INSTABILITY MECHANISM OF FLEXIBLE BEAM AXIALLY MOVING IN A CONSTRAINED REGION

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The dynamic behavior of the flexible beam, which is pulled into the slit of the elastic wall, is discussed with Multibody Dynamics formulation and experiments. This behavior is called "Spaghetti Problem".In the first step, the gap size of the slit is though to affect the lateral deformation of the beam. Dynamic behavior of the beam is simulated numerically and examined the accuracy of the presented formulation by the gap size and the pulling velocity of the beam as parameters. It is clarified that the gap size and the pulling velocity influence the increase of the lateral vibration near the inlet of the slit.In the second step, This study deals with a theoretical stability analysis of flow-induced vibration generated in a flexible web moving in a fluid-filled narrow space with shear fluid flow. In the stability analysis, the basic equations of fluid flow around the moving web are based on the Navier-Sokes equations integrated over the gap width between the moving web surface and side w … More all, assuming that the gap width is enough small compared with the length of the web. The structural vibration equation of the moving web in the transverse motion is based on the Kirchhoff-Love's thin-plate model. From these basic equations, the equations of the fluid-structure coupling motion are obtained, employing the moving boundary conditions of the surface of the moving web. And these equations are linearized around the equilibrium position, and the solution of these equations is obtained by using the muti-modal expansion method and applying the Galerkin's method. The characteristic equation of the system is derived as a function of the axially moving speed of the web. And the stability and frequency of the system are defined by the imaginary and real part of the complex eigen values of the characteristics equation respectively.As a result, the analytical results show that flutter type instability (traveling-wave type flow-induced vibration) and divergence type instability occur in the axially moving web due to the shear fluid flow with increasing the axially moving speed of the web. And the analytical results clarify the region of these two types of instability with varying the added mass parameter of the fluid. Less