Transient longitudinal waves in 2D square lattices with Voigt elements under concentrated loading

Abstract

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.