由赫兹接触压力加载并由惯性维持平衡的圆柱体的弹性响应

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-04-03 DOI:10.1098/rspa.2023.0891
Pierric Mora, Fabien Treyssède, Laurent Laguerre
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引用次数: 0

摘要

我们推导了线赫兹接触弹性圆柱体的顺应性。圆柱体通过与刚体运动成比例的体力保持静态平衡。位移是通过设置积分量规测量的,如果问题取决于时间,积分量规相当于规定净线性动量和角动量为零。研究涵盖了代表无限小或有限接触位移(包括部分滑移)的各种情况。通过重温一个可称为 "振动土壤上的重圆柱体 "的经典示例,对这一发展进行了说明。以准静态近似的封闭形式给出了系统的四个接触共振和受迫响应,并与参考数值解进行了比较。这些公式还可用作组合由多个圆柱体组成的系统的顺应性矩阵的构件。
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Elastic response of a cylinder loaded by a Hertzian contact pressure and maintained in equilibrium by its inertia

We derive the compliance of an elastic cylinder submitted to a line Hertzian contact. The cylinder is maintained in static equilibrium by bulk forces that are proportional to rigid body motions. Displacements are measured by setting integral gauges that amount to prescribing zero net linear and angular momentum, if the problem were to depend upon time. Various cases are covered, representing either infinitesimal or finite contact displacements, including partial slip. The developments are illustrated by revisiting a classical example in what could be called The heavy cylinder on a vibrating soil. The four contact resonances and forced response of the system are given in closed form in the quasi-static approximation, and compared against a reference numerical solution. The formulae can also be used as building blocks to assemble the compliance matrix of a system comprising several cylinders.

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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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