随着功能梯度梁的跨高比从小(厚梁)变到大(薄梁),梁的变形受到剪切变形的影响就会从大变到小.为了准确分析功能梯度梁的变形,跨高比小的厚梁采用Timoshenko梁模型,而跨高比大的薄梁采用Euler-Bernoulli梁模型.采用这两种梁模型进行功能梯度梁自由振动的有限元计算,分析单元刚度矩阵、质量矩阵和模态阵型等存在的差异.通过数值算例,研究了这两种梁模型的差异对模态应变能法的损伤识别指标的影响.对于厚梁,Timoshenko梁模型的损伤指标优于Euler-Bernoulli梁模型;对于很薄的梁(例如,l/h=25时的薄梁),Euler-Bernoulli梁模型的损伤指标优于Timoshenko梁模型.
With the change of span-depth ratio of functionally graded (FG) beam from small (thick beam) to large (thin beam),the effect of shear deformation on the beam deformation decrease.In order to analyze the deformation of the beam accurately,Timoshenko beam model is used for the thick beam with small span-depth ratio and Euler-Bernoulli beam model is used for thin beam large span-depth ratio.In this paper,free vibration is calculated based on the two beam models by a finite element method (FEM) to further analysis on the difference between element stiffness matrix,mass matrix and modal mode.Numerical examples are given to analyze the effect of those differences on the damage identification index.The damage indices of Timoshenko beam model are better than those of Euler-Bernoulli beam model in thick beam,while the damage indices of Euler-Bernoulli beam model are better than those of Timoshenko beam model in thin beam (for example l/h =25).
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