The propagation of in-plane P-SV waves in a layered elastic plate with periodic interface cracks: exact versus spring boundary conditions

Abstract

The propagation of in-plane (P-SV) waves in a symmetrically three-layered thick plate with a periodic array of interface cracks is investigated. The exact dispersion relation is derived based on an integral equation approach and Floquet's theorem. The interface cracks can be a model for interface damage, but a much simpler model is a recently developed spring boundary condition. This boundary condition is used for the thick plate and also in the derivation of plate equations with the help of power series expansions in the thickness coordinate. For low frequencies (cracks small compared to the wavelength) the three approaches give more or less coinciding dispersion curves, and this is a confirmation that the spring boundary condition is a reasonable approximation at low frequencies.

Effective spring boundary conditions for a damaged interface between dissimilar media in three-dimensional case

“…An imperfection can be simulated as a set or multiple cracks (Achenbach, 1989;Achenbach and Zhang, 1990) or as a deviation from perfect contact (Tattersall, 1973;Baik and Thompson, 1984), and this leads to a modification of the continuous boundary conditions at the interface. Although the approaches are technically different, they lead to similar results related to wave propagation in composites with damaged interfaces (Baik and Thompson, 1984;Achenbach, 1989;Golub and Boström, 2011;Kvasha et al, 2011).…”

“…The present paper is an extension of previous work on distributions of strip-like cracks between dissimilar media (Boström and Golub, 2009;Golub, 2010;Golub and Boström, 2011;Kvasha et al, 2011) and the study of Boström and Wickham (1991), where a distribution of circular contacts between two identical half-spaces were considered. The aim of this study is to obtain expressions for the spring boundary conditions in three dimensions describing wave propagation through a damaged interface between dissimilar isotropic media in terms of elastic moduli and damage parameters.…”

Dispersion of an inhomogeneous sandwich plate having imperfect interfaces and supported by the Pasternak foundation

“…Different researchers have examined many dissimilar problems and analyzed vibrational response inhomogeneous beam composed of alternating stiffsoft components [6], three-layered laminate [7], three-layered plate [8][9][10][11][12][13], five-layered plate [14], multicomponent elastic rod, bar and wave-guides [15][16][17][18][19] due to the extensive uses of layered structures in current innovative and hybrid technology. Furthermore, the authors [20][21][22][23][24][25][26][27] have highlighted the effects of external forces such as damping effects, magneto-electroelastic, thermal stress, hygrothermal response, magnetic fields, and rotation on the propagation of waves in multilayer media.…”

Dispersion of elastic waves in the three-layered inhomogeneous sandwich plate embedded in the Winkler foundations

“…[26][27][28][29][30][31] Likewise, for the significance of cracks and void pores on the propagation of waves in layered mediums, see Refs. 32,33 and the references therein. In the dynamical and static dispersion analysis of plates and beams interacting with elastic foundations, most researchers used innovative foundation models.…”