Abstract

The conventional modified couple stress theory cannot model the correct behavior of the longitudinal dispersion and acts the same as the classical theory in the face of such problems. In this paper, the micro-inertia-based couple stress theory is used to triumph over this deficiency. The developed theory is imposed to tackle the longitudinal dispersion of aluminum beams in two distinct scales. Convenient available experimental data obtained for a macro-scale aluminum rod and aluminum crystals are utilized to determine the corresponding micro-inertia length scale parameters and show the scale-dependent nature of this parameter for the first time. In addition, a higher order micro-rotation relation is employed to describe the higher order micro-inertia effects. This relation leads to a developed equation of motion containing an additional term compared with the first-order relation. The obtained results indicate that only higher order micro-inertia effect that is proposed in this study for the first time is able to capture the highly nonlinear behavior of dispersion curves (including an extremum/inflection point), which has experimentally been observed for phonons propagating in the longitudinal direction in an aluminum crystal.

中文翻译：

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基于修正偶应力理论的纵向色散的高阶和尺度相关的微惯性效应

摘要

常规的修正偶应力理论无法对纵向色散的正确行为建模，因此面对此类问题，其行为与经典理论相同。在本文中，基于微惯性的耦合应力理论用于克服这一缺陷。提出了发达的理论来解决铝梁在两个不同尺度上的纵向色散问题。利用从大型铝棒和铝晶体获得的方便的可用实验数据来确定相应的微惯性长度尺度参数，并首次显示该参数的尺度依赖性。另外，采用更高阶的微旋转关系来描述更高阶的微惯性效应。与一阶关系相比，该关系导致了发达的运动方程，其中包含一个附加项。所得结果表明，本研究中首次提出的只有更高阶的微惯性效应才能捕获色散曲线（包括极值/拐点）的高度非线性行为，这在声子传播实验中已经观察到在铝晶体的纵向上。