Nonlinear Dynamics And Resonance Behavior Analysis Of Functionally Graded Cylindrical Shells

Functionally Graded Material(FGM)is usually a new non-homogeneous composite two different materials(made bythe metal andceramic), a research on the nonlinear issue of initial geometrical imperfection clamped-clamped FGMcircular cylindrical shell is presented in this paper.Functionally Graded Material has a good advantage at the extreme temperature environment(high temperature,big temperature difference) under repeated work and could relieve the thermal stress.In aerospace,military and other fields, the cylindrical shell structure with a large number of applications, and the structures have initial geometric imperfections inevitably.The structures is also usually affected by the thermal loads and mechanical loads which is likely to cause serious damage.Therefore, the study of FGM cylindrical shell nonlinear issue also caused the extensive concern of many scholars.Considering the influence of thermal stress,damping and mechanical loads andthe symmetric mode ofcircular cylindrical shellbased on Classical plate and shell theory,von-Karman type nonlinear strain-displacement relationship and Hamilton’s variationalprinciple,the governing differential equations of FGM cylindrical shells are obtainedin this paper. The governing differential equations are discretized by using Galerkin’s method and ordinary differential equations are obtained. In this paper,consider the boundry conditions clamed-clamed, a research on the nonlinear dynamicsof initial geometrical imperfection FGMcircular cylindrical shell is presented,the main research contents have the following points:(1)In this paper,based on Classical plate and shell theory,von-Karman type nonlinear strain-displacement relationship and Hamilton’s variationalprinciple,the governing differential equations of FGM cylindrical shells are obtainedin this paper.(2)The influences of the thermal stress, damping and mechanical loads are studied, when the vibration response of functionally graded cylindrical shells subjected toplane loads.And compared the different volume fractions, temperature fields,thickness-radius ratios and length-radius ratios of the system’s nonlinear vibration response.(3)Within the transverse loads and plane loads, ordinary differential equationare obtained by using multi-scale perturbation analysis method under the case of 1:2 internal resonance of polar coordinates averaged equations.Functionally graded cylindrical shellsof the amplitude frequency response analysis were studied in different volume fractions, temperatures, dampings, transverse loads and plane loads, and also analyzed the characteristics of system response amplitude withtransverse loads and plane loads in the bifurcation phenomenon.(4)Under the transverse loads, by comparing thenonlinear response of different initial geometric imperfectionsform and different volume fractions of functionally graded cylindrical shell, studied the linear frequency with imperfections and without imperfections under the different volume fractions, thickness-radius ratios and length-radius ratios. Using the method of Runge-Kutta, have analyzed thedynamic responseaccording to different types of imperfections and different volume fractions.