Nonlinear Vibrations and Stability of an Axially Moving Plate Immersed in Fluid

In this paper,the nonlinear forced vibrations and stability of an axially moving large deflection plate immersed in fluid are investigated.Based on von Karman's large deflec・tion plate theory and taking into consideration the influence of fluid-strueture interaction,axial moving and axial tension,nonlinear dynamic equations are obtained by applying D'Alembert's principle.These dynamic equations are further discretized into ordinary differential equations via the Galerkin method.The frequency-response curves of system are obtained and examined.Then numerical method is used to analyze the bifurcation behaviors of immersed plate.Results show that as the parameters vary,the system displays periodic,multi-periodic,quasi-periodic and even chaotic motion.Through the analysis on global dynamic characteristics of fluid-strueture interaction system,rich and varied nonlinear dynamic characteristics are obtained,and various ways that lead to chaotic motion of the system are further revealed.

Transverse vibration characteristics of axially moving viscoelastic plate

The dynamic characteristics and stability of axially moving viscoelastic rectangular thin plate are investigated. Based on the two dimensional viscoelastic differential constitutive relation, the differential equations of motion of the axially moving viscoelastic plate are established. Dimensionless complex frequencies of an axially moving viscoelastic plate with four edges simply supported, two opposite edges simply supported and other two edges clamped are calculated by the differential quadrature method. The effects of the aspect ratio, moving speed and dimensionless delay time of the material on the trans- verse vibration and stability of the axially moving viscoelastic plate are analyzed.

Dynamic stability of axially accelerating viscoelastic plates with longitudinally varying tensions

The dynamic stability of axially accelerating plates is investigated. Longitudi- nally varying tensions due to the acceleration and nonhomogeneous boundary conditions are highlighted. A model of the plate combined with viscoelasticity is applied. In the viscoelastic constitutive relationship, the material derivative is used to take the place of the partial time derivative. Analytical and numerical methods are used to investigate summation and principal parametric resonances, respectively. By use of linear models for the transverse behavior in the small displacement regime, the plate is confined by a viscous damping force. The generalized Hamilton principle is used to derive the govern- ing equations, the initial conditions, and the boundary conditions of the coupled planar vibration. The solvability conditions are established by directly using the method of mul- tiple scales. The Routh-Hurwitz criterion is used to obtain the necessary and sufficient condition of the stability. Numerical examples are given to show the effects of related parameters on the stability boundaries. The validity of longitudinally varying tensions and nonhomogeneous boundary conditions is highlighted by comparing the results of the method of multiple scales with those of a differential quadrature scheme.