In this paper we investigate the influence of rotational viscosity on the plane shear-rotational wave propagation in the linear isotropic reduced Cosserat medium. In such a continuum body points possess independent rotational and translational degrees of freedom, but the material does not resist to the gradient of microrotation. Stress tensor is asymmetric, but the couple stress is zero. For the elastic reduced Cosserat medium a band gap is present, where no running waves exist, and the logarithmic decrement is infinitely large. It was shown before that introducing viscoelasticity we may qualitatively change the dispersion behaviour. This work investigates the case of rotational viscosity, related to the difference between micro- and macrorotation. We show that in this case running decaying waves appear in the band gap domain, and their logarithmic decrement becomes finite. The dispersion relation for the real part of the wave number has a decreasing part. This means that the group velocity of these waves is opposed to their phase velocity, the behaviour characterizing double negative acoustic metamaterials.

在本文中，我们研究了旋转粘度对线性各向同性还原Cosserat介质中的平面剪切旋转波传播的影响。在这样的连续体中，体点具有独立的旋转和平移自由度，但是材料不抵抗微旋转的梯度。应力张量不对称，但偶应力为零。对于弹性还原的Cosserat介质，存在带隙，其中不存在运行波，并且对数减量无限大。之前已经证明引入粘弹性可以定性地改变分散行为。这项工作调查了旋转粘度的情况，这与微观旋转和宏观旋转之间的差异有关。我们表明，在这种情况下，运行中的衰减波出现在带隙域中，并且它们的对数减量变得有限。波数的实部的色散关系具有减小的部分。这意味着这些波的群速度与它们的相速度相反，这种行为是双重负声超材料的特征。