功能梯度Levinson梁自由振动响应的均匀化和经典化表示

发布时间：2018-04-20 05:21

本文选题：功能梯度材料梁 + Euler-Bernoulli梁理论　；参考：《振动与冲击》2017年18期

【摘要】：在两端简支边界条件下,给出了Levinson高阶剪切变形理论下功能梯度材料(FGM)梁的固有频率与参考均匀Euler-Bernoulli(E-B)梁的固有频率之间的解析转换关系。假设FGM梁的材料性质沿着梁的高度任意连续变化,通过分析FGM Levinson梁和均匀E-B梁的自由振动控制方程以及边界条件在数学上的相似性,推导出了用参考均匀E-B梁的固有频率表示的FGM Levinson梁的固有频率的解析式;从而,将复杂的耦合微分方程边值问题的求解简化为一些与梁的材料非均匀特性及几何特性有关的系数的计算问题。从而实现了Levinson剪切变形理论下FGM梁的振动响应的经典化和均匀化表示,可为工程应用提供便利。
[Abstract]:Under the condition of simply supported boundary at both ends, the analytic transformation relationship between the natural frequency of functionally graded material (FGM) beam and the reference uniform Euler-Bernoullilide (E-B) beam is given under the Levinson high-order shear deformation theory. Assuming that the material properties of the FGM beam vary arbitrarily and continuously along the height of the beam, the free vibration governing equations of the FGM Levinson beam and the uniform E-B beam and the mathematical similarity of the boundary conditions are analyzed. The analytical formula of the natural frequency of FGM Levinson beam expressed by the natural frequency of the reference uniform E-B beam is derived. The solution of the boundary value problem of the complicated coupled differential equation is simplified as the calculation problem of some coefficients related to the material inhomogeneity and geometric characteristics of the beam. Thus the classical and uniform representation of the vibration response of the FGM beam under the Levinson shear deformation theory is realized, which can provide convenience for engineering application.
【作者单位】：扬州大学水利与能源动力工程学院;扬州大学建筑科学与工程学院;
【基金】：国家自然科学基金(11272278;11672260)
【分类号】：O32

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