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A fractional nonlocal time-space viscoelasticity theory and its applications in structural dynamics

机译：分数非局部时间空间粘弹性理论及其在结构动力学中的应用

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摘要

To overcome the long wavelength and time limits of classical elastic theory, this paper presents a fractional nonlocal time-space viscoelasticity theory to incorporate the non-locality of both time and spatial location. The stress (strain) at a reference point and a specified time is assumed to depend on the past time history and the stress (strain) of all the points in the reference domain through nonlocal kernel operators. Based on an assumption of weak non-locality, the fractional Taylor expansion series is used to derive a fractional nonlocal time-space model. A fractional nonlocal Kevin-Voigt model is considered as the simplest fractional nonlocal time-space model and chosen to be applied for structural dynamics. The correlation between the intrinsic length and time parameters is discussed. The effective viscoelastic modulus is derived and, based on which, the tension and vibration of rods and the bending, buckling and vibration of beams are studied. Furthermore, in the context of Hamilton's principle, the governing equation and the boundary condition are derived for longitudinal dynamics of the rod in a more rigorous manner. It is found that when the external excitation frequency and the wavenumber interact with the intrinsic microstructures of materials and the intrinsic time parameter, the nonlocal space-time effect will become substantial, and therefore the viscoelastic structures are sensitive to both microstructures and time.
机译：为了克服经典弹性理论的长波长和时间限制，本文提出了一种分数非函数时空粘弹性理论，用于纳入两个时间和空间位置的非局部性。假设参考点和指定时间的应力（应变）依赖于通过非本地内核运算符的过去的时间历史和参考域中所有点的应力（应变）。基于弱非局部性的假设，分数泰勒膨胀序列用于得出分数非函数时间空间模型。分数非局部kevin-voIGT模型被认为是最简单的分数非函数时间空间模型，并选择用于适用于结构动态。讨论了内在长度和时间参数之间的相关性。研究了有效的粘弹性模量，并且研究了杆的张力和振动和梁的弯曲，屈曲和振动的振动。此外，在汉密尔顿原则的背景下，控制方程和边界条件始于杆的纵向动态以更严格的方式。结果发现，当外部激发频率和波数与材料的内在微观结构和本征时间参数相互作用时，非函数时空效应将变得大幅度，因此粘弹性结构对微结构和时间敏感。

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  • 来源
    《Applied Mathematical Modelling》 |2020年第8期|116-136|共21页
  • 作者

    Li Li; Rongming Lin; Teng Yong Ng;

  • 作者单位

    School of Mechanical and Aerospace Engineering Nanyang Technological University Nanyang Avenue Singapore 639798 Republic of Singapore;

    School of Mechanical and Aerospace Engineering Nanyang Technological University Nanyang Avenue Singapore 639798 Republic of Singapore;

    School of Mechanical and Aerospace Engineering Nanyang Technological University Nanyang Avenue Singapore 639798 Republic of Singapore;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Nonlocal space-time theory; Viscoelasticity; Fractional-order equation; Structural dynamics; Energy dispassion;

    机译：非函数时空理论;粘弹性;分数级方程;结构动态;能量消除;

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