Stability and Nonlinear Response Analysis of Parametric Vibration for Elastically Constrained Pipes Conveying Pulsating Fluid

Usually, the stability analysis of pipes with pulsating flow velocities is for rigidly constrained pipes or cantilevered pipes. In this paper, the effects of elastic constraints on pipe stability and nonlinear responses under pulsating velocities are investigated. A mechanical model of a fluid-conveying pipe under the constraints of elastic clamps is established. A partial differential-integral nonlinear equation governing the lateral vibration of the pipe is derived. The natural frequencies and mode functions of the pipe are obtained. Moreover, the stable boundary and nonlinear steady-state responses of the parametric vibration for the pipe are established approximately. Furthermore, the analytical solutions are verified numerically. The results of this work reveal some interesting conclusions. It is found that the elastic constraint stiffness in the direction perpendicular to the axis of the pipe does not affect the critical flow velocity of the pipe. However, the constraint stiffness has a significant effect on the instability boundary of the pipe with pulsating flow velocities. Interestingly, an increase in the stiffness of the constraint increases the instable region of the pipe under parametric excitation. However, when the constraint stiffness is increased, the steady-state response amplitude of the nonlinear vibration for the pipe is significantly reduced. Therefore, the effects of the constraint stiffness on the instable region and vibration responses of the fluid-conveying pipe are different when the flow velocity is pulsating.