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首页> 外文期刊>International Journal of Solids and Structures >A physical perspective of the length scales in gradient elasticity through the prism of wave dispersion
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A physical perspective of the length scales in gradient elasticity through the prism of wave dispersion

机译：通过波散射棱镜的梯度弹性长度尺度的物理透视

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摘要

The goal of this study is to understand the physical meaning and evaluate the intrinsic length scale parameters, featured in the theories of gradient elasticity, by deploying the analytical treatment and experimental measurements of the dispersion of elastic waves. The developments are focused on examining the propagation of longitudinal waves in an aluminum rod with periodically varying cross-section. First, the analytical solution for the dispersion relationship, based on the periodic cell analysis of a bi-layered laminate and Bloch theorem, is compared to two competing models of gradient elasticity. It is shown that the customary gradient elastic model with two length-scale parameters is able to capture the dispersion accurately up to the beginning of the first band gap. On the other hand, the gradient elastic model with an additional length scale (affiliated with the fourth-order time derivative in the field equation) is shown to capture not only the first dispersion branch before the band gap, but also the band gap itself and the preponderance of the second branch. Closed form relations between the microstructure parameters and the intrinsic length scales are obtained for both gradient elasticity models. By way of the asymptotic treatment in the limit of a weak contrast between the laminae, a clear physical meaning and scaling of the length-scale parameters was established in terms of: (i) the microstructure (given by the size of the unit cell and the contrast between the laminae), and (ii) thus induced dispersion relationship (characterized by the location and the width of the band gap). The analysis is verified through an experimental observation of wave dispersion, and wave attenuation within the band gap. A comparison between the analytical treatment, the gradient elastic model with three intrinsic length scales, and experimental measurements demonstrates a good agreement over the range of frequencies considered.
机译：这项研究的目的是通过对弹性波的色散进行分析处理和实验测量，以了解物理意义并评估梯度弹性理论中固有的长度标尺参数。这些进展集中在检查纵波在横截面周期性变化的铝棒中的传播。首先，基于双层层压板的周期单元分析和Bloch定理，针对色散关系的解析解与两个梯度弹性竞争模型进行了比较。结果表明，具有两个长度尺度参数的惯常梯度弹性模型能够准确地捕获色散，直到第一个带隙的开始。另一方面，具有附加长度比例（与场方程中的四阶时间导数相关）的梯度弹性模型显示为不仅捕获带隙之前的第一色散分支，而且捕获带隙本身和第二分支的优势。对于两个梯度弹性模型，都获得了微观结构参数和固有长度尺度之间的闭合形式关系。通过在薄层之间的弱对比极限内进行渐近处理，建立了明确的物理意义和长度尺度参数的缩放，其依据为：（i）微观结构（由晶胞的大小和层之间的对比度），以及（ii）由此引起的色散关系（由带隙的位置和宽度表征）。通过实验观察波的色散和带隙内的波衰减，可以验证分析结果。分析处理，具有三个固有长度尺度的梯度弹性模型与实验测量值之间的比较表明，在所考虑的频率范围内具有良好的一致性。

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