Hydroelastic dynamic analysis of axially moving plates in continuous hot-dip galvanizing process

For the purpose of understanding the vibrational characteristics of moving plates in continuous hot-dip galvanizing process, the linear and nonlinear free vibrations of an axially moving rectangular plate coupled with dense fluid having a free surface are investigated. The fluid is assumed to be incompressible, inviscid and irrotational in this study. Effect of free surface waves of the fluid is taken into account in the analysis. The classical thin plate theory is adopted to formulate the equation of motion of the 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 added mass of the plate. The system is solved by applying directly the method of multiple scales to the governing partial-differential equations and boundary conditions. Results show the immersion depth, moving speed, fluid-plate density ratio, stiffness ratio and aspect ratio all have significant effects on the natural frequencies of the immersed moving plate. The nonlinear frequencies of the plate-fluid system are influenced by initial amplitude, moving speed and nonlinear coefficient. It is also shown that the 1:1 and 1:3 internal resonances of the immersed moving plate can occur at certain speeds. Owing to the internal resonance, amplitude ratio of the two internal resonance modes shows multi-value characteristics. With the increase of nonlinear coefficient, the internal resonance phenomenon becomes more and more intense.