Propagation of shear elastic waves in composites with a random set of spherical inclusions (effective field approach) |
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| Institution: | 1. Instituto Tecnológico y de Estudios Superiores de Monterrey, CEM, DPG, Apdo Postal 6-3, Atizapan, Edo de México, 52926, Mexico;2. Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, Mexico;1. Friedrich Wilhelm Bessel Institut Forschungsgesellschaft m. b. H., Bremen 28359, Germany;2. Faserinstitut Bremen e.V., Bremen 28359, Germany;3. University of Bremen (FB4), Bremen 28359, Germany;4. Institut für Mikrosensoren, -aktoren und systeme (IMSAS), Bremen 28359, Germany;1. Computational Mechanics Lab., Department of Civil Engineering, Indian Institute of Science, Bangalore 560012, India;2. Advanced Computational Mechanics Lab., Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA;3. Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA;1. TMT Observatory Corporation, Pasadena, CA 91105, United States;2. Technion – Israel Institute of Technology, Technion City, Haifa 32000, Israel;3. California Institute of Technology, 2100 E California Blvd, Pasadena, CA 91125, United States;1. Institute of Metallurgy and Materials Science, 25 Reymonta Street, PL 30-059 Kraków, Poland;2. AGH University of Science and Technology, Faculty of Materials Science and Ceramics, Mickiewicza 30 Street, PL 30-059 Kraków, Poland;1. School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China;2. State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, China |
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| Abstract: | The work is dedicated to the problem of plane monochromatic shear wave propagation through elastic matrix composite materials with a homogeneous random set of spherical inclusions. The effective field method (EFM) and quasi-crystalline approximation are used for the calculation of phase velocity and attenuation factor of the mean wave field propagating through the composite. The version of the method developed in the work allows us to obtain the dispersion equation for the wave vector of the mean wave field that serves for all frequencies of the incident field, properties and volume concentrations of the inclusions. The long- and short-wave asymptotic solutions of the dispersion equation are found in closed analytical forms. Numerical solutions of this equation are constructed in a wide region of frequencies that covers the long-, middle- and short-wave regions of the propagating waves. The phase velocities and attenuation factors of the mean wave field in the composites are analyzed for various elastic properties, density and volume concentrations of the inclusions. Comparisons of the predictions of the method with some numerical computation of the effective parameters of matrix composites are presented; possible errors in predictions of the velocities and attenuation factors of the mean wave field in the composites are indicated and discussed. |
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