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 differentialintegral 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.

A ground-limited nonlinear energy sink

The nonlinear energy sink(NES)is outstanding in vibration control for the well-known character of energy targeted transmitting and resonance automatically capturing.To enhance the practicability,this paper proposes a ground-limited NES.The novel design can be encapsulated in a certain box.However,as the vibration region of NES is limited,the control efficiency of it must be considered seriously.Hence,the ground-limited NES is discussed via the analytical method,the simulation method,and especially the experiment in forced vibration.All parameters involved in this study are obtained through the parameter identification based on the experimental platform.The piecewise nonlinearity is fitted into the continuous nonlinearity by the hyperbolic tangent function.Then the harmonic balance method(HBM)is used during the analytical processing to promote the accuracy of the solution.The direct numerical method produces results to verify the analytical method together with the experimental records.The discussion on the control parameters shows that a proper limiting spring can effectively reduce the vibration of the NES while the cost of the control efficiency is small.In a word,this work provides a simple and reliable approach for restricting the NES,which is beneficial to the design of the NES and broadens the application of the NES in engineering.