Existence and Uniqueness of Micropolar Elastic Stoneley Waves With Sliding Contact and Formulas for the Wave Slowness

Abstract

The existence of Stoneley waves propagating in two micropolar isotropic elastic half-spaces with sliding contact was considered by Tajuddin (1995, Existence of Stoneley Waves at an Unbonded Interface Between Two Micropolar Elastic Half-Spaces, ASME J. Appl. Mech., 62, 255–257). However, the existence of Stoneley waves was proved only for the case when two half-spaces are incompressible or Poisson solids and their material properties are close to each other. In this paper, the authors investigate the existence of micropolar elastic Stoneley waves with sliding contact for the general case when two micropolar isotropic elastic half-spaces are arbitrary. By using the complex function method, the authors have established the necessary and sufficient conditions for a micropolar elastic Stoneley wave to exist and have proved that if a micropolar elastic Stoneley wave exists, it is unique. When the micropolarity is absent, the established existence result recovers the necessary and sufficient condition for the existence of an elastic Stoneley wave with a sliding contact that was found by Barnett and co-workers (1988, Slip Waves Along the Interface Between Two Anisotropicelastic Half-Spaces in Sliding Contact, Proc. R. Soc. London, Ser. A, 415, 389–419) by using the interface impedance matrix method. Explicit formulas for the slowness (the inverse of velocity) of micropolar elastic Stoneley waves have also been derived which will be of great interest in both theoretical and practical aspects.