Nonlinear Vibration Characteristics of Cantilevered Fluid-Conveying Pipe with Circular Motion Constraint
In this paper,the spatial bending vibration of a cantilevered fluid-conveying pipe with circular motion constraints was studied to explore the influence of constraint stiffness coefficient and constraint placement position on the two kinds of periodic motion of pipeline(including planar periodic motion and spatial periodic motion)and their stabilities.Firstly,the vibration equation was obtained by simulating the action of the motion constraint on the pipeline as a nonlinear cubic spring mode based on the existing literature.Secondly,the vibration equation was discretized into a system of ordinary differential equa-tions by the Galerkin method.The relevant coefficients(including the rate of change of critical eigenval-ue with velocity and the nonlinear resonant term)that determine the qualitative dynamical properties of the system were given in combination with the projection method based on the center manifold-normal form theory and averaging method.By setting the truncated mode numbers to 6,the aforementioned co-efficients were calculated at several sets of constrained stiffness values and constrained positions.And then,the influence of motion constraints on the periodic motion of the pipeline was studied.The follow-ing conclusions were drawn:Increasing the constraint stiffness at a fixed constraint position or increasing the distance from the constraint position to the fixed end of the pipeline while keeping the constraint stiffness constant,both will reduce the mass ratio interval corresponding to the stable planar periodic motion of the pipeline,and increase the mass ratio interval corresponding to the stable spatial periodic motion;the farther the constraint position from the fixed end of the pipeline,the more significant the in-fluence of the changes in the constraint stiffness on the dynamic behavior of the pipeline.Finally,the 6-mode Galerkin discretization equation of the original vibration equation was numerically solved at some specific mass ratios to calculating the oscillation frequencies and generating the configuration diagrams,phase diagrams,and Poincaré mapping diagrams,which validates the relevant conclusions obtained by projection and averaging methods.
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