O. Avila-Pozos, A. Movchan and S. Sorokin., Propagation of Elastic Waves along Interfaces in Layered Beams. IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, Solid Mechanics and Its Applications, 2004, Volume 113, Chapter 1, 53-61, DOI: 10.1007/1-4020-2604-8_6
An asymptotic model is proposed for the analysis of a long-wave dynamic model for a layered structure with an imperfect interface. Two layers of isotropic material are connected by a thin and soft adhesive: effectively the layer of adhesive can be described as a surface of discontinuity for the longitudinal displacement. The asymptotic method enables us to derive the lower-dimensional differential equations that describe waves associated with the displacement jump across the adhesive.