A Note on the Lambert W Function: Bernstein and Stieltjes Properties for a Creep Model in Linear Viscoelasticity-Reference-Cited by-同舟云学术

A Note on the Lambert W Function: Bernstein and Stieltjes Properties for a Creep Model in Linear Viscoelasticity

Published:2023-08-26 Issue:9 Volume:15 Page:1654
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Mainardi Francesco¹^ORCID,Masina Enrico²^ORCID,González-Santander Juan Luis³^ORCID

Affiliation:

1. Department of Physics, University of Bologna, and INFN, Via Irnerio 46, I-40126 Bologna, Italy

2. Department of Mathematics, University of Bologna, Piazza Porta San Donato, I-40127 Bologna, Italy

3. Department de Mathematics, University of Oviedo, C Leopoldo Calvo Sotelo 18, 33007 Oviedo, Spain

Abstract

The purpose of this note is to propose an application of the Lambert W function in linear viscoelasticity based on the Bernstein and Stieltjes properties of this function. In particular, we recognize the role of its main branch, W0(t), in a peculiar model of creep with two spectral functions in frequency that completely characterize the creep model. In order to calculate these spectral functions, it turns out that the conjugate symmetry property of the Lambert W function along its branch cut on the negative real axis is essential. We supplement our analysis by computing the corresponding relaxation function and providing the plots of all computed functions.

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2073-8994/15/9/1654/pdf

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