Pulse waves in the viscoelastic Kelvin-Voigt model: a revisited approach
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917360548446208 |
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| author | Gonzalez-Santander, Juan Luis Mainardi, Francesco Mentrelli, Andrea |
| author_facet | Gonzalez-Santander, Juan Luis Mainardi, Francesco Mentrelli, Andrea |
| contents | We calculate the mechanical response $r(x,t$) 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 $r(x,t$ as $x,t \to 0,\infty$ for both step- and delta-type pulses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03897 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pulse waves in the viscoelastic Kelvin-Voigt model: a revisited approach Gonzalez-Santander, Juan Luis Mainardi, Francesco Mentrelli, Andrea General Mathematics 41A60, 44A10, 35L20, 33C10 We calculate the mechanical response $r(x,t$) 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 $r(x,t$ as $x,t \to 0,\infty$ for both step- and delta-type pulses. |
| title | Pulse waves in the viscoelastic Kelvin-Voigt model: a revisited approach |
| topic | General Mathematics 41A60, 44A10, 35L20, 33C10 |
| url | https://arxiv.org/abs/2602.03897 |