The Inverse Of Material Properties Of Functionally Graded Materials Based On The Ultrasonic Guided Waves And Fuzzy Algorithm

Recent advances in materials processing and engineering have led to a new class of materials called functionally graded materials(FGMs).It is a new type of composite material with continuous changes in performance and function which can be obtained by the combination of two or more than two materials.FGMs have broad application prospects in many fields,such as high-temperature-resistant materials in nuclear,chemical plants,ship,computer circuit board,military,biology and medicine,etc.Different varieties of FGM volume fraction result in different material properties of FGM.So,It is an urgent problem to detect whether the characteristic of FGM is consistent with the design and whether it is degraded in use.In the manufacturing process of functionally graded materials,the initial stress will occur inevitably,which has a great influence on the wave characteristics.In this paper,we first study the guided waves and vibrations in functionally graded materials.Firstly,in the context of “Mechanics of Incremental Deformations”,the guided wave propagation in FGM plates under gravity,homogeneous initial stress in the thickness direction and inhomogeneous initial stress in the wave propagation direction is investigated;based on the “Biot incremental deformation” theory,the guided wave propagation characteristics(finite width and height)of functionally graded rod with rectangular cross-section under initial stress are studied;based on the Legendre polynomial method,the vibration modal frequencies of FGM disk structure are calculated.The studying on the characteristics of guided wave of FGM structure can give theoretical guidance for inversion of material properties using guided wave group velocity and the frequency of mode of vibration.Secondly,the guided wave group velocity and the frequency of the vibration mode of the FGM disk are obtained by using the Legendre polynomial series method and Mathematica numerical program,respectively.Then,based on the nonlinear mapping relation between the guided wave group velocity and the frequency of vibration mode and the volume content of material,the inverse model of material properties of FGM structure is established.Finally,based on the characteristics of the guided wave dispersion and multi-mode,an inverse method by combining genetic algorithm and fuzzy algorithm is presented to determine the material properties of FGM.Through numerical examples,the applicability and reliability of this method is proved.