| Most of the mechanical properties of functionally gradient materials(FGM)are studied based on the idealized model,and the pores caused by the defects of the preparation process and method are often ignored.The existence of pores causes a large error between the theoretical value and the practical application,so it is particularly important to study the influence of pores on the properties of FGM.In this paper,the governing differential equations of the free vibration and buckling of a rectangular plate of porous FGM and a rectangular plate of porous FGM under four edges compression on elastic foundation are derived by using two kinds of pore theory systems,the characteristic equations expressed by the dimensionless natural frequency and the dimensionless buckling load are obtained through the transformation of dimensionless and DTM,the dimensionless natural frequency and the dimensionless critical buckling load are obtained by changing the parameters.In the first chapter,the development background and current situation of FGM are described,and the research status of porous FGM is emphatically discussed.Firstly,the function description of spatial distribution of FGM is introduced.Secondly,the influence of porosity on elastic modulus,density and Poisson's ratio of materials is listed.Finally,the development,application and concept of differential transformation method are expounded.In chapter two,the free vibration and critical buckling load of porous FGM plates are studied.The properties of FGM are closely related to the porosity,which affects the elastic modulus,Poisson's ratio and density of FGM.Based on classical thin plate theory,the use of Hamilton principle quadrilateral rectangular plate pressure porous FGM is established the mathematical model of free vibration and buckling,the dimensionless,using DTM to transform,through iteration,get porous dimensionless natural frequency of rectangular plates with FGM and the dimensionless critical buckling load.The problem is reduced to the free vibration of FGM rectangular plate with zero porosity and compared with its exact solution.It is found that the calculation accuracy of the differential transformation method is higher,and the effectiveness of the method in solving the free vibration and buckling problems of FGM rectangular plate under four sides compression is verified.The results show that the porous FGM of rectangular plate elastic modulus decreases with increasing of gradient index and porosity,and further analyzes the six kinds of boundary conditions,the length-width ratio at constant gradient index,the porosity of the dimensionless natural frequencies and the influence of the critical buckling load,and the aspect ratio under different boundary conditions,the influence of the load on the dimensionless natural frequencies.In chapter three,based on the classical thin plate theory and considering the modified mixing rate model with different pore distribution,the free vibration and critical buckling load characteristics of a rectangular plate of porous FGM with four sides under compression on Winkler elastic foundation are studied.First use the definition in the physical,by Hamilton variational principle is derived on the Winkler elastic foundation quadrilateral rectangular plate pressure porous FGM the governing differential equations of free vibration and dimensionless,then using DTM to transform,calculating the dimensionless natural frequencies and the algebraic characteristic equation of critical buckling load.The problem was reduced to a FGM plate with zero porosity and compared with the existing literature to verify its effectiveness.Finally,the effects of gradient index,porosity,foundation stiffness coefficient,boundary condition,aspect ratio and four side compression load on dimensionless natural frequency of rectangular plates with porous FGM and the effects of each parameter on dimensionless critical buckling load are calculated and analyzed.Finally,a summary of the research results is made,and a new idea for the next research direction is proposed. |
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