Dynamic Nonlinear Analysis of Functionally Graded Flow Pipelines with Defects Based on Different Foundation Layouts

Purpose The dynamic characteristics of fluid-conveying pipelines with an initial deflection on nonlinear elastic foundation with local distribution and discrete point arrangement are studied. Methods Based on the Euler-Bernoulli beam theory, the nonlinear dynamic control equation with initial imperfections is established under the influence of the von Kármán nonlinear effect and initial imperfections. Then by introducing the Dirac delta function and Heaviside function, the mathematical model of locally distributed coupling and discrete point coupling between pipeline and elastic foundation is established. The effects of two different nonlinear elastic foundation layouts, local layout, and discrete point layout, on the dynamic behavior of pipelines are studied by means of a bifurcation diagram, phase diagram, and power spectral density diagram. Results Through numerical analysis, it is shown that the functionally graded pipeline has very rich dynamic characteristics under different elastic foundation distribution and initial defect effect. Conclusion The parameters such as the position of the spring, the nonlinear spring stiffness, the length of the support section spring, and the amplitude of the initial defect have a significant effect on the vibration behavior of the pipeline system under different foundation layouts under pulsating flow.