Stability of a pipeline section with an elastic support

We systematically study the stability of a pipeline section filled with a moving nonviscous fluid. The computational scheme of the pipeline is a rod one of whose ends is rigidly fixed and the other is elastically supported. For the problem parameters we take the fluid relative mass, the fluid flow rate, and the rigidity of the elastic support. We study the dynamic buckling frequencies and modes for various critical values of the parameters and the behavior of characteristic exponents on the complex plane. We also analyze the influence of the elastic support on the position of the stability region boundaries and on the type of buckling in the transition to a critical state.