Vibration And Instability Of Tube Arrays In Cross-Flow

The flow-induced vibration and stabilities of tube arrays in cross-fluid were studied. Based on the fluid-elastic-instability-theory, with the Chen’s unsteady model used, the appropriate expressions of fluid forces were obtained and the differential equations of tubes were established. Galerkin Methods were utilized to change the governing partial differential equations into a set of ordinary differential equations, the eigenvalue method was used to analyze the stabilities of linear systems, by cubic non-linear stiffness considered, the response and instabilities of non-linear systems were analyzed. The main contents of this thesis are as follows:(1) Based on the Chen’s unsteady model, the figures of fluid-damping coefficients and fluid-stiffness coefficients versus reduced flow velocity were obtained.(2) The single tube and three tubes in cross-flow were investigated, the differential equations of tubes were established, the eigenvalue method was used to analyze the stabilities of linear systems. Numerical integrations results show that the system lose its stabilities by fluttering.(3) By cubic non-linear stiffness considered, the response and instabilities of non-linear systems were analyzed. The Runge-Kutta method was utilize to analyze the method, by means of the phase portraits and time history graphs, the instabilities and bifurcation of the nonlinear system were analyzed. Some interesting phenomena can be obtained, the response is stable while the fluid velocity is on the small side; as the increase of fluid velocity, the system generates limit cycle flutter. Phenomenon is more complex for three tubes, the system undertakes bifurcation through the path of periodic 1-periodic 2-periodic 1 after reaching the critical velocity.