Circumferential Mode Order Research Articles

A modal separation measurement technique for broadband noise propagating inside circular ducts

A measurement technique which separates broadband noise propagating inside circular ducts into the acoustic duct modes is developed. The technique is also applicable to discrete frequency noise. The acoustic modes are produced by weighted combinations of the instantaneous outputs of microphones spaced around the duct circumference. The technique is compared with the cross spectral density approach presently available and found to have certain advantages, and disadvantages. Considerable simplification of both the new technique and the cross spectral density approach occurs when no correlation exists between different circumferential mode orders. The properties leading to uncorrelated modes and experimental tests which verify this condition are discussed. The modal measurement technique-is applied to the case of broadband noise generated by flow through a coaxial obstruction (nozzle or orifice) in a pipe. Different circumferential mode orders are shown to be uncorrelated for this type of noise source.

Letter

Electrical motors are widely used and are often required to satisfy comfort specifications. Thus, vibration response estimations are necessary to reach optimum machine designs. This work presents an improved analytical model to calculate vibration response of an electrical machine. The stator and windings are modelled as a double circular cylindrical shell. As the stator is a laminated structure, orthotropic properties are applied to it. The values of those material properties are calculated according to the characteristics of the motor and the known material properties taken from previous works. Therefore, the model proposed takes into account the axial direction, so that length is considered, and also the contribution of windings, which differs from one machine to another. These aspects make the model valuable for a wide range of electrical motor types. In order to validate the analytical calculation, natural frequencies are calculated and compared to those obtained by Finite Element Method (FEM), giving relative errors below 10% for several circumferential and axial mode order combinations. It is also validated the analytical vibration calculation with acceleration measurements in a real machine. The comparison shows good agreement for the proposed model, being the most important frequency components in the same magnitude order. A simplified two dimensional model is also applied and the results obtained are not so satisfactory.

Acoustic transmission loss of pipes excited by internally propagating plane waves

A control valve constitutes a source of mechanical vibration, nearfield imcompressible pressure fluctuations and radiated acoustic waves. An ideal mechanical vibration filter placed several wavelengths from the source will remove the influence of the first two excitations from the response of the downstream pipe. The internal propagation of acoustic energy, however, is unaffected and so the transmission loss of pipes to these propagating waves is of concern. In the plane-wave region, Morfey, Heckl, and others have measured acoustic radiation far greater than their estimates. This work has been directed towards explaining these differences. Experiments with plane acoustic excitation of steel and P.V.C. pipes were performed. Different gases were used inside the P. V. C. pipe, for which the wall response was forced, to investigate the radiation from subsonic and supersonic axisymmetric wave motion. Close agreement was found, in contrast to the case of steel pipes, where a strong resonant response occurred. This theoretically unpredicted resonant response (which was about 45 dB above the forced estimate) contained all resonant modes but was dominanted by the modes with the highest circumferential mode order. The acoustic radiation, however, was greater than the forced estimate by only 25 dB, since it is determined by the most efficient radiators—the n=1 “bending” modes. Only these latter modes are damped by the pipe supports; the measured Q of these modes was about 100. Similarly these modes are most strongly coupled to the excitation, and consequently the n=1 modes control the radiation. It was found that the application of surface damping treatments caused reductions of 10 to 20 dB in response, but only 2–5 dB in power radiated. This is because surface damping treatments are particularly effective on higher-order circumferential modes and much less effective on the n=1 modes, in which there are no changes in circumferential radius of curvature. It is concluded that a significant reduction in power radiated requires damping procedures directed specifically at the n=1 modes. Experiments in progress suggest that for the pipes studied, a Q less than 20 for n=1 modes is required to achieve the lower bound power radiated corresponding to a forced response.