The Analysis Of The Inherent Vibro-acoustic Characteristics Of Typical Noncircular Cross Section Column Shells

The work of the thesis is a part of the research project supported by the National Natural Sciencen Foundation of China and the Research Fund for the Doctoral Program of Higher Education. The aim of the paper is to research the vibro-acoustic characterisitics of the two kinds of typical noncircular cylindrical shells:elliptical cylindrical shell and eccentric cylindrical shell which are caused by manufacturing error or exsist in the practical engineering. Based on wave propagation method, according to the geometric characterisitics and the condition of coupling with the with the surrounding medium, double Fourier series expansion method and transfer matrix method are applied in the systematical research on the vibra-acoustics characterisitics of elliptical cylindrical shell and eccentric cylindrical shell in vacuum, filled with fluid and immersed in fluid. The influence of ellipticity, eccentricity and hydrostatic pressure on the natural frequencies of the structure is emphatically discussed. The details of the low-noise construction technology of these noncircular cylindrical shells are discussed, which has certain guiding significance for theory research and engineering application.The reserches which are related to the work are introduced briefly. First, the outlines of the studies about the vibro-acoustic characterisitics of cylindrical shell in vacuum, the vibro-acoustic characterisitics of cylindrical shell-fluid coupled system and the stability of cylindrical shell are given. Then, the reviews of the studies of the vibro-acoustic characterisitics of noncircular cylindrical shell in vacuum and coupled with fuid, and the stability of noncircular cylindrical shell are presented.In part two of the thesis, the free vibration of elliptical cylindrical shell is studied based on wave propagation method and the mode superposition method, the components of displacements are expressed in a double Fourier series. According to the expression of the radius of curvature of the cross section, through mathematical operation, the partial differential equations with variable coefficients are converted into a finite set of linear algebraic equations, which are truncated to uncouple the circumferential modes. The natural frequencies of elliptical cylindrical shell with different parameters are then obtained. The main parameters which influence the natural frequency of the structure are analyzed and the relationships between these parameters and the natural frequency are obtained.The free vibration of eccentric cylindrical shell is then studied. Starting with the geometry characteristic of the cross section of eccentric cylindrical shell, the eccentric problem is converted into a circumferentially varying thickness problem. In view of the disadvantage of the Fourier series expansion method, the vibration equations are written in a matrix differential equation by using the transfer matrix method. Besides, the precise integration method is introduced to ensure the calculation accuracy of the natural frequencies. The main parameters which influence the natural frequency of the structure are analyzed.The column shell structure is widely used in all kinds of liquid storage container and underwater structure. Due to the presence of the fluid, the vibration of the structure will couple with the sound field in fluid to form an acoustic-structure coupled vibration. The fourth part of the thesis, the characteristics of the acoustic-structure coupled vibration of elliptical cylindrical shell filled with fluid and immersed in fluid are investigated. The vibration equations of the coupled system are established by using the transfer matrix of the state vector of the shell. The wave equation of acoustic medium is described by using the Helmholtz equation in elliptic cylindrical coordinates. By solving the Helmholtz equation in the elliptic cylindrical coordinates, the analytical expression of acoustic pressure in elliptic cylindrical coordinates is discussed. The influences of the acoustic pressure and the ellipticity are discussed.The characteristics of the acoustic-structure coupled vibration of eccentric cylindrical shell filled with fluid and immersed in fluid are investigated. The free vibration equations of the coupled system are obtained by using the transfer matrix method, while the analytical expression of acoustic pressure is represented in the form of Bessel functions according to the Helmholtz equation in the cylindrical coordinates. The relationships between the natural frequency and the main parameters are probed and the influences of the acoustic pressure and the eccentricity are discussed.In practical engineering, the liquid storage containers and underwater structures will generally under the hydrostatic pressure. In the sixth and seventh part of the thesis, the characteristics of the acoustic-structure coupled vibration of fluid-filled and submerged elliptical cylindrical shell and eccentric cylindrical shell under hydrostatic pressure are studied. The vibration equations including the static prestress caused by hydrostatic pressures are obtained by applying the transfer matrix method. The influences of the main parameters (the hydrostatic pressure e.g.) are investigated. Moreover, an analytical method to predict the elastic critical pressure of submerged elliptiacal and eccentric cylindrical shell based on the relationship between the fundamental natural frequency and hydrostatic pressure is carried out, which provides a new idea and approach to nondestructively predict the critical load of the submerged elliptiacal and eccentric cylindrical shell.A systematical research on the vibra-acoutic characterisitics of elliptical and eccentric cylindrical shells under different medium conditions are presented in the thesis which can serve the theoretical basis for the low-noise construction technology of these two kinds of noncircular cylindrical shells. Besides, the method to predict the elastic critical pressure of the structure presented in the thesis can provides a new idea and approach to nondestructively predict the critical load of the submerged elliptiacal and eccentric cylindrical shell.