Method of first integrals and interface, surface waves

Abstract

The method of first integrals (MFI) based on the equation of motion for the displacement vector, or  based on the one for the traction vector was introduced  recently in order to find explicit secular equations of Rayleigh waves whose characteristic equations (i.e the equations determining the attenuation factor) are fully quartic or are of higher order (then the classical approach is not applicable). In this paper it is shown that, not only to Rayleigh waves,  the MFI can be applicable also to other waves by running it on the equations for mixed vectors. In particular: (i) By applying the MFI  to the equations for the displacement-traction vector  we get the explicit dispersion equations of Stoneley waves in twinned crystals (ii)  Running the MFI on the equations for the traction-electric  induction vector and the traction-electrical potential vector provides the explicit dispersion equations  of SH-waves in piezoelastic materials. The obtained dispersion equations are identical with the ones previously derived using the method of polarization vector, but the procedure of  deriving them is more simple.