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 couplestress are mainly discussed based on the numerical results.It is found that the couple-stress mainly influences the transverse modes of elastic waves.
Reflection and transmission of an incident plane wave at five types of possible interfaces between two dipolar gradient elastic solids are studied in this paper. First, the explicit expressions of monopolar tractions and dipolar tractions are derived from the postulated function of strain energy density. Then, the displacements, the normal derivative of displacements, monopolar tractions, and dipolar tractions are used to create the nontraditional interface conditions. There are five types of possible interfaces based on all possible combinations of the displacements and the normal derivative of displacements. These interfacial conditions with consideration of microstructure effects are used to determine the amplitude ratio of the reflection and transmission waves with respect to the incident wave. Further, the energy ratios of the reflection and transmission waves with respect to the incident wave are calculated. Some numerical results of the reflection and transmission coefficients are given in terms of energy flux ratio for five types of possible interfaces. The influences of the five types of possible interfaces on the energy partition between the refection waves and the transmission waves are discussed, and the concept of double channels of energy transfer is first proposed to explain the different influences of five types of interfaces.
The direction dependence of surface wave speed and the influence of electrically and magnetically short/open circuit are investigated in this paper. First, the elastic, piezoelectric and piezomagnetic coefficients in the considered ordinate system are obtained by Bonde transformation from those in the crystal axis ordinate system. Then, the secular equation of surface wave is derived from the free traction condition on the surface of half space with consideration of short/open circuit case. Some numerical examples are given. The direction dependence of surface wave speed and the influences of short/open circuit are shown graphically and discussed based on the numerical results.
In the present paper, the effective propagation constants of elastic SH waves in composites with randomly distributed parallel cylindrical nanofibers are studied. The surface stress effects are considered based on the surface elasticity theory and non-classical interfacial conditions between the nanofiber and the host are derived. The scattering waves from individual nanofibers embedded in an infinite elastic host are obtained by the plane wave expansion method. The scattering waves from all fibers are summed up to obtain the multiple scattering waves. The interactions among random dispersive nanofibers are taken into account by the effective field approximation. The effective propagation constants are obtained by the configurational average of the multiple scattering waves. The effective speed and attenuation of the averaged wave and the associated dynamical effective shear modulus of composites are numerically calculated. Based on the numerical results, the size effects of the nanofibers on the effective propagation constants and the effective modulus are discussed.
The relection 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 relection waves to the incident wave can be determined. Then, the relection coeficients in terms of energy lux ratios are calculated numerically, and the normal energy lux conservation is used to validate the numerical results. Based on these numerical results,the inluences of the boundary parameters, which relect the mechanical behavior of elastic support, on the relection energy partition are discussed. Both the incident longitudinal wave（the P wave） and incident transverse wave（the SV wave） are considered.
The reflection and transmission properties of thermo-elastic waves at five possible interfaces between two different strain gradient thermo-elastic solids are investigated based on the generalized thermo-elastic theory without energy dissipation （the GN theory）. First, the function of free energy density is postulated and the constitutive relations are defined. Then, the temperature field and the displacement field are obtained from the motion equation in the form of displacement and the thermal transport equation without energy dissipation in the strain gradient thermo-elastic solid. Finally, the five types of thermo-elastic interracial conditions are used to calculate the amplitude ratios of the reflection and transmission waves with respect to the incident wave. Further, the reflection and transmission coefficients in terms of energy flux ratio are calculated and the numerical results are validated by the energy conservation along the normal direction. It is found that there are five types of dispersive waves, namely the coupled longitudinal wave （the CP wave）, the coupled thermal wave （the CT wave）, the shear wave, and two evanescent waves （the coupled SP wave and SS wave）, that become the surface waves at an interface. The mechanical interfacial conditions mainly influence the coupled CP waves, SV waves, and surface waves, while the thermal interracial conditions mainly influence the coupled CT waves.
