Shear-induced wrinkling in accelerating thin elastic discs

IF 1.7 3区 数学 Q2 MATHEMATICS, APPLIED
Ciprian D. Coman
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Abstract

Abstract The wrinkling instabilities produced by in-plane angular accelerations in a rotating disc are discussed here in a particular limit of relevance to very thin plates. By coupling the classical linear elasticity solution for this configuration with the Föppl–von Kármán plate buckling equation, a fourth-order boundary-value problem with variable coefficients is obtained. The singular-perturbation character of the resulting problem arises from a combination of factors encompassing both the pre-stress (due to the spinning motion) and the geometry of the annular domain. With the help of a simplified multiple-scale perturbation method in conjunction with matched asymptotics, we succeed in capturing the dependence of the critical (wrinkling) acceleration on the instantaneous speed of the disc as well as other physical parameters. We show that the asymptotic predictions compare well with the results of direct numerical simulations of the original bifurcation problem. The limitations of the formulae obtained are also considered, and some practical suggestions for improving their accuracy are suggested.

Abstract Image

加速薄弹性圆盘剪切引起的起皱
摘要本文讨论了旋转圆盘中平面内角加速度所产生的起皱不稳定性,并对非常薄的板进行了特殊的限制。将该构形的经典线性弹性解与Föppl-von Kármán板屈曲方程耦合,得到了一个四阶变系数边值问题。由此产生的问题的奇异摄动特性是由包括预应力(由于旋转运动)和环形域的几何形状的因素的组合引起的。借助简化的多尺度摄动方法,结合匹配渐近性,我们成功地捕获了临界(起皱)加速度与圆盘瞬时速度以及其他物理参数的依赖关系。我们证明了渐近预测结果与原始分岔问题的直接数值模拟结果相比较。文中还考虑了所得公式的局限性,并提出了提高公式精度的一些实用建议。
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来源期刊
CiteScore
2.90
自引率
10.00%
发文量
216
审稿时长
6-12 weeks
期刊介绍: The Journal of Applied Mathematics and Physics (ZAMP) publishes papers of high scientific quality in Fluid Mechanics, Mechanics of Solids and Differential Equations/Applied Mathematics. A paper will be considered for publication if at least one of the following conditions is fulfilled: The paper includes results or discussions which can be considered original and highly interesting. The paper presents a new method. The author reviews a problem or a class of problems with such profound insight that further research is encouraged. The readers of ZAMP will find not only articles in their own special field but also original work in neighbouring domains. This will lead to an exchange of ideas; concepts and methods which have proven to be successful in one field may well be useful to other areas. ZAMP attempts to publish articles reasonably quickly. Longer papers are published in the section "Original Papers", shorter ones may appear under "Brief Reports" where publication is particularly rapid. The journal includes a "Book Review" section and provides information on activities (such as upcoming symposia, meetings or special courses) which are of interest to its readers.
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