Nonlinear Vibration Of Functionally Graded Material Structures

This paper discusses the problems of bending,post-buckling and large amplitude vibration of functionally graded circular plate and beams under uniform thermal load.Firstly,by using the concept of the physical neutral surface concept under the classic plate / beam theory,the nonlinear motion equations of fun ctionally graded circular plates and beams are derived.Secondly,the Ritz-Kantorovich method is used to eliminate time variables,and the nonlinear equations of motion are converted into a set of nonlinear ordinary differential equations about spatial var iables.Finally,the shooting method is used to numerically solve the resulting equations.The main content of this article includes the following aspects:1.This paper briefly introduces the basic principle of functional gradient,its definition,development,and its research status in vibration.At the same time,the numerical solution used in this paper(the shooting method)is simply introduced.2.Static mechanical behavior of FGM circular plates.The numerical results show that under thermal load,the clamped FGM circular plate undergoes buckling deformation;while the simply supported FGM circular plate undergoes more complicated thermal bending deformation.As the gradient index increases,the rigidity of the circular plate increases.3.Dynamic mechanical behavior of FGM circular plates.The paper specifically analyzes the effects of boundary conditions,amplitude,gradient index,and thermal load on the nonlinear vibration of the functionally graded plate structure.Studies have shown that the vibration response of the clamped and simply supported FGM circular plates,and the linear and nonlinear vibration behaviors are all made significantly different by the existence of thermal deformation.The hardening of the thermal over-buckling deformation plate is limited,and excessive thermal over-buckling deformation will also reduce the rigidity of the FGM circular plate.Therefore,the influence of thermal deformation on the vibration response of FGM circular plates is complicated.4.Static mechanical behavior of FGM beams.The numerical results show that under uniform thermal load,the changing law of clamp beam and simply supported beam is similar to that of circular plate.The only difference is that there are multiple values for simply supported beams.5.Dynamic mechanical behavior of FGM beams.The same kinds of factors as the functional gradient board are considered.The results show that the effect of amplitude on the natural frequencies of simply supported and clamped FGM beams is significantly different from that of circular plates.It doesn't increase blindly It is known from the data that FGM beams with thermal over-buckling have more significant hardening behavior.