Free vibration analysis of Timoshenko pipes conveying fluid with gravity and different boundary conditions

Abstract In this paper, the free vibration of Timoshenko pipes conveying fluid with gravity and different boundary conditions is analyzed by using the weak form quadrature element method. The dimensionless frequency and critical flow velocity have been calculated considering various parameters such as the mass ratio of pipe to fluid, slenderness ratio, and gravity. The numerical results with different numbers of discrete points are tested, and the results show that the method has a fast convergence speed. Some numerical results are compared with the existing literature, which proves that the weak form quadrature element method has high accuracy and computational efficiency. This paper shows that the weak form quadrature element method is a preferred method for analyzing fluid-conveying pipes with various boundary conditions.