Yan Qing Wang

Vibrations of Axially Moving Vertical Rectangular Plates in Contact with Fluid

The vibration characteristics of an axially moving vertical plate immersed in fluid and subjected to a pretension are investigated, with a special consideration to natural frequencies, complex mode functions and critical speeds of the system. The classical thin plate theory is adopted for the formulation of the governing equation of motion of the vibrating plates. The effects of free surface waves, compressibility and viscidity of the fluid are neglected in the analysis. The velocity potential and Bernoulli’s equation are used to describe the fluid pressure acting on the moving plate. The effect of fluid on the vibrations of the plate may be regarded as equivalent to an added mass on the plate. The formulation of added mass is obtained from kinematic boundary conditions of the plate–fluid interfaces. The effects of some system parameters such as the moving speed, stiffness ratios, location and aspect ratios of the plate and the fluid-plate density ratios on the above-mentioned vibration characteristics of the plate–fluid system are investigated in detail. Various different boundary conditions are considered in the study.

STUDY ON THE DYNAMIC BEHAVIOR OF AXIALLY MOVING RECTANGULAR PLATES PARTIALLY SUBMERSED IN FLUID

The natural frequencies, complex modes and critical speeds of an axially moving rectangular plate, which is partially immersed in a fluid and subjected to a pretension, are investigated. The effects of free surface waves, compressibility and viscidity of the fluid are neglected in the analysis. The subsection functions are used to describe the discontinuous characteristics of the system due to partial immersion. The classical thin plate theory is adopted to formulate the equations of motion of a vibrating plate. The velocity potential and Bernoulli’s equation are used to describe the fluid pressure acting on the moving plate. The effect of fluid on the vibrations of the plate may be equivalent to the added mass on the plate. The effects of distance ratio, moving speed, immersed-depth ratio, boundary conditions, stiffness ratio and aspect ratio of the plate as well as the fluid-plate density ratios on the free vibrations of the moving plate-fluid system are investigated.

Nonlinear vibration response and bifurcation of circular cylindrical shells under traveling concentrated harmonic excitation

The nonlinear vibration of a cantilever cylindrical shell under a concentrated harmonic excitation moving in a concentric circular path is proposed. Nonlinearities due to large-amplitude shell motion are considered, with account taken of the effect of viscous structure damping. The system is discretized by Galerkin’s method. The method of averaging is developed to study the nonlinear traveling wave responses of the multi-degrees-of-freedom system. The bifurcation phenomenon of the model is investigated by means of the averaged system in detail. The results reveal the change process and nonlinear dynamic characteristics of the periodic solutions of averaged equations.

Nonlinear Dynamics of a Translational FGM Plate with Strong Mode Interaction

This paper examines the nonlinear dynamics of a translational functionally graded material (FGM) plate. The plate is composed of nickel and stainless steel, and its property is graded in the thickness direction that obeys a power-law distribution. By adopting the Karman nonlinear geometrical relations, the equation of motion is derived from the D’Alembert’s principle by considering the dynamic equilibrium relationships for the out-of-plane vibration of the plate. The equation of motion is discretized by using the Galerkin method and thus a series of ordinary differential equations with mode-coupling terms are obtained. These ordinary differential equations are then solved by utilizing the method of harmonic balance. The analytical results are verified by the adaptive step-size fourth-order Runge–Kutta technique. The stability analysis of analytical solutions is also carried out by introducing small perturbation for steady state solutions. Both natural frequency and nonlinear frequency-amplitude characteristics are presented. In the translational FGM plate, strong nonlinear mode interaction phenomenon has been detected. The nonlinear frequency response shows intensive hardening-spring characteristics. Moreover, various system parameters such as power-law distribution, translating speed of the plate, in-plane tension force, damping coefficient and external excitation amplitude are selected as the controlled variables to present parametric study. Their effects on the nonlinear dynamical response of the translational FGM plate are highlighted.

Stability and dynamics of axially moving unidirectional plates partially immersed in a liquid

The stability and dynamics of an axially moving unidirectional plate partially immersed in a liquid and subjected to a nonlinear aerodynamic excitation are investigated. The method of singular functions is adopted to study the dynamic characteristics of the unidirectional plates with discontinuous characteristics. Nonlinearities due to large-amplitude plate motions are considered by using the classical nonlinear thin plate theory, with allowance for the effect of viscous structural damping. The velocity potential and Bernoullis equation are used to describe the fluid pressure acting on the unidirectional plate. The effect of fluid on the vibrations of the plate may be equivalent to added mass of the plate. The formulation of added mass is obtained from kinematic boundary conditions of the plate–fluid interfaces. The system is discretized by Galerkins method while a model involving two degrees of freedom, is adopted. Attention is focused on the behavior of the system in the region of dynamic instability, and several motions are found by numerical simulations. The effects of the moving speed and some other parameters on the dynamics of the system are also investigated. It is shown that chaotic motions can occur in this system in several certain regions of parameter space.

Real-Time Vibration Control of Steel Strip Immersed in Fluid for a Continuous Hot-Dip Galvanizing Line

A method of combining theoretical analysis with numerical simulation is presented to achieve real-time vibration control of steel strip immersed in fluid during continuous hot-dip galvanizing process. Theoretical and numerical methods are employed to investigate inherent properties of strip and immersed strip, respectively. Multivariate quadratic regression is adopted to fit the ratio of natural frequencies. Keeping inherent frequencies far from excitations is taken as optimization objective, based upon field testing results. Real-time vibration control of immersed strip near the air knife box is carried out by varying production parameters. The results reveal that width, thickness, tension and molten zinc have noticeable and highly nonlinear effect on inherent properties of steel strip. Axial speed of strip is negligible in calculations of natural frequencies. Wind load of air knife moving relative to strip is the principal source of vibration. The approach of combining theory with numerical computation can meet the requirement of real-time vibration control of alloy strip.