Asymptotic long wave models for a pre-stressed elastic layer with elastically restrained boundaries

• Published in: International journal of solids and structures Vol. 50; no. 11-12; pp. 1944 - 1953
• Main Authors: Mukhomodyarov, Rinat R., Rogerson, Graham A.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2013
• Subjects: Asymptotic models; Asymptotic properties; Boundaries; Boundary conditions; Constraints; Dirichlet problem; Elastic layers; Elastically restrained boundary conditions; Long waves; Mathematical models; Pre-stressed elastic layer; Vibration; Pre-stressed elastic layer; Long waves; Asymptotic models; Elastically restrained boundary conditions
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2013.02.014

Long wave dispersion phenomena is investigated in respect of a pre-stressed incompressible elastic layer subject to elastically restrained boundary conditions (ERBC). Such conditions can be treated as a generalisation of classical free and fixed-face boundary conditions, allowing investigating of the transition between the Neumann and Dirichlet statements of the problem. Symmetric elastically restrained boundary conditions are introduced, followed by both a numerical investigation and a multi-parameter asymptotic analysis of the dispersion relations. All possible asymptotic regimes are grouped into classes based on the magnitude of the associated restraint parameter. A long wave low frequency model is developed to describe motion associated with the fundamental modes for small values of the restraint parameters. Four high frequency models are developed describing asymptotic regimes connected with vibration within the vicinity of the thickness resonances.