The propagation of transient waves in two-dimensional square lattices

The aim of this article is to study the attenuation transient low-frequency waves in 2D lattices both plane and antiplane problems. main idea that analytical solutions problems mechanics discrete periodic media can be obtained by a method asymptotic inversion Laplace Fourier transforms vicinity quasi-front infinitely long waves; moreover, it possible take into account contribution short waves. Using method, we obtain asymptotics perturbations formulations under local load. Besides, show equations describing motion square lattice represented form two linearly independent wave equations, each which contains one unknown function only. By analogy with theory elasticity, equation describes propagation shear lattice, while other longitudinal As result, shown that, homogeneous infinite load specified such manner either predominantly or are formed. also solved finite difference method. qualitative quantitative correspondence numerical shown.