Surface waves at the interface between an inviscid fluid and a dipolar gradient solid |
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| Institution: | 1. Institute of Petroleum Geology and Geophysics, Russian Academy of Sciences, Ac. Koptyug Pr. 3, 630090 Novosibirsk, Russia;2. NTNU, S.P. Andersens veg 15a, 7491 Trondheim, Norway;1. International Research Center on Mathematics and Mechanics of Complex Systems, University of L׳Aquila, 67100 L׳Aquila, Italy;2. Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, Créteil, France;1. Dpto. Matemática Aplicada and IUMA, Universidad de Zaragoza, Pedro Cerbuna, 12, Zaragoza E-50009, Spain;2. Centro Universitario de la Defensa, Academia General Militar, Ctra. Huesca s/n, Zaragoza E-50090, Spain;1. Department of Mathematics, National Central University, Jhongli 32001, Taiwan;2. Department of Computer Science, University of Colorado, Boulder, CO 80309, USA;1. National Research University Higher School of Economics, Moscow 101000, Russia;2. Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695, USA;3. Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia |
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| Abstract: | This paper is about the dispersion analysis of surface waves propagating at the interface between an inviscid fluid and a higher gradient homogeneous elastic solid modelled as a dipolar gradient continuum. In order to compare the results, a second gradient model is also evaluated. The analysis is carried out by finding the roots of the secular equation, and by carefully studying their physical meaning. As it is well known, higher gradient continua are dispersive, i.e. phase and group velocities are frequency dependent. As a consequence, the existence of surface waves will indeed depend on frequency. In order to investigate the behaviour of surface waves in this specific fluid–solid configuration, a complete dispersion analysis is performed, with a particular focus on the frequency range in which the phase velocity of shear waves is lower than the speed of waves of the fluid. Surface waves of the type Leaky Rayleigh and Scholte–Stoneley are observed in this frequency range. This work extends the knowledge on surface waves in the case of higher gradient solids and applications of these results can be found in the field of non-destructive damage evaluation in micro structured materials, composites, metamaterials and biological tissues. |
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| Keywords: | Gradient elasticity Dipolar gradient Second gradient Surface waves Dispersion |
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