The Analysis Of Dynamic Characteristics Of FGM Beam And Plate Resting On Elastic Foundation

Functionally graded material will be different two or more properties of the material according tocertain rules designed to combine by particular method, both sides of the structure by varying thematerial composition to meet different application requirements. Functionally graded material is anew type of non-uniform composite material, with its position in the space of continuous changes inthe volume content of components, which makes the nature of the structure of the location in spaceare also continuous changes, thereby eliminating the material properties of the mutation, you canbetter avoid or reduce the phenomenon of stress concentration.FGM can give full play to high temperature ceramic, and metal corrosion-resistant high strength,good toughness characteristics, but also a very good solution to match the force of metal and ceramicbond strength caused by low heat expansion coefficient of non-conforming issues. Functionallygraded materials in high temperature environment and mechanical loading show good performance,are consider for future spacecraft, the mechanical industry and nuclear industry in areas such as apotential materials. Therefore, the problem of the mechanical behavior of functionally gradedstructure have been extensively investigated and become one of the most important key issues inmechanics.First, functionally graded materials free vibration problem. Based on classical beam theory,first-order shear-deformation theory derived from FGM beam dynamics equations. Then, usingdifferential quadrature method to study the theory in the two homogeneous material under the beamand FGM beam free vibration problem, the use of numerical results from the study of the materialgradient nature of factors such as slenderness ratio on the impact of beam vibration, and compared thecorresponding results under a variety of theoretical differences.The transverse vibration problems of functionally graded plate are investigated in this paper. Thedynamic equations for thin and thick plates are formulated based on the theories of thin plates andfirst-order shear deformation. The numerical solutions of vibration of plates under multiple boundaryconditions are calculated by DQM through transforming fourth-order ordinary differential equationswhich are two-point boundary problems with unknown quantities of deflections into linear algebraicequations with deflections at some discrete points unknown. The effects of boundary conditions andlength-width ratios on vibration characteristics are also researched. Finally, the dynamic equations offunctionally graded plates are derived through classical theory of thin plates, and the effects ofgradation parameters on properties of plates are discussed. Considering two models of Winkler and Pasternak foundations, the effects of foundationparameters on the vibration characteristics of functionally graded beams and plates on elasticfoundations are discussed in detail. Furthermore, the influences of gradation parameters and boundaryconditions on intrinsic frequencies are also investigated. It shows that: increasing foundationparameters will raise intrinsic frequencies of functionally graded beams on elastic foundations;increasing gradation parameters will reduce natural frequencies of structures; especially between zeroand five of p values, natural frequencies will decrease at the sharpest rate.