Dynamics And Stability Of Space-Dependent Pipes Conveying Fluid

The pipe conveying fluid plays important roles in both engineering applications and theoretical researches.It has been regarded as a new model of dynamical problem for the study of fluid-structure interaction as well as nonlinear dynamics theories.The typical pipe conveying fluid can be equivalently processed via a relatively simple beam model.The mathematical equations are concisely described,and the theoretical results can be verified by experiments that are relatively easy to implement.The study of the pipe conveying fluid can be used as a theoretical tool to understand the dynamic behavior of complex and diverse fluid-structure systems,and to explore and discover new dynamic phenomena and characteristics.Therefore,its research has received extensive attention.Studies on uniform constant-section pipes conveying fluid have shown that such systems can produce buckling instability through static bifurcation or flutter instability through dynamic bifurcation.Based on the study of uniform constantsection pipes conveying fluid,this paper explores and analyzes the stability and dynamic behavior of two types of space-dependent pipes.The possible nonlinear behavior of such pipes is studied to reveal the causes of various mechanical phenomena in the fluid-structure interaction system,and the influence of key parameters is studied to realize the parameter optimization of pipes conveying fluid in practical applications.The main contents are as following:1.The stability and dynamic behavior of inhomogeneous geometry structure pipes conveying fluid are analyzed by studying corrugated pipes.The flow velocity is assumed to harmonically vary along the pipe rather than the time.The dimensionless equation is discretized using the differential quadrature method.Subsequently studied are effects of the mean flow velocity and two key parameters of the corrugated pipe,namely the amplitude of the corrugations and the total number of the corrugations.Unique results are demonstrated in this system.The corrugated pipe will lose stability by flutter even if it has been supported at both ends.And when the total number of the corrugations is sufficient,this flutter instability occurs at a micro flow velocity.These phenomena are verified via the Runge-Kutta method.The critical flow velocity of divergence is analyzed in detail.Compared with the uniform pipes,the critical velocity will be reduced due to the corrugations,thus accelerating the divergence instability.Specifically,the critical flow velocity decreases if the amplitude of the corrugations increases.However,the critical flow velocity cannot be monotonously reduced by the increase in the total number of the corrugations.An extreme point appears which can be used to realize parameter optimization of corrugated pipes in practical applications.2.The stability and dynamic behavior of inhomogeneous material pipes conveying fluid are analyzed by studying three-dimensional functionally graded material pipes.The differential quadrature method is used to solve the dimensionless governing equation which is derived via the Hamilton method.The effects of the functional gradient material parameters and flow velocity on the pipes are then studied.The results show that the variation of radial and toroidal material parameters changes the effective stiffness so that the natural frequencies of the system are correspondingly changed,and their effects on stability are inapparent.However,the variation of axial parameter has a large impact on the stability of the system.Similar to the corrugated pipes,flutter instability at a micro flow velocity occurs.For the pinned-pinned pipes,the axial power law index will cause a jump phenomenon to the critical flow velocity in a certain area.In conclusion,the dynamical behavior of the space-dependent pipes conveying fluid is analyzed in detail,which reveals that the effects of non-uniform structure and non-uniform material on the dynamic behavior of the pipes conveying fluid are significant.Both the Newtonian derivation and the Hamiltonian derivation are utilized to gain the governing equations and the DQM is used to solve the equations.The nonuniform characteristic of the pipe results in flutter instability even if the pipe is supported at both ends,which deepen the understanding of the dynamic behavior of such systems.Meanwhile,some key parameters are analyzed to improve the stability,and the results can be used to realize the parameter optimization for the engineering application of pipes conveying fluid.