Haar Wavelet Method And Research On Its Application In Structural Vibration Analysis

Beam, cylindrical and conical shell and annular plate structures and their combination are typical components of the submarine and ships. The vibration research on these kinds of structures has important theoretical and practical significance for the vibration-acoustic analysis and design of ships, and also has been a hot issue in the field of vabrations engineering. Therefore, it is important to study the accurate and fast numerical method for vibration analysis and theoretical research of shell structures. In the recent years, as a powerful mathematical tool, wavelet functions have been widely noted. Since wavelet functions have a set of merits, such as compact and orthogonal and so on, then its application is more and more important in numerical analysis. In this thesis, an effective method is developed based on compact Haar wavelet and mesh-free discretization, which can be applied to analyze the vibrations of structural mechanics. The main objective of this paper focuses on the vibration analysis of conical, cylindrical shells and annular plates with various boundary conditions based on the Haar wavelet discretization method. The contents of the dissertation are as follows:Firstly, the basic principle of Haar wavelet and the theory of mesh-free discretization are examined. Then a Haar wavelet discretization method is developed. The highest derivatives of the unknown variables in the equations are expressed as Haar wavelet series and their integral. The constants appearing from the integrating process are determined by boundary conditions, and thus the equations as well as boundary conditions are transformed into a set of algebratic equations. Then the method is applied to resolved differential equations. The application of one dimension and two dimensions of Haar wavelet is introduced in detail. Accuracy, stability and reliability of the current method for solving the free vibrations of beams and plates are validated by comparing the present results with those in the literature and very good agreement is observed.Then it presents a novel and efficient solution for free vibrations of thin cylindrical shells subjected to various boundary conditions based on the classical thin theory by using the Haar wavelet discretization method. The displacement fields are expressed as producteds of Fiourier series for circumferential direction and Haar wavelet series and their integral along the meridional direction. By adding the boundary conditions, the algebraic equations are obtained and then natural frequencies of shells are solved. The detailed parameters analysis is carried out to study the effect of boundary condition and geometrical parameters on the free vibration analysis of cylindrical shells.Then the following section mainly focuses on the free vibration analysis of composite laminated and FGM conical, cylindrical shells and annular plates with various boundary conditions based on the first order shear deformation theory, using the Haar wavelet discretization method. Effects of some geometrical and material parameters on the natural frequencies of composite shells are discussed. Some new results for shells are presented,which may serve as benchmark solutions. The natural frequencies of conical, cylindrical shells and annular plates are easily obtained by one Matlab program using the developed method.