Free Vibration Analysis of Pipes Conveying Fluid Based on Linear and Nonlinear Complex Modes Approach

In this paper, linear and nonlinear complex modes are used to analyze the free vibration of pipes conveying fluid involving the gyroscopic properties of the system. The natural frequencies, complex mode functions and time domain responses of the admissible mode functions based on discretized model are obtained using the invariant manifold method and compared with those of the continuous model. A good agreement has been achieved if the admissible mode functions for the static beams are adopted. The energy contributions of different admissible modes to the modal motions are also studied which explores the gyroscopic coupling variation among the admissible modes for different fluid velocities. Nonlinear complex modes are constructed for the nonlinear case and the morphology of the modal motions is demonstrated for different initial energy to show the contribution of the nonlinear terms. ‘Traveling waves’ are found for the transverse vibrations of the pipes conveying fluid due to the gyroscopic effects, contrary to the “standing waves” found for the pipes without moving fluid.