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Memory and dynamic response of a thermoelastic functionally graded nanobeams due to a periodic heat flux
Mechanics Based Design of Structures and Machines ( IF 3.9 ) Pub Date : 2021-02-25 , DOI: 10.1080/15397734.2021.1890616
Ahmed E. Abouelregal 1, 2 , Husam E. Dargail 1, 3
Affiliation  

Abstract

This study highlights the introduction of a new mathematical model for functionally graded thermoelastic nanobeams (FGNB) which contains a free choice of the kernel function and time delay. The basic equations that govern the proposed model have been constructed on the basis of Hamilton’s principle, Euler-Bernoulli's assumptions, Eringen’s theory and three-phase-lag memory dependent heat conduction. The FGNB is due to a heat flux depending on time. The nanoscale beams can be regarded as non-homogeneous composite structures and typically vary from the ceramic at the bottom of the beam to the metal on the top with a continuous structural transmission along with the thickness of the beam. Utilizing the Laplace integral transform, the problem is solved analytically. The variations in moment distribution, temperature, displacement and deflection are illustrated graphically for the various kernel functions, time delays, the influence of the nonlocal parameter, and periodic pulse. Compared with the current thermoelastic models, the implications of the present model are discussed.



中文翻译:

由于周期性热通量引起的热弹性功能分级纳米梁的记忆和动态响应

摘要

本研究重点介绍了功能梯度热弹性纳米梁 (FGNB) 的新数学模型,该模型包含自由选择的核函数和时间延迟。管理所提出模型的基本方程是根据哈密顿原理、欧拉-伯努利假设、埃林根理论和三相滞后记忆相关热传导构建的。FGNB 是由于随时间变化的热通量。纳米级梁可以被视为非均匀复合结构,通常从梁底部的陶瓷到顶部的金属变化,具有连续的结构传输以及梁的厚度。利用拉普拉斯积分变换,解析地解决了该问题。力矩分布、温度的变化,对于各种核函数、时间延迟、非局部参数的影响和周期性脉冲,以图形方式说明了位移和偏转。与当前的热弹性模型相比,讨论了当前模型的含义。

更新日期:2021-02-25
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