利用Taylor展开法研究Lamb波在功能梯度材料中的传播特性

超声技术可用于对功能梯度材料(FGMs)的性质进行评估. 由于FGMs性质的非均匀性,采用分布函数来描述FGMs弹性常数和密度沿厚度方向的变化趋势,并提出利用Taylor展开的方法来解决分布函数为任意函数时的FGMs中Lamb波的传播问题. 利用本征函数展开法得到了铁基氧化铝FGMs中Lamb波的相速度色散曲线,讨论了材料性质分布对铁基氧化铝FGMs中Lamb波传播特性的影响. 为FGMs性质(沿板厚方向变化)的反演提供了理论依据. 关键词： 功能梯度材料 Lamb波 Legendre多项式 分布函数

Analysis of Lamb waves propagation in functional gradient materials using Taylor expansion method

The technology of ultrasound can be used to evaluate properties of functionally graded materials(FGMs). Because of the inhomogeneity of the FGM properties, distribution function is used to describe the FGM elastic constant and density which are assumed to vary in the direction of the thickness. Taylor expansion method is used to solve Lamb wave propagation problems in FGMs, in which the distribution function is an arbitrary function. Phase velocity dispersion curves for Lamb waves in iron-based alumina FGMs are obtained by using an extension of the Legendre polynomial approach, and the effects of the gradient variation of iron-based alumina FGMs properties on Lamb wave propagation characteristics are discussed in detail. The conclusion could be useful for inversing elastic constant and density, which are varied along the thickness direction, of FGMs.