A treatment for the study of dynamic instabilities of fluid-conveying pipes

In this brief communication, a treatment is reported to study the instability behaviors of fluid-conveying pipes. With the help of the properties of the defined parabolic functions in dispersion relations, the various instability conditions and ranges of the systems with respect to structural and fluid parameters can be determined and classified in a more direct manner, which can help to better understand the dynamical properties of long pipes conveying fluid. The treatment method suggested in this paper can also be extended for the instability analysis of other dynamic systems.