated by a sphere with a cyclically vibrating surface has been calculated by this model. The results are coincident with those yielded by an analytical method. The calculation of sound power radiated by a static sphere source gives the model and the numerical method additional proof of their validity. It illustrates that the improved model and its numerical method are valid, reasonable and useful.

Accurate determination of total sound power radiated from a rectangular panel

Radiation of sound from planar vibrating panels has been extensively studied for years. In most of these investigations, the total sound power is approximately obtained from the modal radiation efficiencies without considering the contributions from modal cross couplings. The primary reason for doing this is perhaps that the inclusion of cross-coupling terms may result in a tremendous increase in computational load, particularly when a large number of structural modes is involved. In a recent paper [R. D. Snyder and N. Tanaka, J. Acoust. Soc. Am. 97, 1702–1709 (1995)], an approximate estimate of the cross-coupling terms from the modal radiation efficiencies was discussed. It is, however, valid only in a low-frequency range and deteriorates rapidly as frequency increases. In this paper, the effect of modal cross couplings on the total sound power radiated from a simply supported rectangular panel is discussed. A formula is derived for an accurate and efficient calculation of the cross-coupling terms which allows for effortlessly including the effects of the modal cross couplings in the total sound power calculation. In addition, the present formulation is valid in the whole frequency range. Results are presented.

Characterization of a removable, hemianechoic floor in Health Canada’s large anechoic chamber

Health Canada is interested in promoting the use of quieter industrial machinery through sound power measurement and labeling. To measure sound power under standard hemianechoic conditions, a removable floor was installed and tested in the anechoic chamber. The floor had dimensions 13 m× 9 m and was constructed from 2.8-cm-thick concrete tiles. It was designed to have a sound absorption coefficient below 0.06 in the range 50 Hz–20 kHz, as required by sound power measurement standards. Characterization of the acoustical performance using ISO3745 indicated that measurements were acceptable to a distance of more than 2 m. In situ estimates of the absorption coefficient using acoustic intensity showed the local absorption coefficient could be improved by sealing the joints in the floor. The intensity technique also showed that below 125 Hz, the absorption coefficient was limited by the floor dimensions. In situ vibration measurements of individual floor tiles suggested that the absorption coefficient was acceptable under acoustical excitation. Floor vibration and reradiation of sound power can be a problem in any room. Calculation of sound power radiated from the floor using vibration measurements (ISO/TR7849) was found useful for determining if a source should be vibration isolated.

Structure-borne sound power emission from resiliently mounted fans: case studies and diagnosis

A method for calculating the structure-borne sound power emission through the resilient mounts of machines is investigated by comparing calculated power with in situmeasured power for a range of fans on concrete floors. The structure-borne sound power is the structure-borne equivalent of the airborne sound power of the source and is of great potential interest in predicting structure-borne sound. Initially, the simplifying assumptions invoked in the derivation are investigated by using data obtained from a typical fan installation. For the case studied it was found that the relative phases of the excitation at the various mount points could be assumed to be random, allowing significant simplification in the formulation. In addition, spatial averages of the free velocity of the machine source and the mobility of the supporting floor over the mount positions were found to be adequate. Furthermore, power transmission by rotations was shown to be insignificant compared with that due to vertical translation. These findings are not general but serve to increase confidence that acceptably accurate calculation of structure-borne sound power is feasible by using simplified formulations. Power has been calculated for four fan installations and compared with the directly measured power. In three of the cases the measured power significantly exceeded the calculated values indicating the presence of a dominant flanking transmission path (i.e., the mounts were bridged in some way). In one case the flanking via a duct support was quantified and was shown to dominate transmission through the mounts. In other cases reasonable agreement was obtained although some flanking transmission was still present.

Calculation of the structure-borne sound power emission from machines

The structure-borne sound power emission from vibration sources is the closest analogue to airborne sound power and has tremendous potential benefit in prediction of sound levels in buildings and machines. However, the concept has yet to find wide application because the large number of terms needed to calculate power makes practical implementation difficult. In the paper, some simplifying assumptions are investigated, aiming to reduce the number of terms while maintaining acceptable accuracy. In general, the power through one contact point between a machine and its foundation depends on the velocity contributions from other points. The phase angles of these coupling contributions are investigated by measurement of free velocities and the mobility matrix at the seven mount points of a large, resiliently mounted fan. The assumption is that any phase angle is equally likely and this is shown to be reasonable at the frequencies considered. It is shown that a simplified calculation of sound power, using just seven terms causes little loss in accuracy compared with the full 28-term formulation.

Radiation of Sound by Airfoils that Accelerate near the Speed of Sound

This work shows theoretically that airfoils accelerating at a speed near to, but less than, the speed of sound can be powerful emitters of sound. The sound generation is due to both lift and thickness effects. The airfoil is replaced by volume velocity and body force distributions, and the solutions are obtained by standard methods. A rotating blade is replaced by a lineal progression of accelerating “torpedoes” representing the rotor tips. The sound of lift and thickness effects is radiated strongly forward. Sound power calculations made for thickness radiation alone for a series of airfoil shapes show some reduction of radiated sound with tip shape, and a promising correlation with experimental results.

Über die akustischen probleme der kühltürme

The acoustic problems of cooling towers The paper surveys the different sources of noise in the cooling towers of air conditioning plants, particularly those of fans and water. The empirical formulas for noise evaluation of cooling towers, with axial and centrifugal fans, are given together with a numerical example of total sound power and octave band sound level calculations for a 180-ton refrigeration tower made from three equal units.

Power-Level Criteria for Noise Control

Speech intelligibility in rooms such as classrooms, conference rooms, theaters, and auditoria, where a speaker must be heard by a “marginal” listener at the far end of the room, depends on the ratio of noise power to speech power regardless of room size and absorption. Thus the expression of noise criteria in terms of power is both simpler and more accurate in assuring speech intelligibility than the present practice of specifying sound-pressure levels. In a paper, “Simplifying Room Sound Power Calculations” [ASHRAE J. (July 1963); ASHRAE Trans. (1963)], the author found that the mean octave-band sound-power level in the speech frequency range should not exceed 44 dB re 10−12 W for 0.8 articulation index with normal voice power. A total range of 12 dB covers variations of speech intelligibility and speech power. For other types of rooms, the acceptable noise power is proportional to room-surface area. A simplified chart is also presented for estimating “room effect” from room size and type. The advantages of the direct use of sound-power level as a criterion are shown by further experience.

Sabine Reverberation Equation and Sound Power Calculations

Three reverberation time equations and three sound power equations are scrutinized for their utility in the calculation of sound power from measurements of the average steady-state sound pressure level and reverberation time in a reverberant room. It is noted that the Sabine reverberation time equation is theoretically plausible for this use, even in a moderately absorbing room, providing it can be established that the average sound energy density decays exponentially with time. The sound power calculation may also be performed in terms of the “Sabine absorption” which is simply the absorption computed (by the Sabine equation) from the observed reverberation time and room volume. The “Sabine absorption coefficient” may exceed unity; indeed, it approaches infinity as the walls of the room become completely absorbing. An experiment was performed in a concrete room of volume 1350 ft3, to which three amounts of sound absorbing material were added. Under these four conditions the appropriate measurements were made with two independent systems (one having half-octave bands, the other third-octave bands), from which were calculated the sound power spectra of a printing calculator and a unit heater. In addition to simplicity, both theory and experiment support use of the “Sabine absorption” instead of the “room constant” in the calculation of sound power.