Reflection and transmission of elastic waves through a couple-stress elastic slab sandwiched between two half-spaces

The reflection and transmission of elastic waves through a couple-stress elastic slab that is sandwiched between two couple-stress elastic half-spaces are studied in this paper. Because of the couple-stress effects, there are three types of elastic waves in the couple-stress elastic solid, two of which are dispersive. The interface conditions between two couple-stress solids involve the surface couple and rotation apart from the surface traction and displacement. The nontraditional interface conditions between the slab and two solid half-spaces are used to obtain the linear algebraic equation sets from which the amplitude ratios of reflection and transmission waves to the incident wave can be determined. Then, the energy fluxes carried by the various reflection and transmission waves are calculated numerically and the normal energy flux conservation is used to validate the numerical results. The special case, couple-stress elastic slab sandwiched by the classical elastic half-spaces, is also studied and compared with the situation that the classical elastic slab sandwiched by the classical elastic half-spaces. Incident longitudinal wave (P wave) and incident transverse wave (SV wave) are both considered. The influences of the couple-stress are mainly discussed based on the numerical results. It is found that the couple-stress mainly influences the transverse modes of elastic waves.

[1]  Gennady Mishuris,et al.  Steady-state propagation of a Mode III crack in couple stress elastic materials , 2012, International Journal of Engineering Science.

[2]  P. Wei,et al.  In-plane wave propagation through a microstretch slab sandwiched by two half-spaces , 2017 .

[3]  Xiao Guo,et al.  Dispersion relations of elastic waves in one-dimensional piezoelectric phononic crystal with mechanically and dielectrically imperfect interfaces , 2016 .

[4]  F. Jiao,et al.  Wave propagation through an inhomogeneous slab sandwiched by the piezoelectric and the piezomagnetic half spaces , 2017, Ultrasonics.

[5]  Ömer Civalek,et al.  Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams , 2011 .

[6]  Y. Pao,et al.  The effects of couple-stresses on the propagation and reflection of plane waves in an elastic half-space , 1967 .

[7]  M. Ghazisaeidi,et al.  Effects of couple stresses on anti-plane problems of piezoelectric media with inhomogeneities , 2007 .

[8]  R. Toupin.  Elastic materials with couple-stresses , 1962 .

[9]  R. C. Alverson,et al.  The effect of couple-stresses on the diffraction of plane elastic waves by cylindrical discontinuities , 1969 .

[10]  H. F. Tiersten,et al.  Effects of couple-stresses in linear elasticity , 1962 .

[11]  P. Wei,et al.  Reflection and transmission through a microstructured slab sandwiched by two half-spaces , 2016 .

[12]  Rajneesh Kumar,et al.  Propagation of SH-waves in couple stress elastic half space underlying an elastic layer , 2013 .

[13]  H. G. Georgiadis,et al.  High-frequency Rayleigh waves in materials with micro-structure and couple-stress effects , 2003 .

[14]  M. Ristinmaa,et al.  Rayleigh waves obtained by the indeterminate couple-stress theory , 2000 .

[15]  A. Piccolroaz,et al.  Steady-state propagation of a mode II crack in couple stress elasticity , 2013, International Journal of Fracture.

[16]  C. Su,et al.  Propagation of Longitudinal Waves in Microporous Slab Sandwiched between Elastic Half-Spaces , 2008 .

[17]  W. T. Koiter.  COUPLE-STRESSES IN THE THEORY OF ELASTICITY, I & II , 1969 .

[18]  P. Wei,et al.  Wave Propagation Through a Micropolar Slab Sandwiched by Two Elastic Half-Spaces , 2016 .

[19]  P. Tong,et al.  Couple stress based strain gradient theory for elasticity , 2002 .