Rayleigh wave equations with couple stress: Modeling and dispersion characteristic

Abstract

In elastostatics, the scale effect is a phenomenon in which the elastic parameters of a medium vary with the specimen size when the specimen is sufficiently small. Linear elasticity cannot explain the scale effect because it assumes that the medium is a continuum and does not consider microscopic rotational interactions within the medium. In elastodynamics, wave-propagation equations are usually based on linear elasticity. Thus, nonlinear elasticity must be introduced to study the scale effect on wave propagation. We have developed one of the generalized continuum theories, a so-called couple-stress theory, into solid earth geophysics to build a more practical model of the underground medium. The first-order velocity-stress wave equation is derived to simulate the propagation of Rayleigh waves. Body and Rayleigh waves are compared using elastic theory and couple-stress theory in a homogeneous half-space and a layered space. The results indicate that couple stress causes the dispersion of surface waves and S-waves even in a homogeneous half-space. The effect is enhanced by increasing the source frequency and characteristic length, despite its insufficiently clear physical meaning. Rayleigh waves are more sensitive to the couple-stress effect than are body waves. Based on the phase-shifting method, it is determined that Rayleigh waves exhibit different dispersion characteristics in the couple-stress theory than in the conventional elastic theory. For the fundamental mode, dispersion curves tend to move to a lower frequency with an increase in characteristic length [Formula: see text]. For the higher modes, the dispersion curve energy is stronger with a greater characteristic length [Formula: see text].