The Propagation Characteristics Of Nonlinear Waves In Functional Graded Beams

Beams are one of the most common structure s in engineering.Many structural parts can be regarded as beams or rods in civil or mechanical engineering. Due to the unique mechanical performance characteristics of FGMs, Functionally graded materials have been widely used in a variety of engineering fields. In this paper, the propagation characteristics of nonlinear waves in the functionally graded material are researched and the theoretical basis for the engineering application is provided.There are five chapters in this paper. In chapter one, the background of the subject, research background and the trend of research development are discussed. The basic theory and research methods of nonlinear wave propagation are presented in chapter two. The chapter three is the core of the paper, in which propagation characteristics of the nonlinear wave is studied in FGM beams.On the basis of chapter three, the thermal elastic wave is studied in chapter four. I n this paper, the some novel results and conclusions are drawn, the main research contents and achievements are as follows:(1)The material properties of FGM beams are presumed to vary continuously through the thickness of the beams, the neutral plane site of the functionally graded material beams was determined, the location of neutral axis is related to the modulus of elasticity of two kinds of materials and functionally gradient index parameter, the results of example show that modulus of elasticity of two kinds of materials and functionally gradient index parameter exert great influence on the the neutral plane site of FGM beams. All this provide the necessary preditions for the research of using unlayered beam theory.(2) The nonlinear wave equations of the FGM beams was established by Hamilton's principle and Euler equation, based on the specific characteristics of the wave equation, periodic solutions and Jacobi elliptic function expansion method, the influence of the material parameters on the dispersion relation and propagation characteristics of the nonlinear wave is investigated. it can be found that wave amplitude and wave width of the nonlinear wave in the large deflection of the FGM beams is related to the gradient index N changes by numerical analysis. The theoretical and numerical analysis show that the nonlinear factors have little effect on the image of the curve of spectrum, but exert a significantly influence on the dispersion relation expression.(3) On the basis of the thermo elastic theory, nonlinear thermal elastic wave in FGM beams was established by Hamilton's principle and Euler equation, and the effect of stable temperature on the width and the amplitude of nonlinear thermal elastic wave is explored.Obtained conclusions are useful for research on FGMs, moreover; all these provide theoretical guidance for non-invasive detection.