Study On Vibration Characteristics Of Moving Plates And Shells And Its Applications In Surface Quality Control

Moving plates and shells are widely used in various fields of engineering. The most common types of moving systems are axially moving plates, rotating cylindrical shells and axially moving cylindrical shells. Experts pay more attention to their different characteristics during vibrations in the state of motion. For a long time, vibrations of axially moving plates have been studied by using models of axially moving strings or beams. This kind of simplification will result in error in case of dynamic research on medium width plates. In recent ten years focus on the model of plate begins to warm up, but the researches are limited to analysis in theory and ignore its strong engineering background. Investigations on axially moving cylindrical shells are seldom reported because the problem is difficult to solve due to the adoption of multi-component material and taking large deformation into account. A discussion of the issues involved has great theoretical as well as practical significance. Although studies on vibrations of rotating cylindrical shells are implemented for a long time, investigations on inherent properties attract major attention. It is necessary to carry out research on forced vibration generally excited by a normal action.Aiming at the problems that exist in the study of moving plates and shells, axially moving thin plates, rotating thin cylindrical shells and axially moving composite cylindrical shells are selected to investigate vibration characteristics of moving plates and shells closely based on engineering applications. Theoretical method, numerical method and experimental study are employed during the research process. In addition, some research achievements are applied to on-line control of strip surface quality in a continuous hot-dip galvanizing line. The main content and innovations of the dissertation can be briefly described as follows:(1) Investigations on transverse vibration of an axially moving thin plate are implemented considering the combined effect of usual factors in engineering. Governing equations of an axially moving thin plate are derived through the Hamilton’s principle, taking account of axial speed, tension, damping, vibration of supports and nonlinear loads. Influence of main controlled parameters on inherent properties and displacement response of the thin plate is analyzed. The results are agreement with field experience of the continuous hot-dip galvanizing process, namely that speed improvement and tension reduction will make it more difficult for steel strip to decrease amplitude near air knives. Furthermore, an approach for calculating natural properties of assembling cantilever plates is developed.(2) Research on method of real-time vibration control for steel strip partially immersed in fluid is carried out and an overall solution for on-line control of surface quality in a continuous hot-dip galvanizing line is presented. Vibration models for different types of strips in cooling section are established. The validity of assumptive supports in the vibration models is confirmed by finite element method. Analysis of field test results is used to find main vibration sources of steel strip. Finite element simulation is employed to implement parametric study on inherent property and displacement response of the strip partially immersed in a molten Zn pot. A method of combining theoretical analysis with finite element simulation is provided to decrease amplitude of steel strip near air knives. At the same time, multivariate quadratic regression and varying production parameters are introduced into this method. In addition, this method has the advantage of speediness, small error and easiness of programming. An off-line vibration forecasting system is developed based on this method and an overall solution for on-line control of surface quality is proposed.(3) Study on nonlinear vibration characteristics of axially moving, multi-Layered cylindrical shells made from composites is developed. A method of combining tests with theory analysis is presented to investigate dynamic elastic moduli of composite thin cylindrical shells. The Lorentzian function between frequency of exciting force and dynamic elastic modulus is obtained. Based on the analysis above, Runge-Kutta and multiscale methods are employed to study nonlinear vibration characteristics of axially moving, multi-Layered cylindrical shells made from composites. Conclusions with different methods coincide and the phenomenon of internal resonance is observed. Research on vibration characteristics with different parameters is implemented and stability of the system is further discussed. The results reveal that nonlinear vibration characteristics of composite cylindrical shells with laminated material appear to be softening. (4) Analysis on wavy vibration of a rotating thin cylindrical shell taking account of geometric nonlinearities under the action of a normal exciting force is provided. Complex analysis is made to study linearly wavy vibration of a rotating thin cylindrical shell under the action of a normal exciting force. A mathematical expression of travel ing-wave resonance frequencies is obtained. Asymptotic approach is introduced to investigate the effect of geometric nonlinearities on nonlinearly natural frequencies of cylindrical shell. The results reveal that nonlinearly natural frequencies appear a hardening phenomenon due to geometric nonlinearities. Multimode analysis with numerical method is implemented to analyze nonlinearly wavy vibration of a rotating thin cylindrical shell taking account of geometric nonlinearities under the action of a normal exciting force. The results indicate that the axial mode of second order is of strong effect on the main vibration mode. On this basis, averaging method with two axial modes as well as one circumferential mode is employed to study the system. The results further engage in the analysis of parametric vibration as well as stability and reveal that multivalue solutions achieved from averaging method are closer to solutions of numerical approach than that acquired from harmonic balance method.