Wave propagation analysis in 2D nonlinear hexagonal periodic networks based on second order gradient nonlinear constitutive models |
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| Institution: | 1. LEMTA, Université de Lorraine, 2, Avenue de la Forêt de Haye, TSA 60604, 54504 Vandoeuvre-les Nancy, France;2. Faculty of Engineering, Section III, Lebanese University, Campus Rafic Hariri, Beirut, Lebanon;3. Unité de Recherche de Mécanique des Solides, Structures et Développements Technologiques, ESSTT, Université de Tunis, BP56, Bab Mnara 1008, Tunisia;1. Department of Aerospace Engineering, Texas A&M University, College Station, Texas 77843-3123, USA;2. Mechanical Engineering Program, Texas A&M University at Qatar, Engineering Building, Education City, P.O. Box 23874, Doha, Qatar;3. Department of Engineering and Physics, Karlstad University, Karlstad 65188, Sweden;4. Department of Mechanical Engineering, Texas A&M University, College Station, Texas 77843-3123, USA;1. LEMTA, Université de Lorraine. 2, Avenue de la Forêt de Haye, TSA 60604 Nancy, France;2. Faculty of Engineering, Section III, Lebanese University, Campus Rafic Hariri, Beirut, Lebanon |
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| Abstract: | We analyze the propagation of nonlinear waves in homogenized periodic nonlinear hexagonal networks, considering successively 1D and 2D situations. Wave analysis is performed on the basis of the construction of the effective strain energy density of periodic hexagonal lattices in the nonlinear regime. The obtained second order gradient nonlinear continuum has two propagation modes: an evanescent subsonic mode that disappears after a certain wavenumber and a supersonic mode characterized by an increase of the frequency with the wavenumber. For a weak nonlinearity, a supersonic mode occurs and the dispersion curves lie above the linear dispersion curve (vp =vp0). For a higher nonlinearity, the wave changes from a supersonic to an evanescent subsonic mode at s=0.7 and the dispersion curves drops below the linear case and vanish for certain values of the wavenumber. An important decrease in the frequency occurs for both subsonic and supersonic modes when the lattice becomes auxetic, and the longitudinal and shear modes become very close to each other. The influence of the lattice geometrical parameters of the lattice on the dispersion relations is analyzed. |
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| Keywords: | Hexagonal lattices Second gradient nonlinear continuum models Homogenization Wave dispersion effects |
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