Study On Nonlinear Vibration Of Special Moving Components For Cylindrical Panels And Plates Partially Immersed In Fluid

Cylindrical panels and plates partially immersed in fluid are widely used in various fields of engineering. For example, aero engine blades and continuous hot-dip galvanizing steel plates in steel industry. Experts pay more and more attentions to their different vibration characteristics under working state. For a long time, vibrations of blades have been studied by simplifying them as models of beams or plates. This simplification will lead to error in terms of dynamic research on moderate or low aspect ratio blades. In recent ten years study on the model of cylindrical panels begins to warm up. Under the state of working, blades are easy to resonate and arose to fatigue damage. The shrouded dry friction damper can effectively suppresses vibration of blades and increases high cycle fatigue life. However, due to the complex model of cylindrical panels, and the complexity of contact characteristics and movement behavior for dry friction damper, together with the geometric nonlinearity accompanied with the vibration of blades, it would be hard to study the dynamic characteristics of shrouded blade of cylindrical panel. For this reason, most of studies focus on its inherent characteristic, while the study of forced vibration, frequently appeared in engineering, draws few attentions. The model of axially moving plates partially immersed in fluid comes from line of hot galvanized zinc in steel industry. Because of vibration of steel plate in continually hot galvanized zinc line, quality problems, like vibration ripple and failure to reach standard galvanized depth, appear in the steel industry. So it would be of great theoretical and engineering importance to make relative study in this area.Through aero engine blade and continually hot zinc-galvanized steel plate, application instances of which in engineering, and by simplifying the models of them as shrouded blade of rotating cylindrical panel and axially moving plates partially immersed in fluid while considering their application background, this paper studies theoretical and numerical analysis of nonlinear dynamic characteristic for especial moving components(cylindrical panels and plates partially immersed in fluid). By studying the nonlinear dynamic analysis of two typical examples, this paper aims to provide an effective method to study this kind of components. Main tasks and results of this paper are as following:(1) Study vibration characteristic of shrouded blade of rotating cylindrical panel. A new analytic approach for calculating natural properties and nonlinear vibration response for shrouded blade of cylindrical panel is developed.A numerical example is solved to verity the accuracy of the proposed methed.Adopting thin-walled cylindrical panel to simulate the structure of blade, and simplify the shroud as spring system, the nonlinear vibration equations are obtained by using Donnell’s nonlinear shallow-shell theory, the process of which also consider interaction force between shrouds, geometric nonlinearity, damping, installation angle and periodic stimulation. Considering complex boundary conditions of cantilever cylindrical panel, one-way analytic function is introduced to variation equation to reduce it into ordinary equation in another way and so to solve its inherent characteristic. Then, Runge-Kutta method and multiple scale method are also introduced to study the characteristic of nonlinear vibration for shrouded blade of rotating cylindrical panel. Conclusions drawn by these two methods are the same. Parameter vibration analysis is also made. Studying results show that shrouded dry friction damper structure leads to incontinuity of system vibration, and the vibration energy of the blade system fails to accumulate continually, thus effectively reduce the vibration amplitude.(2) Study stability and dynamic bifurcation phenomenon of shrouded blade of rotating cylindrical panel. The changing process of periodic solution and nonlinear dynamic characteristics for shrouded blade of cylindrical panel are analysed,while system parameter changes in the whole parametric space. Using Lyapunov first approximate theory to analyze system stability, and multiple scale method to obtain average equation and bifurcation equation. Through studying global behavior of average equation in different parameter sets in the whole parametric space, the connection and conversionof moving states for shrouded blade of cylindrical panel are showed Analytic results show that, while system parameter locates in specific area, system has the phenomenon of changing property of moving, namely bifurcation.(3) Study characteristic of nonlinear vibration of axially moving plates partially immersed in fluid.For the first time reveals that there is1:3internal resonance in plates partially immersed in fluid,and discusses the mechanism that1:3internal resonance produces. Using the liquid-solid interface coupling conditions of that the speed of liquid keeps the same with the normal speed of thin plate, the action of liquid on thin plate is regarded as equivalent to added mass, furtherly, plates partially immersed in fluid are simplified as step plate with equal rigidity and different damp and density. Based on Von K arman thin plate large deflection equation, nonlinear bending equation of thin plate is established, which consider geometric nonlinearity, axial tension, axial moving speed, fluid-solid interaction, damp and external stimulation etc. It was found that, under the action of actual load, zinc-galvanized plate only has bending vibration, not torsional vibration, thus only the bending vibration of axial moving plates partially immersed in fluid was studied. And also, strangeness theory is introduced to study the inherent characteristic of system. With this basis, two neighbour modalities are chosen to study, separately under Runge-Kutta method and multiple scale method, results of these two methods mate well. The influences of different factors on internal resonate system are also carried out, and the creating mechanism of1:3internal resonate system is also investigated. Results show that1:3internal resonate system has complex and variable nonlinear vibration characteristics.(4) Study stability and dynamic bifurcation phenomenon of1:3internal resonate system. Firstly describes the complex bifurcation curves of axially moving plates partially immersed in fluid which contain1:3internal resonance. Near the first order modality, due to1:3internal resonance, two order modalities coupled each other, and the analytic expression of boundary curve in parameter plane can be drawn. Through numerical method, this paper firstly displays the complex bifurcation phenomenon of system which contains1:3internal resonance. Compared with bifurcation curve of the system in the second modality, this paper shows modal coupling characteristics of1:3internal resonance system and its complex dynamics behavior.