Analysis of a Shear beam model with suspenders in thermoelasticity of type III
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916562686967808 |
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| author | Chabekh, Meriem Chougui, Nadhir Torres, Delfim F. M. |
| author_facet | Chabekh, Meriem Chougui, Nadhir Torres, Delfim F. M. |
| contents | We conduct an analysis of a one-dimensional linear problem that describes the vibrations of a connected suspension bridge. In this model, the single-span roadbed is represented as a thermoelastic Shear beam without rotary inertia. We incorporate thermal dissipation into the transverse displacement equation, following Green and Naghdi's theory. Our work demonstrates the existence of a global solution by employing classical Faedo-Galerkin approximations and three a priori estimates. Furthermore, we establish exponential stability through the application of the energy method. For numerical study, we propose a spatial discretization using finite elements and a temporal discretization through an implicit Euler scheme. In doing so, we prove discrete stability properties and a priori error estimates for the discrete problem. To provide a practical dimension to our theoretical findings, we present a set of numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06373 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis of a Shear beam model with suspenders in thermoelasticity of type III Chabekh, Meriem Chougui, Nadhir Torres, Delfim F. M. Analysis of PDEs Numerical Analysis 74K10, 74F05, 74H20, 74H40, 65M60, 65M15 We conduct an analysis of a one-dimensional linear problem that describes the vibrations of a connected suspension bridge. In this model, the single-span roadbed is represented as a thermoelastic Shear beam without rotary inertia. We incorporate thermal dissipation into the transverse displacement equation, following Green and Naghdi's theory. Our work demonstrates the existence of a global solution by employing classical Faedo-Galerkin approximations and three a priori estimates. Furthermore, we establish exponential stability through the application of the energy method. For numerical study, we propose a spatial discretization using finite elements and a temporal discretization through an implicit Euler scheme. In doing so, we prove discrete stability properties and a priori error estimates for the discrete problem. To provide a practical dimension to our theoretical findings, we present a set of numerical simulations. |
| title | Analysis of a Shear beam model with suspenders in thermoelasticity of type III |
| topic | Analysis of PDEs Numerical Analysis 74K10, 74F05, 74H20, 74H40, 65M60, 65M15 |
| url | https://arxiv.org/abs/2501.06373 |