Analysis Of Nonlinear Stability And Vibration For Composite Laminated Shallow Spherical Shells In Hydrothermal Environment

This paper studied the nonlinear static stability, nonlinear free vibration and nonlinear forced vibration under harmonic excitation of composite laminated shallow spherical shells in hydrothermal environment.In Chapter I, a detailed investigation on nonlinear stability and vibrations of plates and shells in hydrothermal environment is summarized. The history and development in this field are introduced as well. Finally, the content and investigating methods in this thesis are introduced.In Chapter II, nonlinear static stability of symmetrically laminated composite shallow spherical shells in hydrothermal environment is investigated. Based on the first-order shearing deformation theory, considering hydrothermal effect, the nonlinear governing equations of laminated composite shallow spherical shells under uniform static load are built. Then the equations are solved by modified iteration method to achieve the loads-displacement relation. The extremum buckling principle is employed to determine the critical buckling load. The influences of boundary conditions, geometric parameters, temperature and humidity on static buckling are discussed as well.In Chapter III, nonlinear free vibration and nonlinear forced vibration under harmonic excitation of composite laminated shallow spherical shells in hydrothermal environment are investigated. The nonlinear dynamic governing equations of symmetrically laminated composite shallow spherical shells in hydrothermal environment are built. Using Galerkin method, the nonlinear dynamic governing equations are solved, and the response equation of composite laminated shallow spherical shells in hydrothermal environment is obtained. For the free vibration, the modified Lindstedt-Poincare method is used to obtain the ratio expression of nonlinear vibration frequency to natural frequency and the amplitude-frequency response curve as well. Then, the influences of boundary conditions, geometric parameters, temperature and humidity on static buckling are discussed. For the forced vibration, a harmonic excitation is adopted. The ratio expression of excitation frequency to natural frequency is achieved by harmonic balance method. And the amplitude-frequency curve is plotted. Then, the influences of boundary conditions, geometric parameters, temperature and humidity on static buckling are discussed.In Chapter IV, the whole paper is summarized and some useful conclusions are obtained. Finally, farther investigations about this problem are prospected.