Deformations of one-dimensional block media

TL;DR

This paper investigates wave propagation in one-dimensional block media, presenting mathematical models, numerical calculations, and asymptotic solutions, and comparing these approaches to understand pulse behavior over time.

Contribution

It introduces mathematical models for wave propagation in discrete one-dimensional block media, including numerical and asymptotic solutions, and compares their effectiveness.

Findings

Numerical calculations of perturbation parameters.

Asymptotic solutions at large times.

Comparison between numerical and analytical results.

Abstract

The paper gives a description of wave propagation in discrete-periodic one-dimensional media with block structure. For one-dimensional problems mathematical models are proposed that describe block structures in the form of a mass chain or bars connected by elastic springs and viscous dampers. For these models, the numerical calculations of the parameters of perturbations are obtained as well as asymptotic solutions at large time since the beginning of pulse action. The numerical calculations and analytical solutions are compared.