Nonlinear Dynamics Of An Axially Moving Plate Immersed In Fluid

In this paper,the nonlinear vibration characteristics of the liquid-immersed plate with four sides simply supported by a periodical excitation are studied.Considering the effects of fluid-structure interaction,axial displacement,axial tension,and damping,the dynamic equations of the system are established by using the D'Alembert's principle.The Galerkin method was used to disperse the original partial differential equations and got the nonlinear differential equations in the modal coordinates.Then the parameters of nonlinear differential equations were non-dimensionalized.The numerical method was used to analyze the bifurcation behavior of the system when amplitude,velocity,and frequency of external excitation changed.Using the phase diagram and Poincare map to identify the nonlinear dynamic behavior of the system.It was found that the fluid-solid interaction system exhibits periodic motion,double-periodic motion,almost periodic motion and chaotic motion at different states.The multi-scale method was used to analyze the nonlinear vibration characteristics of liquid-immersed plates,obtaining system modal response curve.Changing parameters such as axial movement speed and vibration amplitude to study the influences of these parameters on the nonlinear characteristics.Finally,the stability of the periodic solution and the bifurcation are studied.The following conclusions were obtained through research:in the numerical analysis of the nonlinear dynamic behavior of the axially moving liquid immersion plate with four sides,there are three chaotic precursors,period-doubling bifurcation,explosive bifurcation and almost periodical delivery.When the dimensionless excitation amplitude,motion velocity,and external excitation frequency of the plate are changed,bifurcation or chaos occurs simultaneously in the bifurcation diagram of displacement and velocity at the midpoint of the plate.With the change of parameters,the system may have a jump phenomenon.The system exhibits the hard characteristics under the effects of fluid-structure interaction,axial movement and axial tension.The excitation force plays a decisive role in the occurrence of saddle-node bifurcation.The axial movement speed plays a minor role in the amplitude-frequency characteristics.The influence of damping on the minimum force amplitude required for the occurrence of saddle knot bifurcation is positively correlated.The greater the cubic degree of the addition al stiffness,the smaller the minimum force required for the saddle knot to branch.