A new modified Lekhnitskii formalism a la Stroh for steady-state waves in anisotropic elastic materials

For the analysis of a two-dimensional steady-state motion such as the surfa ce wave in an anisotropic elastic half-space, the Stroh formalism has alway s been employed. The solutions are in terms of the elastic stiffnesses C-al pha beta. The Lekhnitskii formalism for elastostatics that provides the sol utions in terms of the reduced elastic compliances s'(alpha beta) is not ap plicable for two-dimensional steady-state motion. We present a new modified Lekhnitskii formalism in the style of Stroh that can be employed for analy zing two-dimensional steady-state motion. In contrast to the Stroh formalis m for which one computes the eigenvector b in terms of the eigenvector a, t he new modified Lekhnitskii formalism can compute the eigenvector b without computing the vector a. This feature is attractive in the study of surface waves because the Vector b is related to the surface traction. The vanishi ng of the surface traction at the boundary of the half-space is the key in the surface wave theory. Application to one-component surface waves shows t hat the conditions for such waves are easily deduced. Motivated by the new modified Lekhnitskii formalism we show that an eigenrelation for the vector b can also be derived for the Stroh formalism. (C) 2000 Elsevier Science B .V. All rights reserved.