Analysis Of Nonlinear Vibration And Static And Dynamic Stability Of FGM Shallow Conical Shells

The problem of nonlinear static stability under thermo-mechanical field,nonlinear free vibration,nonlinear forced vibration under harmonic excitation and dynamic buckling under impact loads,of symmetrically FGM shallow conical shells are investigated.In Chapterâ… ,a detailed investigation on functionally gradient materials is summarized. The history and development in this field are introduced.And the definition,application and mechanical research status and progress of the FGM are summarized.Finally,the content and investigating methods in this dissertation are introduced.In Chapterâ…¡,the problem of nonlinear static stability of symmetrically FGM shallow conical shells when temperature field and stress field are coupled is analyzed.The nonlinear governing equation of FGM shallow conical shells,the physical parameters of which varies as power-law type,is deduced under thermo-mechanical field.Tthe governing equation solved by Galerkin method to achieve the loads-displacement relation.The extremum buckling principle is employed to determine the critical buckling load.The influences of boundary conditions, gradient constants,geometric parameters and temperature difference on static buckling are discussed as well.In Chapterâ…¢,nonlinear free vibration,nonlinear forced vibration under harmonic excitation and dynamic buckling under impact loads of symmetrically FGM shallow conical shells are investigated.The nonlinear dynamic governing equation of symmetrically FGM shallow conical shells is built.Using Galerkin method,the nonlinear dynamic governing equation is solved,and the nonlinear dynamic response equation of symmetrically FGM shallow conical shells 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, gradient constants and geometric parameters on nonlinear vibration are discussed.For the forced vibration,the harmonic excitation is adopted to achieve the ratio expression of the excitation frequency to natural frequency and amplitude-frequency curve as well.Then,the influences of boundary conditions,gradient constants,geometric parameters and excitation on nonlinear vibration are discussed.For the nonlinear impact buckling,the Runge-Kutta method is introduced to numerically solve the nonlinear dynamic response equation and the impact response curve is achieved.Budiansky-Roth motion criterion expressed by the displacement of the peak of the shell is employed to determine the critical impact buckling load.The influences of boundary conditions,geometric parameters and gradient constants on impact buckling are discussed as well.In Chapterâ…£,the whole paper is summarized and some useful conclusions are obtained. Then,farther investigations about this problem are prospected.