Study Of The Dynamic Stability And Intelligent Control Based On Wavelets Analysis

The research of dynamic stability involve some subjects,and it is a new research developed recent decades.It is very complex of its unstablity mechanization because of it is a nonlinear differential equation,so it has not achive a common view.Wavelets analysis can solve many difficult problems that Fourier analysis can not solve, which has become a new bench developing rapidly in mathematical field.It is an innovation of the tools and methods for research recently, and becomes the focus of many subjects. The numerical method based on quasi wavelets is a new numerical method that has not only the high accuracy of global methods but also the flexibility of local methods.So it is very good for the numerical solution of nonlinear partial equations. The numerical method based on quasi wavelets is a new means of study the numerical solution of the dynamic stability differential equations.In the thesis,author have done some research about the facets discussed above.(1) A comprehensive introduction to the theory of dynamic stability is given. The concept of parametric resonance and Floquet's theory is introduced.The spectral analyses of the areas of Mathieu-Hill equations are made. All the process is realized by programming in Matlab.(2) The differentiate criterion of dynamic stability in china and abroad are mainly detailed. Author deduce a 'double parameter' criterion by the condense of two tips and the maximum deflection, then the criterion is suitable to dynamic stability.The deflection of pole suffer parametric resonance can be given through method based on quasi wavelets,and it is suitable for use.(3) The definition and classification of the theory of intelligent structures are provide and the brief but overall introduction to its research approach is given and its research history is reviewed, types and characteristics of intelligent material elements have been introduced too. And the basic equations of piezoelectric material have been given.Then according to process of Matlab,it is compared between the unstability area of the general pile and the intelligent structure suffer parametric resonance.(4) Then spread the methods to frame structure, the application of finite element method(FEM) is described emphatically.The Lagrangian equations is used to derive the element stiffness matrix, element mass matrix and element geometric stiffness matrix. Then according to Hamilton principle, both the dynamic finite element equations for the intelligent structure are formulated with isoparametric element of bending plate or bending beam.It is also shown that system equations for static structural mechanics and static buckling are only a special case of the system equations of dynamic instability. Lastly, test has been done to checking the control property of the intelligent structures and the process of reduction.