Many gas transmission facilities utilizing centrifugal compressors and large diameter piping experience high amplitude high-frequency noise and vibration. In addition to being a nuisance noise problem, failures of thermowells, instrumentation, and attached small-bore piping can result. Such problems can also occur in the piping itself when high flow velocities and internal obstructions are present. Many times, high frequency noise problems are treated with acoustical insulation (lagging) on the pipe. However, with an understanding of the underlying physics of two- and three-dimensional acoustics it is often possible to modify the piping design to reduce or eliminate the high frequency energy. Two high-frequency energy generation mechanisms predominate in most industrial processes; flow induced (Vortex shedding) and pulsation at multiples of running speed (blade-pass frequency). Once this energy is generated, amplification may occur from acoustical and/or structural resonances, resulting in high amplitude vibration and noise. Many tools exist for analysis of structural resonances and one-dimensional acoustical resonances. Analysis of high-order acoustics can be accomplished using sophisticated numerical methods (FEA, or BEA); however, a simplificaiton of the three dimensional wave equation which has been reduced to a function of zeroes of the 1st order Bessel function, the speed of sound, and internal pipe dimension can also be used successfully. Several references provide lists of the zeroes of the Bessel function; however, most of these references only provide solutions up to m,n = 6. Field tests have identified cross-wall modes up to m = 30. Therefore, a table is provided for zeros for m = 0–32 and n = 0–8.

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