Side branches are small diameter pipes attached to a main pipeline. If a high noise level is present in the pipeline then the side branch may suffer from damaging vibration or fatigue. The mechanics of the vibration involve an acoustic resonance of the fluid within the side branch which is coupled to a structural resonance. The particular conditions investigated in this paper are where the acoustic and structural natural frequencies coincide. It is shown that the resonant vibration amplitude is controlled by the following factors: (i) the degree of correlation of the acoustic wavelength with the distances between bends in the side branch, (ii) the structural and acoustic damping and (iii) the ratio of the structural mass to the mass of the internal fluid. Simple equations are presented for conditions that will result in coupling and for the maximum amplitude of the coupled vibration.

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