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Transient thermoelastic response of a size-dependent nanobeam under the fractional order thermoelasticity
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2021-05-12 , DOI: 10.1002/zamm.202000379
Wei Peng 1 , Yongbin Ma 2 , Tianhu He 1, 2
Affiliation  

With the miniaturization of structures, such as MEMS/NEMS, the size-dependent effect has become an issue and attracted much attention. The well-known theories describing the size-dependent effect mainly include the nonlocal elasticity theory, the strain gradient theory and the modified coupled stress theory. Based on these theories, a number of works have been conducted to explore the size-dependent behaviors of structures or devices in micro/nano-scale, among them, majorities are on elastic performances, while, minorities are on thermoelastic performances. It is inevitable for structures suffering changeable temperature, as a consequence, thermal-induced stress and deformation occur in structures and they are worth being fully concerned. For thermoelastic behaviors limited to small scale problems, the classical Fourier's heat conduction law may fail, meanwhile, new models, for example, fractional order heat conduction model, have been developed to modify Fourier's law. In present paper, the transient thermoelastic response of a nanobeam subjected to a ramp heating is investigated by combining the nonlocal elasticity theory and the fractional order heat conduction model. The governing equations are formulated and then solved by Laplace transform and its numerical inversion. The non-dimensional temperature, displacement, stress, and deflection in the nanobeam are obtained and illustrated graphically. In calculation, the effects of the ramp-heating time parameter, the nonlocal parameter and the fractional order parameter on the considered physical quantities are examined and discussed in detail.

中文翻译:

分数阶热弹性下尺寸相关纳米梁的瞬态热弹性响应

随着MEMS/NEMS等结构的小型化,尺寸依赖效应成为一个问题并引起了广泛关注。描述尺寸相关效应的著名理论主要包括非局部弹性理论、应变梯度理论和修正耦合应力理论。基于这些理论,已经进行了许多工作来探索微/纳米尺度结构或器件的尺寸依赖性行为,其中大多数是弹性性能,而少数是热弹性性能。结构受温度变化的影响是不可避免的,因此结构中会发生热致应力和变形,值得充分关注。对于仅限于小规模问题的热弹性行为,经典傅立叶' s 的热传导定律可能会失效,同时,已经开发了新的模型,例如分数阶热传导模型来修正傅立叶定律。在本文中,通过结合非局部弹性理论和分数阶热传导模型,研究了受到斜坡加热的纳米梁的瞬态热弹性响应。制定控制方程,然后通过拉普拉斯变换及其数值反演求解。获得并以图形方式说明了纳米梁中的无量纲温度、位移、应力和偏转。在计算中,详细检查和讨论了斜坡加热时间参数、非局部参数和分数阶参数对所考虑物理量的影响。分数阶热传导模型已被开发用于修改傅立叶定律。在本文中,通过结合非局部弹性理论和分数阶热传导模型,研究了受到斜坡加热的纳米梁的瞬态热弹性响应。制定控制方程,然后通过拉普拉斯变换及其数值反演求解。获得并以图形方式说明了纳米梁中的无量纲温度、位移、应力和偏转。在计算中,详细检查和讨论了斜坡加热时间参数、非局部参数和分数阶参数对所考虑物理量的影响。分数阶热传导模型已被开发用于修改傅立叶定律。在本文中,通过结合非局部弹性理论和分数阶热传导模型,研究了受到斜坡加热的纳米梁的瞬态热弹性响应。制定控制方程,然后通过拉普拉斯变换及其数值反演求解。获得并以图形方式说明了纳米梁中的无量纲温度、位移、应力和偏转。在计算中,详细检查和讨论了斜坡加热时间参数、非局部参数和分数阶参数对所考虑物理量的影响。通过结合非局部弹性理论和分数阶热传导模型,研究了经受斜坡加热的纳米梁的瞬态热弹性响应。制定控制方程,然后通过拉普拉斯变换及其数值反演求解。获得并以图形方式说明了纳米梁中的无量纲温度、位移、应力和偏转。在计算中,详细检查和讨论了斜坡加热时间参数、非局部参数和分数阶参数对所考虑物理量的影响。通过结合非局部弹性理论和分数阶热传导模型,研究了经受斜坡加热的纳米梁的瞬态热弹性响应。制定控制方程,然后通过拉普拉斯变换及其数值反演求解。获得并以图形方式说明了纳米梁中的无量纲温度、位移、应力和偏转。在计算中,详细检查和讨论了斜坡加热时间参数、非局部参数和分数阶参数对所考虑物理量的影响。获得并以图形方式说明了纳米梁中的无量纲温度、位移、应力和偏转。在计算中,详细检查和讨论了斜坡加热时间参数、非局部参数和分数阶参数对所考虑物理量的影响。获得并以图形方式说明了纳米梁中的无量纲温度、位移、应力和偏转。在计算中,详细检查和讨论了斜坡加热时间参数、非局部参数和分数阶参数对所考虑物理量的影响。
更新日期:2021-05-12
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