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The modeling of a slightly curved pipe conveying fluid usually adopts the Euler–Bernoulli beam theory. In this paper, a dynamic model of the slightly curved pipe conveying fluid based on the Timoshenko beam theory is established for the first time. The complex mode method is used to obtain the frequencies, the modes, and the first critical velocity of the slightly curved pipe. Two kinds of initial configurations of the pipe with fixed–fixed boundary conditions are studied. Based on the Galerkin truncation method, the natural frequencies of the slightly curved pipe are also obtained with the generalized eigenvalue method. Moreover, the Coriolis force caused by the fluid is equivalent to the damping matrix. Therefore, a novel finite element model of the curved pipe considering fluid influence is developed. The numerical simulation method is extended to calculate the mode and frequency of the slightly curved pipe. Numerical results show that all the three methods have high accuracy when calculating the natural frequencies of the transverse vibration of the slightly curved pipe conveying fluid. However, the developed finite element method does not show the effect of flow velocity when determining the modes. Moreover, the initial bending cannot be ignored when analyzing the vibration characteristics of the slightly curved pipe conveying fluid.

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