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Title: Mixing of two collinear Rayleigh waves in an isotropic nonlinear elastic half-space

Nonlinear mixing of two collinear, initially monochromatic, Rayleigh waves propagating in the same direction in an isotropic, nonlinear elastic solid is investigated analytically. A system of coupled ordinary differential equations is derived based on the Lagrange equations of the second kind to predict the evolution of the higher harmonic and combination frequency components of the fundamentals waves. Numerical results show that the energy transfer is larger for higher frequencies, and that the oscillation of the energy between the different frequency components depends on the amplitudes and frequencies of the fundamental waves. Furthermore, it is illustrated that the horizontal velocity component can form a shock wave while the vertical velocity component can form a pulse. The occurrence of these effects is independent of the specific fundamental frequencies and amplitudes that are mixed. However, the nonlinear interaction is more efficient when the mixing frequencies are close to each other which increases both effects. The analytical model is then extended by implementing diffraction effects in the parabolic approximation.
Authors:
;  [1] ;  [2] ;  [3]
  1. School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332 (United States)
  2. School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA and G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332 (United States)
  3. Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208 (United States)
Publication Date:
OSTI Identifier:
22263818
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1581; Journal Issue: 1; Conference: 40. annual review of progress in quantitative nondestructive evaluation, Baltimore, MD (United States), 21-26 Jul 2013, 10. international conference on Barkhausen noise and micromagnetic testing, Baltimore, MD (United States), 21-26 Jul 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; APPROXIMATIONS; DIFFRACTION; ENERGY TRANSFER; INTERACTIONS; LAGRANGE EQUATIONS; MIXING; MONOCHROMATIC RADIATION; OSCILLATIONS; PULSES; RAYLEIGH WAVES; SHOCK WAVES; SOLIDS