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首页> 外文期刊>Composite Structures >On the modal behavior of a three-dimensional functionally graded cantilever beam: Poisson's ratio and material sampling effects
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On the modal behavior of a three-dimensional functionally graded cantilever beam: Poisson's ratio and material sampling effects

机译：关于三维功能梯度悬臂梁的模态行为：泊松比和材料采样效应

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摘要

Modal behavior of a three-dimensional (3D) homogeneous and functionally graded (FG) cantilever beam is studied using the Rayleigh-Ritz (RR) method and the finite element method (FEM). The effect of Poisson's ratio and material sampling point on the natural frequencies is further addressed using the FEM. The natural frequencies (first three) obtained using the RR method converge as the number of admissible shape functions increase. The natural frequencies (first 15) obtained using the FEM vary considerably with the material gradation, more so for the lower modes than for the higher modes. Poisson's ratio significantly changes the torsional natural frequencies of the homogeneous and graded beams. Considerable change in the natural frequencies is seen for the linear graded beams whose material properties are sampled at the element centroid rather than at Gaussian integration points. This difference is easily observed for beams modeled using a coarse mesh rather than a fine mesh. The natural frequencies of the y direction hyperbolic tangent beam with material nonhomogeneity parameter β = 100 matches well with those of the y direction bi-material beam. The natural frequencies of the power-law graded 3D cantilever beam obtained using the FEM matches closely with the 2D reference (Qian and Ching, 2004 [1]) solution obtained using the meshless local Petrov-Galerkin method.
机译：使用Rayleigh-Ritz（RR）方法和有限元方法（FEM）研究了三维（3D）均匀且功能梯度（FG）悬臂梁的模态行为。泊松比和材料采样点对固有频率的影响可以通过有限元法进一步解决。随着形状函数数量的增加，使用RR方法获得的固有频率（前三个）收敛。使用FEM获得的固有频率（前15个）随材料等级的不同而有很大差异，对于较低的模态比较高的模态更大。泊松比显着改变了均质和渐变梁的扭转固有频率。线性渐变光束的固有频率发生了相当大的变化，其材料特性是在单元质心而非高斯积分点处采样的。对于使用粗网格而不是细网格建模的光束，很容易观察到这种差异。材料非同质性参数β= 100的y方向双曲正切梁的固有频率与y方向双材料梁的固有频率非常匹配。使用FEM获得的幂律梯度3D悬臂梁的固有频率与使用无网格局部Petrov-Galerkin方法获得的2D参考（Qian和Ching，2004 [1]）解决方案紧密匹配。

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