Abstract:

Euler-Bernoulli beam and plug flow theories are adopted to describe the mechanical model of slender fluid-conveying pipe and internal fluid flow model separately. Green’s function method (GFM) is used to derive the Green’s function of the fixed- elastically supported fluid-conveying pipe, sequentially, and the analytical expression of deflection is obtained. The relationships between deflection and exciting position, exciting frequency, velocity of internal fluid, stiffness coefficient of spring and mass ratio are investigated respectively. Critical excitation position is calculated out based on the given data by means of GFM. During the analytical process of the influence of excitation frequency on deflection, GFM is used to solve the natural frequency simultaneously and results are compared with that of differential transformation method (DTM), as a result, GFM is found to be accurate enough. The proposed method can be expanded to study the forced vibration problems with arbitrary kind of support or multiple excitation forces. Research contents can provide accurate results for further reliability design and methodological reference for designers.

Key words: deflection, forced vibration, Green’s function method, fluid-conveying pipe