An excitation spectrum criterion for the vibration-induced fatigue of small bore pipes

The purpose of the study is to determine an easy-to-use criterion to evaluate the risk of vibration induced fatigue of small bore pipes. The failure mechanism considered is the resonant amplification of a stationary broadband excitation of the main pipe by natural modes of the small bore pipe, leading to bending stresses above the fatigue limit of the steel. Based on the Euler beam theory, a simple model is built up for the natural mode shapes of the small bore pipe close to its root. It is shown that the velocity spectrum at the root of the small bore pipe is equal to the RMS value of the bending stress multiplied by a function of the natural frequency, the damping coefficient, the speed of elastic waves in the steel, the Young modulus and a non-dimensional factor weakly depending on the geometry of the small bore pipe. A maximum velocity spectrum can then be deduced, assuming that a small bore pipe vibrates mainly on its natural mode shapes. The maximum excitation spectrum is defined for each frequency f as the one which would generate a maximum bending stress equal to the endurance limit of the steel, would the small bore pipe have a natural frequency equal to f. Using envelope values of the dimensional factor, the stress intensification factor, the peak factor and the endurance limit of the steel, one obtains the following maximum velocity spectrum for the stainless steel : v < 6 mm / s / sqrt(f) and the following maximum velocity spectrum for the ferritic steel : v < 2.7 mm / s / sqrt(f) The velocity spectrum criterion appears less penalizing than the 12 mm/s criterion and more conservative than the strict enforcement of the ANSI-OM3 standard. Comparisons with former studies show that the velocity spectrum criterion leads to the correct fatigue diagnosis.