| The problems of flow induced vibrations of tubes subjected to inclined flows are widely involved in the engineering applications,such as ocean engineering,petroleum engineering,nuclear power source,etc.The researches on flow-induced vibrations of circular pipes have important theoretical significances and engineering application values.The flow induced vibration of a tube in the flow with an inclined angle was studied based on the theory of fluidelastic-instability.The governing equations of a flexible tube in a rigid tube arrays subject to the flow with an inclined angle were established.The eigenvalue methods and the equivalent linearization concept were used separately to analysis the critical velocities when the systems lost stable.The dynamic behaviors of a circular tube under nonlinear constraints were studied.A series of significant results were obtained.The main contributions of this dissertation are as follows:(1)Based on the engineering backgrounds,the mechanism and damages of flow induced vibrations were described,three research methods of flow induced vibrations and their development histories were summarized.And then,the research results of tube under different external flow were introduced.Finally,the significances of choosing the flow with an inclined angle as the flow condition were discussed.(2)The models and dynamical equations of the tube systems with nonlinear constraints were established.Both a cubic spring and a central gap nonlinearity were considered.The inclined flow was divided into two components and the governing equations of the nonlinear systems were established based on the Quasi-Static Model.And the ordinary differential equations were induced by using the Galerkin’s methods.(3)The stabilities of the corresponding linear systems were studied.Firstly,the stabilities of the linear systems were analyzed with the eigenvalue methods.The results show that flutter occurs when the fluid velocity arrives to the critical velocity.And secondly,to study the influences of the inclined angle on the stabilities of the systems,the inclined angles of the flow were changed as a changeable parameter.The results show that the flutter critical flow velocities increase with the increasement of the inclined angles.(4)The dynamical responses of nonlinear systems were carried out.The dynamic behaviors of a tube with a cubic spring nonlinearity and a central gap nonlinearity were considered respectively.The Fourth-Order-Runge-Kutta method was used to calculate the responses of these systems.And a program was used for calculation.The instabilities of the nonlinear systems were analyzed by drawing the bifurcation diagrams,the phase portraits,the time history graphs and the power spectrum diagrams.The dynamic response of a tube with a cubic spring nonlinearity in the cross flow was studied,and the results were compared with the literature to verify the rationality of model and programming in this paper.An equivalent linearization method was used to analyze the limit-cycle flutter phenomenon of the nonlinear systems.It shows that when the flow velocity is small,the system remains stable.When the flow velocity gets to the critical flow velocity,the system goes through complex nonlinear responses such as limit-cycle flutter,periodic-1 oscillation,and quasi-periodic motions with the increasements of the flow velocities. |
