1. Real wave propagation in the isotropic-relaxed micromorphic model
- Author
-
Gabriele Barbagallo, Angela Madeo, Marco Valerio d'Agostino, Rafael Abreu, Ionel-Dumitrel Ghiba, Patrizio Neff, Universität Duisburg-Essen [Essen], Laboratoire de Génie Civil et d'Ingénierie Environnementale (LGCIE), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] (LaMCoS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Institut für Geophysik [Münster], Westfälische Wilhelms-Universität Münster (WWU), Alexandru Ioan Cuza University of Iași [Romania], Institute of Mathematics 'Octav Mayer', and Romanian Academy
- Subjects
Wave propagation ,AMS 2010: 74A10, 74A30, 74A60, 74E15, 74M25, 74Q15 ,General Mathematics ,generalized continuum ,[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] ,FOS: Physical sciences ,General Physics and Astronomy ,02 engineering and technology ,ellipticity ,[PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Mechanics of the solides [physics.class-ph] ,01 natural sciences ,planar harmonic waves ,real wave velocity ,Planar ,0203 mechanical engineering ,acoustic tensor ,micromorphic ,0101 mathematics ,Mathematical Physics ,Research Articles ,positive-definiteness ,Physics ,Cosserat ,Continuum (measurement) ,Mathematical analysis ,Isotropy ,Linear elasticity ,Wave velocity ,General Engineering ,Mathematical Physics (math-ph) ,74A10, 74A30, 74A60, 74E15, 74M25, 74Q15 ,010101 applied mathematics ,rank-one convexity ,020303 mechanical engineering & transports ,Positive definiteness ,micropolar ,Mathematik - Abstract
For the recently introduced isotropic-relaxed micromorphic generalized continuum model, we show that, under the assumption of positive-definite energy, planar harmonic waves have real velocity. We also obtain a necessary and sufficient condition for real wave velocity which is weaker than the positive definiteness of the energy. Connections to isotropic linear elasticity and micropolar elasticity are established. Notably, we show that strong ellipticity does not imply real wave velocity in micropolar elasticity, whereas it does in isotropic linear elasticity.
- Published
- 2017
- Full Text
- View/download PDF