Analysis Of Free Vibration And Stability For Axially Functionally Graded Beams With Non-uniform Cross-section

Functionally graded materials(FGM)are widely used in aerospace industry,civil engineering and energy sources.FGM beams are widely used in these areas,but due to the wide application field and the complexity of the application environment,the mechanical properties and characteristics of the requirements are becoming more demanding.At present,the study of the natural vibration characteristics and stability of functionally graded beam structures has become the focus of attention.However,because of the continuous change of cross-section and material properties,it brings some difficulties to the research.Therefore,based on the Euler-Bernoulli beam theory,this paper presents a simple numerical method,and using infinitesimal method and energy conservation principle,then it is easy to study self-vibration and static stability of the axially functionally graded beams with variable cross section,and the dynamic stability under the elastic stress wave.First of all,this paper summarized the research background,research status,research significance and research methods of the axially functionally graded beams with variable cross section for free vibration characteristics and stability analysis are introduced.Then,based on the Euler-Bernoulli beam theory,a simple and feasible numerical methods is introduced to discuss the natural vibration characteristics of the axially functionally graded beams with variable cross section is discussed.And the natural vibration characteristics of uniform beams,and the influence of variable cross section and axial functionally gradient parameters on the vibration characteiristics of beam are discussed in detail.At the same time,the feasibility of the method is studied.Secondly,analyze problem of static stability of axially functionally graded beams,and the stability of beam with uniform cross section or axially variable stiffness is discussed in this paper.Again,by using the theory of stress wave and instantaneous energy conversion and energy conservation principle,the governing equations of dynamic buckling of functionally graded beams with variable cross-section and the additional boundary conditions for stress wave front are derived.And,before the stress wave reflection on the uniform beam,the dynamic instability characteristics of the uniform beam,variable cross-section beam and the axially material non-uniform beam are studied.Finally,the research work is summarized,and the research direction of the natural vibration characteristics and stability for axially functionally graded beams are introduced.