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# Nonlinear Dynamic Response of a Fluid-Conveying Pipe with a Y-Type Manifold Under Different End Conditions

## Abstract

This article addressed the discussion on the nonlinear dynamic response of a fluid-conveying pipe with a Y-type manifold under different end conditions. In which, the pipe element was regarded as an Euler-Bernoulli beam and the control volume of the flowing fluid was simplified as a jet. The governing equation of such a nonlinear dynamic problem was derived using Hamilton’s principle and the momentum equation for the steady flow condition. The Galerkin method and the RungeKutta method with fourth-order truncation were used for solving the governing equation. To validate the numerical model, the numerical results were compared with the existing literature and showed in good agreement. In addition, parametric analyses of the nonlinear dynamic response have been done. Among which, the parameters such as the angle of the manifold, the aspect ratio, the end constraints of the pipe and the flow velocity were taken into consideration. It was concluded that : (1) the dimensionless critical flow velocity of the fluidconveying pipe rises up significantly and the dimensionless peak deflection decreases as the angle between the central axis of pipe and manifold increases; (2) the dimensionless peak deflection of the pipe goes up as the aspect ratio increases; (3) the dimensionless peak displacement of the pipe increases with an increase in the total number of degrees of freedom at the ends; (4) when the dimensionless velocity is small, dimensionless peak deflection is insensitive to the dimensionless velocity, but when it is large, the dimensionless peak deflection rises up with the increase of the dimensionless velocity; (5) the nonlinear behavior of the pipe is mainly dominated by the first-order mode; (6) the nonlinearity of the pipe is positively correlated with the aspect ratio and the total number of degrees of freedom at the ends, and this effect is significant. However, there is a non-significant inverse correlation between the manifold angle and nonlinearity. The research results in this paper may provide reference for the engineering practice of pipelines.

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