In-plane dynamic response analysis of curved pipe conveying fluid subjected to random excitation

A new approach was presented to analyze the dynamic response of the Timoshenko curved pipe conveying fluid under random excitation. The in-plane motion equations of Timoshenko curved pipe conveying fluid were deduced via Hamiltonʹs principle for the open system, in which the fluid–structure interaction and the effect of shear deformation were taken into account. The exact shape functions describing radial and axial displacements as well as cross-section rotations were found in algebraic-trigonometric form. Based on these shape functions, using virtual work principle, the finite element model of in-plane vibration for Timoshenko curved pipe conveying fluid was established. The pseudo excitation method in conjunction with the complex mode superposition method was performed to solve these equations. In the example, the critical velocities and the natural frequencies of a semi-circular pipe conveying fluid with different boundary condition were discussed. By the proposed method, the displacement and velocity of the curved pipe were derived, and their power spectrum densities and spectral moments were also yielded. Then, the influences of fluid velocities on the natural frequencies and the standard deviation of dynamic response were studied.