基于二维线弹性理论，建立Winkler-Pasternak弹性地基上功能梯度(FGM)梁自由振动控制微分方程。假设材料物性沿梁厚度方向按幂律分布，采用微分求积法(DQM)数值求解4种不同边界FGM梁自由振动无量纲频率特性。将计算结果与Winkler-Pasternak弹性地基梁对比表明，该分析方法对弹性地基梁自由振动研究行之有效。考虑边界条件、梯度指数、跨厚比、地基系数对FGM梁自振频率影响。
Abstract
Based on the two-dimension theory of linear elasticity, the free vibration differential equations for FGM beams resting on Winkler-Pasternak elastic foundations are derived. The material properties change continuously through the thickness of the beam and can vary according to power law distributions. Using differential quadrature method, the dimensionless frequencies of free vibration of FGM beams under four different boundary conditions are investigated. The formulations in this paper are validated by comparing the results with those available in the literature for homogeneous beams on Winkler-Pasternak elastic foundations. The influence of the boundary conditions, material graded index, length-to-thickness ratio and elastic coefficients of foundations on the non-dimensional frequency parameter of the FGM beans are considered.
关键词
Winkler-Pasternak弹性地基 /
FGM梁 /
自由振动 /
无量纲频率 /
微分求积法
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Key words
Winkler-Pasternak elastic foundations /
FGM beams /
free vibration /
dimensionless frequency /
DQM
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参考文献
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