The European Physical Journal E ( IF 1.8 ) Pub Date : 2021-06-14 , DOI: 10.1140/epje/s10189-021-00085-y Haim Diamant 1
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Abstract
Thin elastic sheets supported on compliant media form wrinkles under lateral compression. Since the lateral pressure is coupled to the sheet’s deformation, varying it periodically in time creates a parametric excitation. We study the resulting parametric resonance of wrinkling modes in sheets supported on semi-infinite elastic or viscoelastic media, at pressures smaller than the critical pressure of static wrinkling. We find distinctive behaviors as a function of excitation amplitude and frequency, including (a) a different dependence of the dynamic wrinkle wavelength on sheet thickness compared to the static wavelength; and (b) a discontinuous decrease in the dominant wrinkle wavelength upon increasing excitation frequency at sufficiently large pressures. In the case of a viscoelastic substrate, resonant wrinkling requires crossing a threshold of excitation amplitude. The frequencies for observing these phenomena in relevant experimental systems are of the order of a kilohertz and above. We discuss experimental implications of the results.
Graphic abstract
中文翻译：
弹性和粘弹性基材上弹性片中皱纹的参数激发
摘要
支撑在柔顺介质上的弹性薄板在横向压缩下会形成褶皱。由于侧向压力与板材的变形相关，因此定期改变它会产生参数激励。我们研究了在半无限弹性或粘弹性介质上支撑的板中起皱模式的参数共振，压力小于静态起皱的临界压力。我们发现了作为激发幅度和频率函数的独特行为，包括（a）与静态波长相比，动态皱纹波长对片材厚度的不同依赖性；(b) 在足够大的压力下增加激发频率后，主要皱纹波长不连续减少。在粘弹性基材的情况下，共振起皱需要跨越激发幅度的阈值。在相关实验系统中观察这些现象的频率在千赫兹及以上的数量级。我们讨论了结果的实验意义。
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