Amplitude equations for non-linear Rayleigh waves |
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| Affiliation: | 1. GW Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, United States;2. School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, United States;3. Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208, United States;1. School of Traffic and Transportation Engineering, Central South University, Changsha, Hunan, 410075, China;2. Division of Mechanical and Automotive Engineering, Wonkwang University, Iksan, Jeonbuk 570-749, Republic of Korea;3. College of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha, Hunan, 410114, China;1. Departamento de Termofluidos, Facultad de Ingeniería, UNAM, 04510 CDMX, Mexico;2. Polo Universitario de Tecnología Avanzada, UNAM, 66629 Apodaca N. L., Mexico;3. Facultad de Ingeniería Mecánica, UANL, 66455 Monterrey N. L., Mexico;4. Departamento de Ingeniería Electrónica, Facultad de Ingeniería, UNAM, 04510 CDMX, Mexico;1. Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;2. Philips Research Laboratories, High Tech Campus 34, 5656 AE Eindhoven, The Netherlands;1. Plasma Physics Division, Naval Research Laboratory, Washington, DC 20375, United States;2. ETH Zürich, Zürich, Switzerland;1. Department of Electrical Electronics and Computer Engineering, Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino 275-0016, Japan;2. Department of Architecture and Civil Engineering, Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino 275-0016, Japan |
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| Abstract: | We investigate asymptotic equations describing small amplitude surface elastic waves in the half-plane (Rayleigh waves). For hyperelastic materials such model equations are Hamiltonian systems, and are seen to lead to the formation of singularities in the surface elastic displacement. At the time of singularity formation the Fourier spectra of the solutions exhibit power law decay, and the observed exponents suggest the existence of both differentiable and non-differentiable singular profiles. |
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