Decay for strain gradient porous elastic waves
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Cita com:
hdl:2117/388192
Tipus de documentArticle
Data publicació2023-02
Condicions d'accésAccés obert
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Reconeixement 4.0 Internacional
Abstract
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
CitacióBaldonedo, J. [et al.]. Decay for strain gradient porous elastic waves. "Zeitschrift für angewandte Mathematik und Physik", Febrer 2023, vol. 74, núm. 1, article 35.
ISSN0044-2275
Versió de l'editorhttps://link.springer.com/article/10.1007/s00033-022-01930-6
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