Discrete and generalized continuum models of the dynamics of tetrachiral Cosserat lattices consisting of finite-sized particles with complex connections are elaborated. Macrocharacterstics of the chiral lattice are expressed in terms of its microparameters. The dispersion relations of the models are derived. Analysis and comparison of the models are carried out. The obtained single-field long-wavelength and gradient micropolar models provide a good approximation and are applicable to the analysis of the long-wavelength slowly varying deformations. Two-field long-wavelength and gradient micropolar models are elaborated for a one-dimensional case. As distinct from the single-field models, they are constructed using two vector-functions to approximate deformations of the lattice. Six coupled equations of the two-field models are split into two uncoupled systems of equations. One of them coincides with the equations of the single-field models. Thus, the two-field models exhibit the same accuracy as the single-field models for the long-wavelength deformations. Another system of equations describes short-wavelength rapidly varying deformations, for which the single-field models give significant inaccuracy. The two-field models give exact values of frequencies at the edges of dispersion curves in both the long-wavelength and short-wavelength ranges. This can be useful for modeling directional frequency filters in the framework of continuum mechanics.

详细阐述了由具有复杂连接的有限尺寸粒子组成的四手性 Cosserat 晶格动力学的离散和广义连续模型。手性晶格的宏观特征用其微观参数来表示。推导出模型的离散关系。对模型进行了分析和比较。获得的单场长波长和梯度微极模型提供了很好的近似，适用于长波长缓慢变化变形的分析。针对一维情况详细阐述了二维长波长和梯度微极模型。与单场模型不同的是，它们是使用两个向量函数来构造的，以近似晶格的变形。双场模型的六个耦合方程被分解为两个非耦合方程组。其中之一与单场模型的方程相吻合。因此，对于长波长变形，双场模型表现出与单场模型相同的精度。另一个方程组描述了短波长快速变化的变形，单场模型对此有很大的不准确性。双场模型给出了长波长和短波长范围内色散曲线边缘的准确频率值。这对于在连续介质力学框架中对定向频率滤波器进行建模非常有用。对于长波长变形，双场模型表现出与单场模型相同的精度。另一个方程组描述了短波长快速变化的变形，单场模型对此有很大的不准确性。双场模型给出了长波长和短波长范围内色散曲线边缘的准确频率值。这对于在连续介质力学框架中对定向频率滤波器进行建模非常有用。对于长波长变形，双场模型表现出与单场模型相同的精度。另一个方程组描述了短波长快速变化的变形，单场模型对此有很大的不准确性。双场模型给出了长波长和短波长范围内色散曲线边缘的准确频率值。这对于在连续介质力学框架中对定向频率滤波器进行建模非常有用。