Nonlinear wave propagation analysis in hyperelastic 1D microstructured materials constructed by homogenization |
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| Affiliation: | 1. LEMTA, Universite de Lorraine, 2, Avenue de la Foret de Haye, BP 90161, 54505 Vandoeuvre-les-Nancy, France;2. Faculty of Engineering, Section III, Lebanese University, Campus Rafic Hariri, Beirut, Lebanon;1. Mechanical Engineering Department, United States Naval Academy, 590 Hollway Road, Annapolis, MD, 21402, United States;2. United States Navy, United States;3. Army Research Laboratory, 2800 Powder Mill Rd, Adelphi, MD 20783, United States;1. Department of Applied Mathematics and Science, Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates;2. Departamento de Ingeniería Mecánica, Universidad de Chile, Beauchef 851, Santiago Centro, Santiago, Chile;3. Department of Continuum Mechanics and Structures, Escuela deIngenieros de Caminos, Universidad Politecnica de Madrid, 28040 Madrid, Spain;1. Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 61, avenue du général de Gaulle, 94010 Créteil Cedex, France;2. Faculty of Engineering, International Telematic University Uninettuno, Rome, Italy |
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| Abstract: | We analyze the acoustic properties of microstructured beams including a repetitive network material undergoing configuration changes leading to geometrical nonlinearities. The effective constitutive law is evaluated successively as an effective first and second order nonlinear grade 1D continuum, based on a strain driven incremental scheme written over the reference unit cell, taking into account the changes of the lattice geometry. The dynamical equations of motion are next written, leading to specific dispersion relations. The presence of second gradient order term in the nonlinear equation of motion leads to the presence of two different modes: an evanescent subsonic mode for high nonlinearity that vanishes beyond certain values of wave number, and a supersonic mode for a weak nonlinearity. This methodology is applied to analyze wave propagation within different microstructures, including the regular and reentrant hexagons, and plain weave textile pattern. |
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| Keywords: | Microstructured beams Acoustic properties Geometrical nonlinearities Homogenization methods Effective mechanical properties Dispersion relations Second gradient effective continuum Evanescent subsonic mode Supersonic mode |
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