Dynamics of Timoshenko Beams Conveying Fluid

Abstract

The dynamics of pipes conveying fluid is described by means of the Timoshenko beam theory. The equations of motion are derived and solved ( a) by a finite-difference technique, and ( b) by a variational method. It is shown that the latter is the more efficient method. The eigenfrequencies of the system and its stability characteristics are compared with results obtained previously using the Euler-Bernoulli beam theory, and it is shown that in certain cases (e.g. short pipes) the two sets of results diverge. Experiments indicate that the present theory is more successful in predicting the observed behaviour. Furthermore, the present theory shows that, in some cases, cantilevered pipes may lose stability by buckling, whereas previous theories indicate that the system always loses stability by flutter.