A theoretical model is developed for the transverse vibrations of bellows expansion joints. The model is based on Timoshenko beam theory and includes the added mass effect of an internal fluid. An analytical expression for bellows natural frequencies is developed in the form of a Rayleigh quotient and is presented in a way which is suitable for hand calculations. The results for the first four transverse modes are compared with experiments as well as the predictions of the simplified analysis of the Expansion Joint Manufacturers Association (EJMA). While the present analysis agrees well with experiments, the EJMA approach can be substantially in error due to its neglect of rotary inertia and the convolution distortion component of fluid added mass.

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