Vol. 2, No. 5, 2007

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ISSN: 1559-3959
Resonance phenomena at the interface of two perfectly bonded, prestressed elastic strips

Graham A. Rogerson and Anton V. Krynkin

Vol. 2 (2007), No. 5, 983–996
Abstract

The problem of vibration localized within the vicinity of the interface of two perfectly bonded semiinfinite elastic strips is investigated. The cases of free and forced vibration are both examined in strips composed of prestressed, incompressible elastic material. It is established that the localized interfacial vibration frequencies are functions of an associated interfacial wave speed. A consequence of the prestress is that interfacial waves exist only for certain regimes of primary deformation. For critical values of principal stretches the wave speed may approach either zero, corresponding to quasistatic interfacial deformations, or an associated body wave speed, corresponding to degeneration of the interfacial wave into a body wave. In the case of free vibration, approaching a critical principal stretch value is shown to result in a significant increase in the edge spectrum density. In the forced vibration problem, a corresponding significant decrease in the influence in the resonances is observed. The analysis is carried out within the most general appropriate constitutive framework, and includes a number of numerical illustrations involving neo-Hookean and Varga materials to illustrate the aforementioned phenomena.

Keywords
interfacial vibration, prestress, elasticity
Milestones
Received: 8 February 2007
Accepted: 27 March 2007
Published: 1 July 2007
Authors
Graham A. Rogerson
Department of Mathematics
University of Keele
Keele, Staffordshire ST5 5BG
United Kingdom
Anton V. Krynkin
Department of Mathematics
University of Keele
Keele, Staffordshire ST5 5BG
United Kingdom