Mechanical Analysis Under Coupled Thin Elastic Plate And Fluid Action

Thin elastic plate is one kind of common project components, and the plate and fluid coupling theory is usually used in different engineering field. The thin plate's deformation or motion under the pressure of fluid affect the flow field and alter the fluid load distribution and size. Researches on FSI at home and abroad focus on numerical analysis on static and dynamic problems of coupling systems, and have issued many results. On the contrary, theoretical analysis on FSI has comparatively slow development and has rare available theoretical results. So they have vast potential and great need of development.The thin elastic plate is in a continuous incompressible ideal cross-flow. The kinematic equation and dynamic equation of fluid-solid contact surfaces suitable for small deflection are put forward by united Lagrangian-Eulerian method and the criteria classification of nonlinear FSI problems. Then the partial differential equations are derived for the bending problem of the plate. The velocity potential function corresponding to the rigid plate is presented using doublet theory. And by applying superposition principle, the deflection and stress expressions are derived for small deformation elastic plate. Taken simply supported rectangular plate and clamped circular plate as examples, the deflection and stress of plate, also the velocity of fluid are analyzed. The influences of system parameters on them are discussed.As the plate in a continuous incompressible ideal cross-flow, the kinematic equation and dynamic equation of fluid-solid contact surfaces suitable for large deflection are put forward by united Lagrangian-Eulerian method. Then the partial differential equations are derived for the large deflection problem of the plate. For the solutions of nonlinear equations, the in-plane displacement and the curvature change of thin plate are described as flection. The deflection, in-plane displacement and stress of plate are expressed.For simplicity about viscous fluid, the Reynolds number is assumed small. Because the Reynolds number is the ratio of inertia force and viscous drag force, the inertia force can be neglected at low Reynolds number. And Navier-Stokes equation of fluid movement is almost equal to the Stokes equation. By united Lagrangian-Eulerian method, the influences of plate's vibration in a travelling wave manner on the fluid flow are analyzed in a state of slow viscous flow. Besides, the sloshing problem of incompressible viscous fluid between two rigid solid wall is considered. The influences of surface displacement on internal fluid velocity are given.Using single Lagrangian method, static and dynamic forces analysis of elastic inner plate between different density ideal fluid are discussed. After giving the kinematic equation of fluid and plate as well as boundary condition described by single Lagrangian method, the symmetrical deflection function of inner plate is solved. The vibrations of clamped plate by dynamic disturbance are analyzed. The deflection and stress functions of plate and the vibration of plate by different disturbance are presented by examples. And the influences of parameters on the deformation, stress and natural frequency are given.Applying ANSYS simulate the corresponding problem. The theoretical results are compared with numerical solutions, and error analysis is given. It is shown that the theoretical results effectively.United Lagrangian-Eulerian method and single Lagrangian method for deformation and stress of plate acted by fluid are effective, and lay a good theoretic foundation for new numerical simulate.