Acoustically induced vibration of,and sound radiation from,beams inside an enclosure

The velocity response of a single cylindrical beam to pure tone sound in a rectangular reverberation chamber is analysed. The variation of the response with position within the chamber and the effect of proximity of other similar, parallel beams is considered. A reciprocity relation is established between the response of a beam to sound in the chamber and the sound radiation by such motion when otherwise generated; this relation is found to be valid even for non-diffuse fields, below the Schroeder “large room” frequency (i.e., above this frequency, the average frequency spacing between modes is less than one-third of the bandwidth of a typical mode 1]). The mean square velocity response, averaged over all possible beam positions within the chamber, is found to be directly proportional to the radiation loss factor of that vibrational mode, and inversely proportional to (frequency)³. The maximum normalized response occurs when the beam is excited in its fundamental vibrational mode. One application is to the estimation of fatigue life of heat exchanger tubes in gas-cooled nuclear reactors; the large number of tubes necessitates an estimate of the variation of the tube response with position within the exchanger casing. Another important application is in a reverberation chamber; in many cases a suitable direct excitation experiment is very difficult, or even impossible to perform, while the corresponding reciprocal experiment is relatively easy.