Closed-form solution for evaluating the principal instability regions for conservative pipes conveying pulsating flowing fluid.

The dynamical behaviors of pipes containing pulsating fluids are nonlinear. In such nonlinear systems principal regions of dynamical instability can result from the effect of the periodic excitation of the fluctuated fluid flow. Evaluating the boundary frequencies for these types of instabilities had been carried out by many analytical and numerical methods. In this paper, an approximate "closed-form" solution for evaluating the principal boundary regions of instability for conservative pipes conveying pulsated fluid has been attempted. Bolotin's method was employed to split the boundaries from the stable regions. The resulting coupled-ordinary differential equations is decoupled by neglecting the effect of the mass ratio term and solved analytically. After imposing the specified boundary conditions, then the simplified formulas or transcendental equations were obtained for the pipes under consideration. These equations can give the principal boundary regions in term of the system parameters by simple calculations. The present solution was carefully checked with the "exact" solution where the mass ratio was included. The results showed good agreement for pinned-pinned clamped-pinned and clamped-clamped pipes conveying pulsating fluid. [ABSTRACT FROM AUTHOR]