The reflection elastic waves at the elastically supported boundary of a couple stress elastic half-space are studied in this paper. Different from the classical elastic solid, there are three kinds of elastic waves in the couple stress elastic solid, and two of them are dispersive. The boundary conditions of a couple stress elastic half-space include the couple stress vector and the rotation vector which disappear in the classical elastic solids. These boundary conditions are used to obtain a linear algebraic equation set, from which the amplitude ratios of reflection waves to the incident wave can be determined. Then, the reflection coefficients in terms of energy flux ratios are calculated numerically, and the normal energy flux conservation is used to validate the numerical results. Based on these numerical results, the influences of the boundary parameters, which reflect the mechanical behavior of elastic support, on the reflection energy partition are discussed. Both the incident longitudinal wave (the P wave) and incident transverse wave (the SV wave) are considered.
Reflection Elastic support Couple stress Dispersive waves Energy flux
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N.A. Fleck, G.M. Muller, M.F. Ashby, J.W. Hutchinson, Strain gradient plasticity: theory and experiment, Acta Metall. et Mater. 42 (2) (1994) 475–487.CrossRefGoogle Scholar
J.S. Stölken, A.G. Evans, A microbend test method for measuring the plasticity length scale, Acta Metall. 46 (14) (1998) 5109–5115.Google Scholar
A.C.M. Chong, D.C.C. Lam, Strain gradient plasticity effect in indentation hardness of polymers, J. Mater. Res. 14 (10) (1999) 4103–4110.CrossRefGoogle Scholar
A.W. McFarland, J.S. Colton, Role of material microstructure in plate stiffness with relevance to microcantilever sensors, J. Micromechanics Microengineering 15 (5) (2005) 1060–1067.CrossRefGoogle Scholar
R.D. Mindlin, H.F. Tiersten, Effects of couple stress in linear elasticity, Arch. Ration. Mech. Anal. 11 (1) (1962) 415–448.CrossRefGoogle Scholar
K.F. Graff, Y.H. Pao, The effects of couple-stresses on the propagation and reflection of the plane waves in an elastic half-space, J. Sound Vib. 6 (2) (1967) 217–229.CrossRefGoogle Scholar
H.R. Aggarwal, R.C. Alverson, The effects of couple-stresses on the diffraction of plane elastic waves by cylindrical discontinuities, Int. J. Solids Struct. 5 (5) (1969) 491–511.CrossRefGoogle Scholar
N.S. Ottosen, M. Ristinmaa, C. Ljung, Rayleigh waves obtained by the indeterminate couple-stress theory, Eur. J. Mech. - A/Solids 19 (6) (2000) 929–947.CrossRefGoogle Scholar
H.G. Georgiadis, E.G. Velgaki, High-frequency Rayleigh waves in materials with micro-structure and couple-stress effects, Int. J. Solids Struct. 40 (10) (2003) 2501–2520.CrossRefGoogle Scholar
R. Kumar, K. Kumar, R. Nautiyal, Propagation of SH-waves in couple stress elastic half space underlying an elastic layer, Afr. Mat. 24 (4) (2013) 477–485.MathSciNetCrossRefGoogle Scholar