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首页> 外文期刊>Mathematical Problems in Engineering >Recent Advancements in Fractal Geometric-Based Nonlinear Time Series Solutions to the Micro-Quasistatic Thermoviscoelastic Creep for Rough Surfaces in Contact
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Recent Advancements in Fractal Geometric-Based Nonlinear Time Series Solutions to the Micro-Quasistatic Thermoviscoelastic Creep for Rough Surfaces in Contact

机译：基于分形几何的非线性时间序列求解粗糙接触接触表面准静态热粘弹性蠕变的最新进展

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摘要

To understand the tripological contact phenomena, both mathematical and experimental models are needed. In this work, fractal mathematical models are used to model the experimental results obtained from literature. Fractal geometry, using a deterministic Cantor structure, is used to model the surface topography, where recent advancements in thermoviscoelastic creep contact of rough surfaces are introduced. Various viscoelastic idealizations are used to model the surface materials, for example, Maxwell, Kelvin-Voigt, Standard Linear Solid and Jeffrey media. Such media are modelled as arrangements of elastic springs and viscous dashpots in parallel and/or in series. Asymptotic power laws, through hypergeometric series, were used to express the surface creep as a function of remote forces, body temperatures and time. The introduced models are valid only when the creep approach of the contact surfaces is in the order of the size of the surface roughness. The obtained results using such models, which admit closed-form solutions, are displayed graphically for selected values of the systems' parameters; the fractal surface roughness and various material properties. Results obtained showed good agreement with published experimental results, where the utilized methodology can be further extended to the utilization for the contact of surfaces within micro- and nano-electronic devices, circuits and systems.
机译：为了理解三重接触现象，需要数学模型和实验模型。在这项工作中，使用分形数学模型对从文献中获得的实验结果进行建模。分形几何，使用确定性的Cantor结构，用于对表面形貌进行建模，其中介绍了粗糙表面的热粘弹性蠕变接触的最新进展。各种粘弹性理想化用于模拟表面材料，例如Maxwell，Kelvin-Voigt，Standard Linear Solid和Jeffrey介质。这种介质被建模为平行和/或串联的弹性弹簧和粘性阻尼器的布置。通过超几何级数的渐近幂定律被用来表示表面蠕变作为远程力，体温和时间的函数。引入的模型仅在接触面的蠕变方法大约为表面粗糙度的大小时才有效。使用这样的模型获得的结果（允许采用封闭形式的解决方案）以图形方式显示系统参数的选定值；分形表面粗糙度和各种材料性能。获得的结果与已发表的实验结果很好地吻合，在实验结果中，所采用的方法可以进一步扩展到微电子和纳米电子器件，电路和系统中表面接触的利用。

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  • 来源
    《Mathematical Problems in Engineering》 |2011年第2期|p.1-29|共29页
  • 作者

    Osama M. Abuzeid; Anas N. Al-Rabadi; Hashem S. Alkhaldi;

  • 作者单位

    Mechanical Engineering Department, The University of Jordan, Amman 11942, Jordan;

    Computer Engineering Department, The University of Jordan, Amman 11942, Jordan;

    Mechanical Engineering Department, The University of Jordan, Amman 11942, Jordan;

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