Free vibrations of fluid conveying pipe with intermediate support

In this study, linear vibration of fluid carrying pipe with intermediate support was discussed. Supports located at the ends of the pipe were clamped supports. A support was located in the middle section show the features of a simple support. It was accepted that the fluid velocity varied harmonically by an average speed. The equation of motion and limit conditions of the system were obtained by using Hamilton principle. The solutions were obtained using the Multiple Scale Method, which is one of the Perturbation Methods. The first term in the perturbation series causes the linear problem. Exact natural frequencies were calculated by the solution of the linear problem for the different positions of the support at the center (η), different longitudinal stiffness (vb), different pipe coefficient (vf), different rate of fullness (β) and natural frequencies depending on velocity of the fluid (v0) were calculated exactly. The obtained results were shown in graphics.