Wave propagation in pre-stressed imperfectly bonded compressible elastic layered composites

Abstract

The dispersive behavior of in-plane time-harmonic waves propagating in a pre-stressed imperfectly bonded incompressible symmetric layered composite, has been analyzed recently, symmetric waves by Leungvichcharoen and Wijeyewickrema [Leungvichcharoen, S., Wijeyewickrema, A.C., 2003. Dispersion effects of extensional waves in pre-stressed imperfectly bonded incompressible elastic layered composites. Wave Motion 38, 311–325] and anti-symmetric waves by Leungvichcharoen et al. [Leungvichcharoen, S., Wijeyewickrema, A.C., Yamamoto, T., 2004. Anti-symmetric waves in pre-stressed imperfectly bonded incompressible elastic layered composites. International Journal of Solids and Structures 41, 6873–6894]. In the present paper, the corresponding problems for a symmetric layered composite consisting of compressible isotropic elastic materials are considered. The imperfect interface is simulated by a shear-spring type resistance model, which can also accommodate the extreme cases of perfectly bonded and fully slipping interfaces. The dispersion relation is obtained by formulating the incremental boundary-value problem and using the propagator matrix technique. Similar to the case of the incompressible layered composite, the dispersion relations for symmetric and anti-symmetric waves in the compressible layered composite differ from each other only through the elements of the propagator matrix associated with the inner layer. The behavior of the dispersion curves for symmetric waves is for the most part similar to that of anti-symmetric waves at the low and high wavenumber limits. At the low wavenumber limit, depending on the pre-stress, for perfectly bonded and imperfect interface cases, a finite phase speed may exist only for the fundamental mode while other higher modes have an infinite phase speed. However, for a fully slipping interface, at the low wavenumber limit it may be possible for both the fundamental mode and the next lowest mode to have finite phase speeds. For the higher modes which have infinite phase speeds in the low wavenumber region, an expression to determine the cut-off frequencies is obtained. At the high wavenumber limit, the phase speeds of the fundamental mode and the higher modes tend to the phase speeds of the surface wave or the interfacial wave or the limiting phase speed of the composite. For numerical examples, either a compressible two-parameter neo-Hookean material or a compressible two-parameter Varga material is assumed, and the effect of imperfect interfaces on both kind of waves is clearly evident in the numerical results.