Work

Pulse Waves in the Viscoelastic Kelvin–Voigt Model: A Revisited Approach

Year: 2026

Type: article

Abstract: We calculate the mechanical response rx,t of an initially quiescent semi-infinite homogeneous medium to a pulse applied at the origin, and this is achieved within the framework of the Kelvin–Voigt model. Although this problem has been extensively studied in the literature because of its wide range of applications—particularly in seismology—here, we present a solution in a novel integral form. This integral solution avoids the numerical computation of the solution in terms of the inverse Laplace transform; that is, numerical integration in the complex plane. In particular, we derive integral form expressions for both delta-pulse and step-pulse excitations which are simpler and more computationally efficient than those previously reported in the literature. Furthermore, the obtained expressions allow us to obtain simple asymptotic formulas for rx,t as x,t→0,∞ for both step- and delta-type pulses.

Source: Mathematics

DOI: 10.3390/math14030528

Authors: Juan Luis González-Santander, Francesco Mainardi, Andrea Mentrelli

Institutions: Universidad de Oviedo, Istituto Nazionale di Fisica Nucleare, Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, University of Bologna

Language: English

Topic: Elasticity and Wave Propagation

Subfield: Mechanics of Materials

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Gruppo Nazionale per la Fisica Matematica, Nuclear Physics