Acoustic waves at the interface of a pre-stressed incompressible elastic solid and a viscous fluid

Ottenio, M., Destrade, M. and Ogden, R.W. (2007) Acoustic waves at the interface of a pre-stressed incompressible elastic solid and a viscous fluid. International Journal of Non-Linear Mechanics, 42(2), pp. 310-320. (doi: 10.1016/j.ijnonlinmec.2006.10.001)

Abstract

We analyse the influence of pre-stress on the propagation of interfacial waves along the boundary of an incompressible hyperelastic half-space that is in contact with a viscous fluid extending to infinity in the adjoining half-space. One aim is to derive rigorously the incremental boundary conditions at the interface; this derivation is delicate because of the interplay between the Lagrangian and the Eulerian descriptions but is crucial for numerous problems concerned with the interaction between a compliant wall and a viscous fluid. A second aim of this work is to model the ultrasonic waves used in the assessment of aortic aneurysms, and here we find that for this purpose the half-space idealization is justified at high frequencies. A third goal is to shed some light on the stability behaviour in compression of the solid half-space, as compared with the situation in the absence of fluid; we find that the usual technique of seeking standing waves solutions is not appropriate when the half-space is in contact with a fluid; in fact, a correct analysis reveals that the presence of a viscous fluid makes a compressed neo-Hookean half-space slightly more stable. For a wave travelling in a direction of principal strain, we obtain results for the case of a general (incompressible isotropic) strain-energy function. For a wave travelling parallel to the interface and in an arbitrary direction in a plane of principal strain, we specialize the analysis to the neo-Hookean strain-energy function.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Ogden, Professor Raymond
• Authors: Ottenio, M., Destrade, M., and Ogden, R.W.
• Subjects: Q Science > QC Physics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: International Journal of Non-Linear Mechanics
• ISSN: 0020-7462