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arXiv 1506.08445cond-mat.soft
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弹性基底上单层微球的动力学

Dynamics of a Monolayer of Microspheres on an Elastic Substrate

Samuel P. Wallen, Alexei A. Maznev, Nicholas Boechler

摘要:

我们提出了一个模型,波在弹性基底上的单层球的传播。该模型,它认为矢状极化波,包括:水平,垂直和旋转自由度;正常和剪切球和基板之间的耦合,以及相邻的球体之间;和弹性基板中的波传播的影响。对于单层相互作用的球体,我们发现三个接触共振,其频率给出了简单的封闭形式的表达式。对于单层的孤立球,只有两个共振。接触谐振耦合到衬底中的表面声波,导致模式杂交和“避免交叉”现象。我们提出了一个单层的二氧化硅微球的二氧化硅基板上的色散曲线,假设粘合剂,赫兹相互作用,并比较计算使用有效介质近似的离散模型的单层刚性基板上。虽然有效介质模型不考虑离散晶格效应在短波长,我们发现,它是非常适合描述的单层和基板之间的相互作用在长波长的限制。我们建议,一个完整的图片的离散单层粘附到弹性基板的动态可以找到使用离散和有效介质描述的结果相结合。该模型是潜在的可扩展的使用与微观和宏观尺度的系统,并提供了实验提取接触刚度从测量的声学分散的前景。

英文摘要:

We present a model for wave propagation in a monolayer of spheres on an elastic substrate. The model, which considers sagittally polarized waves, includes: horizontal, vertical, and rotational degrees of freedom; normal and shear coupling between the spheres and substrate, as well as between adjacent spheres; and the effects of wave propagation in the elastic substrate. For a monolayer of interacting spheres, we find three contact resonances, whose frequencies are given by simple closed-form expressions. For a monolayer of isolated spheres, only two resonances are present. The contact resonances couple to surface acoustic waves in the substrate, leading to mode hybridization and "avoided crossing" phenomena. We present dispersion curves for a monolayer of silica microspheres on a silica substrate, assuming adhesive, Hertzian interactions, and compare calculations using an effective medium approximation to a discrete model of a monolayer on a rigid substrate. While the effective medium model does not account for discrete lattice effects at short wavelengths, we find that it is well suited for describing the interaction between the monolayer and substrate in the long wavelength limit. We suggest that a complete picture of the dynamics of a discrete monolayer adhered to an elastic substrate can be found using a combination of the results presented for the discrete and effective medium descriptions. This model is potentially scalable for use with both micro- and macroscale systems, and offers the prospect of experimentally extracting contact stiffnesses from measurements of acoustic dispersion.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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