Analysis Of Nonlinear Free Vibration And Thermal Buckling Behavior Of Porous Functionally Gradient Material Timoshenko Beam

Most of the analyses on the mechanical behavior of structures with different functional gradient materials(FGM),such as beams,plates and shells,have been performed based on idealized material models.However,in the actual production process of FGM,the accuracy of the preparation method and process has not yet reached the extent that the generation of tiny pores inside the material can be completely avoided,and the pores have a great influence on the shear strength,bending strength,tensile strength and compressive strength of the FGM structure,so it is important to analyze and study the mechanical behavior of the porous functional gradient material(PFGM)structure under different working conditions.In this paper,a Timoshenko beam model based on two porosity distributions of the materials is used to analyze the nonlinear free vibration of PFGM beams and the buckling behaviors of different thermal loads under different parameters and boundary conditions,respectively.Chapter 1 firstly introduces the background and current status of FGM research,from which the research results in PFGM are described.Then the functional model of the PFGM beam space distribution adopted in this paper is introduced,followed by the development of the differential transformation method(DTM)and differential quadrature method(DQM)used in this paper for solving the relevant set of control equations and their corresponding concepts.Chapter 2 investigates the thermal buckling and over-buckling behavior of PFGM beams caused by different thermal loads.The governing differential equations for thermal buckling is established based on the Timoshenko beam theory and the corresponding intrinsic structure relations,and the boundary conditions are determined based on the internal force composition of the structure,after that,the equations and boundary conditions are dimensionless and DQM discretized,the nonlinear terms in the equations are linearized according to the buckling modes of the corresponding boundary conditions,and the equations is organized into matrix operations from which the temperature difference values of thermal buckling and post-buckling of the PFGM beam are derived,the total number of nodes in the discretization process is adjusted to ensure the convergence of the resulting results.By degrading the PFGM beam to a porosity-free FGM beam by making the porosity zero and comparing it with the data from related literature,the design content and algorithm of this chapter are verified to be reasonable.Then,the effects of different porosity parameter,aspect ratio and gradient index on thermal buckling and post-buckling temperature difference,as well as the difference of temperature difference values between different thermal loads and boundary conditions are analyzed.In chapter 3,based on the mathematical model in the previous chapter,the effect of free vibration of the system is added,and the governing differential equations for nonlinear free vibration of PFGM beam is established without considering the effect of temperature on the structure,and the linearization of the set of equations is completed by neglecting the terms caused by some of the fine displacements in the equations and establishing the relationship between the nonlinearity in the equations and the axial stretching force generated by large amplitude,and the DTM transformation of the processed set of equations and boundary conditions is performed and solved,and the convergence of the calculation results is ensured by adjusting the number of iterations of the algorithm.By degenerating the PFGM beam into a porosity-free FGM beam by making the porosity zero and comparing it with the data from the related literature,the design content and the reasonableness of the algorithm in this chapter are verified.After that,the effects of gradient index,porosity and length to slenderness ratio on the frequency ratio of dimensionless nonlinear free vibration and the difference of frequency ratio between different boundary conditions are analyzed.Finally,the research results are summarized,and new ideas and improvements are proposed for the next research content.