Fluid-Induced Vibration Response And Stability Analysis Of Parallel Flexible Plates

The plate-type structures are widely used in the integrative design of nuclear fuel element.It is reported that responses such as bucking and flutter may pose a serious dangerous to therunning and safety of the system. So it is of vital theory significance and good applicationvalue to focus on the stability and nonlinear dynamics of such structures. This dissertationmainly addresses systematical studies on the stability and response ofthe plate-type structures in an ideal flow; and it is expected to reveal the mechanism of somecomplex dynamical behavior and to serve as a theoretical basis to the engineeringapplication. The main contributions of this dissertation are as follows: 1. The coupling equations of motion of a two-dimensional elastic plate in uniform axialflows are established and are respectively discreted by both the differential quadraturemethod and the finite difference method. The stability of the discrete systems is studied bythe eigenvalue method, and the calculated results of these two methods are compared, theresults of which show that the elastic plate fixed at both ends (simply supported or clamped)firstly undergoes divergence instability and the discrete system based on the finite differencemethod can obtain better results than that based on the differential quadrature method whenthe effects of the trailing edge of plate on flow are considered. The results of the discretesystem based on the finite difference method reach a good agreement with those in relativeliteratures. 2. The coupling equations of motion of the parallel plates simply supported (or clamped)in uniform axial flow are derived. The differential quadrature method and the finitedifference method are employed to discrete the governing equation, respectively. Thediscrete equations in a matrix form are rewritten in terms of only the structural transversedisplacement by employing the fluid-structure coupling boundary conditions. The eigenvaluemethod is utilized to analyze the stability and modes, the results of which show that theshape of the first order mode of the parallel plates vibrating in flow is different from that ofthe first order bending mode of the plates vibrating in air, which well reveals the effects offlow on the mode shape. 3. A two-dimensional simply supported harmonically excited thin plate subjected touniform incompressible flow is theoretically modeled and a nonlinear cubic stiffness isconsidered in the middle of the plate. The effects of the external force on the dynamicresponses of system are studied. The differential quadrature method is employed to discretethe governing equation and the dynamical responses of the system are calculated by thenumerical method, the results of which show that the flow velocity and the external forceamplitude are the two key parameters which lead the system to exhibit various motions, suchas periodic, quasi-periodic and chaotic motion. 4. A nonlinear model of a two-dimensional simply-supported plate in axial incompressibleflow with cubic stiffness is established. The effect of the leading rigid edge and the trailingrigid edge of plate on flow is considered. The finite difference method is used to discrete thegoverning equation. In order to reduce the computation scale caused by a large number ofthe grids, the main mode reduction method is adopted. The complex responses of system arecalculated by the numerical integration method, the results of which show that variousinteresting motions, such as periodic, quasi-periodic and chaotic motions, occur with thevarying of the flow velocity and the external force amplitude, and the route to chaos is viaperiod-doubling bifurcation or quasi-periodic process. 5. Based on a nonlinear model of a two-dimensional simply-supported plate in axialincompressible flow with cubic stiffness, a harmonic oscillation flow is introduced into thesystem and its effects on the flow-induced responses of the system are investigated, theresults of which show that the system performs periodic, quasi-periodic and chaotic motions.The route to chaos is via period-doubling bifurcation. However, the route from chaos toperiodic motion is intermittent. 6. A theoretical study is presented on the hydroelastic vibration of a two two-dimensionalelastic plate with both bounded fluid and nonlinear stiffness. The nonlinear governingequations are discreted by the finite difference method, and the degrees of freedom of thegoverning equations are reduced by the main mode reduction method. The results areobtained by numerical integration method, the results of which show that various motions,such as periodic, quasi-periodic and chaotic motions, are well illustrated by the bifurcationdiagrams, phase-plane portraits, Poincare maps and time history.