Decay for strain gradient porous elastic waves
We study the one-dimensional problem for the linear strain gradient porous elasticity. Our aim is to analyze the behavior of the solutions with respect to the time variable when a dissipative structural mechanism is introduced in the system. We consider five different scenarios: hyperviscosity and v...
| Autores: | , , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/388192 |
| Acceso en línea: | https://hdl.handle.net/2117/388192 https://dx.doi.org/10.1007/s00033-022-01930-6 |
| Access Level: | acceso abierto |
| Palabra clave: | Thermoelasticity Porosity Strain gradient Exponential decay Slow decay Polynomial decay Numerical behavior Finite elements. Termoelasticitat Porositat Classificació AMS::74 Mechanics of deformable solids::74K Thin bodies, structures Classificació AMS::74 Mechanics of deformable solids::74H Dynamical problems Classificació AMS::74 Mechanics of deformable solids::74F Coupling of solid mechanics with other effects Classificació AMS::65 Numerical analysis::65M Partial differential equations, initial value and time-dependent initial-boundary value problems Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències |
| Sumario: | We study the one-dimensional problem for the linear strain gradient porous elasticity. Our aim is to analyze the behavior of the solutions with respect to the time variable when a dissipative structural mechanism is introduced in the system. We consider five different scenarios: hyperviscosity and viscosity for the displacement component and hyperviscoporosity, viscoporosity and weak viscoporosity for the porous component. We only apply one of these mechanisms at a time. We obtain the exponential decay of the solutions in the case of viscosity and a similar result for the viscoporosity. Nevertheless, in the hyperviscosity case (respectively hyperviscoporosity) the decay is slow and it can be controlled at least by t-1/2 . Slow decay is also expected for the weak viscoporosity in the generic case, although a particular combination of the constitutive parameters leads to the exponential decay. We want to emphasize the fact that the hyperviscosity (respectively hyperviscoporosity) is a stronger dissipative mechanism than the viscosity (respectively viscoporosity); however, in this situation, the second mechanism seems to be more “efficient” than the first one in order to pull along the solutions rapidly to zero. This is a striking fact that we have not seen previously at any other linear coupling system. Finally, we also present some numerical simulations by using the finite element method and the Newmark-ß scheme to show the behavior of the energy decay of the solutions to the above problems, including a comparison between the hyperviscosity and the viscosity cases |
|---|