  The aim of this article is to study the attenuation of transient
low-frequency waves in 2D lattices of point masses connected by Voigt elements,
under an antiplane concentrated loading. The emphasis is on obtaining
analytical estimates for solutions using methods of asymptotic inversion of the
Laplace and Fourier transforms in the vicinity of the quasi-front of infinitely
long waves. In addition, the problems under study are solved by a finite
difference method. The main result of the article is the asymptotic estimates
of low-frequency and high-frequency perturbations in the 2D lattice for long
periods of time under a transient load. It is shown that the obtained
asymptotic estimates qualitatively and quantitatively agree with the results of
numerical calculations.
