| 移动热源作用下基于分数阶应变的三维弹性体热-机响应 |
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| 引用本文： | 黄飞,马永斌.移动热源作用下基于分数阶应变的三维弹性体热-机响应[J].应用数学和力学,2021,42(4):373-384. |
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| 作者姓名： | 黄飞 马永斌 |
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| 作者单位： | 兰州理工大学 理学院, 兰州 730050 |
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| 基金项目： | 国家自然科学基金(12062011；11972176) |
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| 摘 要： | 基于分数阶应变理论，研究了移动热源作用下三维弹性体的热 机动态响应.将分数阶应变理论下的控制方程应用于三维半空间模型，通过Laplace积分变换、双重Fourier变换及其数值反变换对控制方程进行求解，得到了不同热源速度和不同分数阶参数下，无量纲温度、应力、应变和位移的分布规律.结果表明，分数阶应变参数对机械波影响显著而对热波影响有限，热源速度对热 机械波影响显著.
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| 关 键 词： | 三维模型 Laplace变换 Fourier变换 分数阶应变 移动热源 |
| 收稿时间： | 2019-11-15 |
Thermomechanical Responses of 3D Media Under Moving Heat Sources Based on Fractional-Order Strains |
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| Affiliation: | School of Science, Lanzhou University of Technology, Lanzhou 730050, P.R.China |
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| Abstract: | Based on the theory of fractional-order strains, the thermomechanical dynamic responses of 3D elastomers under moving heat sources were studied. The governing equations under the theory of fractional-order strains were applied to the 3D semi-space model, and solved by means of the Laplace transform, the double Fourier transform and its numerical reverse transform. The distributions of non-dimensional temperatures, stresses, strains and displacements were obtained under different heating source velocities and different fractional-order parameters. The results show that, the fractional-order strain parameters have significant effects on mechanical waves but minor effects on heat waves, and the heat source velocity has significant effects on thermomechanical waves. |
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