Dynamic response of thermoelasticity based on Green-Lindsay theory and Caputo-Fabrizio fractional-order derivative

Ying Guo, Pengjie Shi, Jianjun Ma, Fengjun Liu
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Abstract

To extend the applicability and accuracy of the generalized thermoelasticity theory of thermoelasticity theory for one-dimensional problems involving a moving heat source, this study proposes a fractional-order thermoelasticity coupling theoretical model based on the Green-Lindsay theory and the Caputo-Fabrizio fractional-order derivative. The model's uniqueness and reciprocity are well established. To show its application, we analyzed the thermoelastic coupled dynamic response of a fixed-end rod subjected to a moving heat source. Using Laplace transforms and its numerical inverse method, the distribution patterns of non-dimensional displacement, temperature, and stress were obtained. A comprehensive analysis was conducted to investigate the effects of the fractional coefficient, two thermal relaxation time factors, and moving heat source speed on non-dimensional displacement, temperature, and stress. The findings reveal that the fractional coefficient and the speed of the moving heat source significantly influence all non-dimensional physical variables. While the two distinct thermal relaxation time factors have a minimal influence on the non-dimensional temperature, they exert a more pronounced effect on non-dimensional displacement and stress.
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基于格林-林赛理论和卡普托-法布里齐奥分数阶导数的热弹性动态响应
为了扩展广义热弹性理论对涉及移动热源的一维问题的适用性和准确性,本研究提出了基于格林-林赛理论和卡普托-法布里齐奥分数阶导数的分数阶热弹性耦合理论模型。该模型的唯一性和互易性均已确立。为了展示其应用,我们分析了受移动热源作用的固定端杆的热弹性耦合动态响应。利用拉普拉斯变换及其数值反演方法,得到了非尺寸位移、温度和应力的分布模式。综合分析了分数系数、两个热弛豫时间因子和移动热源速度对非尺寸位移、温度和应力的影响。研究结果表明,分数系数和移动热源的速度对所有非尺寸物理变量都有显著影响。虽然两个不同的热松弛时间因子对非尺寸温度的影响很小,但它们对非尺寸位移和应力的影响更为明显。
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来源期刊
CiteScore
11.00
自引率
10.00%
发文量
648
审稿时长
32 days
期刊介绍: International Communications in Heat and Mass Transfer serves as a world forum for the rapid dissemination of new ideas, new measurement techniques, preliminary findings of ongoing investigations, discussions, and criticisms in the field of heat and mass transfer. Two types of manuscript will be considered for publication: communications (short reports of new work or discussions of work which has already been published) and summaries (abstracts of reports, theses or manuscripts which are too long for publication in full). Together with its companion publication, International Journal of Heat and Mass Transfer, with which it shares the same Board of Editors, this journal is read by research workers and engineers throughout the world.
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