The influence of rotary inertia of concentrated masses on the natural vibrations of a clamped-supported pipe conveying fluid

Effects of rotary inertia of concentrated masses on the natural vibrations of a fluid-conveying pipe have been studied by theoretical modeling and numerical calculations. For the analysis, a clamped-supported pipe is assumed and Galerkin's method is used for transformation of the governing equation to the eigenvalue problem. The natural frequencies and mode shapes for the system have been calculated by using the newly developed computer code. In addition, the threshold values of flow velocity for the onset of unstable motions have been investigated. The main conclusions for the present study are (1) rotary inertia gives much change on the higher natural frequencies and mode shapes, (2) the number and location of nodes can be changed by rotary inertia, (3) by introducing rotary inertia, the second natural frequency approaches the first as the location of the concentrated mass approaches the midspan of the pipe, and (4) the critical fluid velocities are unchanged by introduction of rotary inertia and the first three dimensionless values are u∼4.49, 7.73, and 10.91, respectively. (orig.)