Dynamic stability of a semi-circular pipe conveying harmonically oscillating fluid

The dynamic stability of a semi-circular pipe conveying harmonically oscillating fluid is investigated in this study. For analysis, harmonically oscillating flow is regarded as a parametrically excited system with time-varying coefficients. Considering the extensibility and nonlinearity of the semi-circular pipe, the equations of motion and the associated boundary conditions are obtained by using the extended Hamilton principle. Applying Floquet theory to the derived equations, the stability of the pipe is analyzed for variations of the amplitude and oscillating frequency of the fluid velocity. The effects of the mean value for the fluid velocity on the stability are also analyzed. It is found that the semi-circular pipe may become unstable when the fluctuation frequency approaches some multiples or sum of the out-of-plane natural frequencies. Furthermore, it is observed that the instability regions increase with the mean value of the velocity. The results obtained via the stability analysis are verified by time responses computed by using a direct time integration method.