Abstract
We investigate antiplane Stoneley waves, localized at the discontinuity surface between two perfectly bonded half-spaces. Both half-spaces are elastic linear isotropic and possess a microstructure that is described within the theory of couple stress materials with micro-inertia. We show that the microstructure deeply affects wave propagation, which is permitted under broad conditions. This outcome stands in marked contrast to classical elasticity, where antiplane Stoneley waves are not supported and in-plane Stoneley waves exist only under very severe conditions on the material properties of the bonded half-spaces. Besides, Stoneley waves may propagate only beyond a threshold frequency (cuton), for which an explicit expression is provided. For a given frequency above cuton, this expression lends the admissible range of material parameters that allows propagation (passband). In particular, significant contrast between the adjoining materials is possible, provided that Stoneley waves propagate at high enough frequency. Therefore, micro-inertia plays an important role in determining the features of propagation. Considerations concerning existence and uniqueness of antiplane Stoneley waves are given: it is found that evanescent and decaying/exploding modes are also admitted. Results may be especially useful when accounting for the microstructure in non-destructive testing (NDT) and seismic propagation.
Highlights
The quest for proving existence of new types of localized waves, similar in nature to Rayleigh waves occurring at a free surface, begun shortly after the discovery of these in 1885 [30]
In 1911, Love [16, p.165] investigated the possibility of waves propagating at the free surface of a layer in perfect contact with a half-space, in an attempt to explain the problematic appearance of shear horizontal Rayleigh waves in seismograms [19]
We show that, in contrast to classical elasticity (CE), anti-plane Stoneley waves are supported in couple stress (CS) materials under very general conditions concerning the elastic contrast between the media in contact
Summary
The quest for proving existence of new types of localized waves, similar in nature to Rayleigh waves occurring at a free surface, begun shortly after the discovery of these in 1885 [30]. We show that, in contrast to CE, anti-plane Stoneley waves are supported in CS materials under very general conditions concerning the elastic contrast between the media in contact. The co-ordinate system is located in such a way that the plane x2 = 0 corresponds to the contact surface between A and B, see Fig.1 Both half-spaces possess a microstructure, which is described within the theory of linear couple stress (CS) elasticity. The stress state in each half-space depends on the classical Cauchy force stress tensor sk , and on the couple stress tensor μk The latter characterises the polar behaviour of the material such that, for any directed surface of unit normal nk , it determines the internal reduced couple vector q k , acting across that surface q k = (μk )T nk ,. Hereinafter we write μk with the understanding that μkD is meant
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