Abstract:To study the flow-induced dynamics of an inclined fluid conveying pipe containing a lumped mass, two factors including gravity and inclination are introduced into the general governing equation to establish the dynamic differential equation of the present problem, the solution of the above partial differential equation is discretized by Galerkin method based on new shape functions, with further derivation and manipulation, the characteristic equation for calculating natural frequency is finally obtained. After a through calculation for an example, one can find: (1) the upward slopping pipe has lower stiffness than the downward one under the same parameters. (2) With the increase of lumped mass, the natural frequency decreases sharply at first, and then gently under given flowing velocity; but it will not change the critical flowing velocity. (3) With the increase of implementation coordinate of the lumped mass, the natural frequency fluctuates, and it will lead to the variation of critical flowing velocity and instability type. The above investigation can be radiated to study fluid-structure interaction vibration problems of pipe with other supporting types and added factors, it can provide the way for the following research on vibration reliability and other issues in terms of theory and calculation methods.
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