A velocity method for estimating dynamic strain and stress in pipes

A velocity method for estimating dynamic strain and stress in pipe structures is investigated. With this method, predicted or measured spatial average vibration velocity and theoretically derived strain factors are used to estimate maximum strain at the ends of pipes. Theoretical investigation shows that the strain at a point is limited by an expression proportional to the square root of the strain energy density, which in turn is related to its cross-sectional average. For a reverberant field or for an infinite pipe, the average strain energy density is proportional to the mean square velocity. Upon this basis, the non-dimensional strain factor is defined as the maximum strain times the ratio of the sound velocity to the spatial root mean square vibration velocity. Measurements are made confirming that this is a descriptive non-dimensional number. Using a spectral finite element method, numerical experiments are made varying the pipe parameters and considering all 16 homogeneous boundary conditions. While indicating possible limitations of the method when equipment is mounted on pipes, the experiments verify the theoretical results. The velocity method may become useful in engineering practice for assessments of fatigue life.