A remarkable behavior of Rayleigh waves

In this paper, based on the Hermitian property of surface impedance matrices, it has been proven that for Rayleigh waves propagating in traction-free anisotropic elastic half-spaces, the traction vector at any plane parallel to the surface of half-spaces is orthogonal to the displacement vector at the surface. This result generalizes the previous ones discovered by Hassan and Nagy (J. Acoust. Soc. Am. 104 (1998) 3107–3110) for isotropic half-spaces and Royer (J. Acoust. Soc. Am. 123 (2008) 599-601) for orthotropic materials. The orthogonal property may supply us with new approaches to study Rayleigh waves. As will be shown, it provides a new derivation of the explicit secular equation, polarization vector, and Stroh eigenvalues with positive imaginary parts of two-component Rayleigh waves without solving their characteristic equations.