基底上六边形单层微球的接触振动模和球振动模
Contact-based and spheroidal vibrational modes of a hexagonal monolayer of microspheres on a substrate
摘要：
我们研究了密排六角形晶格的球体粘附在衬底上，沿高对称性方向传播的声学模式。该模型，占正常和剪切耦合之间的球体和球体和基板之间，产生三个基于接触的振动模式，涉及平移和旋转运动的球体。此外，我们研究了微扰方法中球-衬底和球-球接触对球振动模式的影响。球体-基板相互作用导致在与基板的接触点处具有非零位移的模式的频率上移。球-球相互作用导致球状模式的色散，将它们转变为传播波，尽管具有小的群速度。基于接触和球形模式的分析色散关系，并与方形晶格的结果进行比较。
英文摘要：
We study acoustic modes of a close-packed hexagonal lattice of spheres adhered to a substrate, propagating along a high-symmetry direction. The model, accounting for both normal and shear coupling between the spheres and between the spheres and the substrate, yields three contact-based vibrational modes involving both translational and rotational motion of the spheres. Furthermore, we study the effect of sphere-substrate and sphere-sphere contacts on spheroidal vibrational modes of the spheres within a perturbative approach. The sphere-substrate interaction results in a frequency upshift for the modes having a non-zero displacement at the contact point with the substrate. Sphere-sphere interactions result in dispersion of spheroidal modes turning them into propagating waves, albeit with a small group velocity. Analytical dispersion relations for both contact-based and spheroidal modes are presented and compared with results obtained for a square lattice.
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