Explicit secular equation and H/V ratio formula of Rayleigh waves in orthotropic micropolar elastic half-spaces

Abstract

The main purpose of this paper is to derive the explicit secular equation and formula of H/V ratio of Rayleigh waves propagating in an orthotropic micropolar elastic half-space. The polarization vector method is used so that the characteristic equation of Rayleigh waves need not to be solved. The obtained secular equation recovers the secular equations of Rayleigh waves propagating in isotropic micropolar elastic and orthotropic (purely) elastic half-spaces. Furthermore, for isotropic micropolar elastic materials of which the micropolar couple modulus is much smaller than the shear elastic modulus, explicit formulas for the velocity and the H/V ratio of Rayleigh waves are derived by utilizing the complex function method. It is shown numerically that the micropolar parameters affect Rayleigh waves weakly in the range of low frequencies (long wavelengths) but considerably in the range of high frequencies. The numerical analysis also indicates that the obtained formulas for the velocity and the H/V ratio are good tools for nondestructively evaluating the micropolar couple modulus using Rayleigh waves of short wavelengths, and if the data of phase velocity and H/V ratio are measured with the same accuracy in practice the H/V ratio formula could be better than phase velocity in inverse problem.