Key publications
1. S. Ide, G.C. Beroza, D.R. Shelly,T. Uchide, "A scaling law for slow earthquakes", NATURE, 447 (7140): 76-79
(2007).
2. D. Manoussaki, E. K. Dimitriadis, and R. S. Chadwick, "Cochlea's Graded Curvature Effect on Low
Frequency Waves", Physical review letters, 96, 088701 (2006).
3. P.H.Segerstad, S. Toll, "Open-cell cellular solids: A constitutive equation for hyperelasticity with deformation
induced anisotropy", International Journal of solids and structures, 45(7-8), 1978-1992
(2008).
Back to Top Home
Features of dynamic models
Propagation of 2D waves in an incompressible elastic layer
subject to primary simple shear deformation.
Wave length considerably exceeds the layer thickness=
long wave with small parameter scaled wave number.
Long wave low and high frequency regimes.
Three boundary value problems: layer with free, fixed and
one fixed one free face.
Very original aspect(!): no analogue of bending and
extension motions.
Back to Top Home
Mathematical methods and dynamic theories
Various perturbation methods.
Long wave low and high frequency regimes.
Application of theories of dynamic elasticity: Kirchhoff plate
theory, refined Timoshenko-Reissner theory.
Asymptotic integration method.
Numerical methods to solve non-linear equations:
Newton-Rapson and bracketing-bisection method.
Key publications
1. J. D. Kaplunov, L. Y. Kossovich and E. V. Nolde, Dynamics of thin walled elastic bodies,
Academic Press (1998).
2. J. D. Kaplunov, E. V. Nolde and G. A. Rogerson, A low frequency model for dynamic motion
w pre-stressed incompressible elastic structures, Proc. R. Soc. Lond., A 456, 2589-2610
(2000).
3. J. D. Kaplunov, E. V. Nolde and G. A. Rogerson, An asymptotically consistent model for
long wave high frequency in a pre-stressed elastic plate, Math Mech Solids, 7, 581-606
(2002).
Back to Top Home
Main results of the project
The fundamental modes exist only in the free faces
problem.
Long wave high frequency: 1D asymptotically consistent
models were derived to describe 2D motion in a layer with
free, fixed and one fixed one free face.
Long wave low frequency: the asymptotically
consistent model yields 1D vector governing equation
- second time and space derivatives of
2 displacements components, 1 space variable.
Back to Top Home
Conferences and summer school
CanCNSM (2008) Canada: 3rd Canadian Conference on
Nonlinear Solid Mechanics.
BAMC (2008) Manchester, UK : British applied
mathematics colloquium.
Euromech Colloquium 481 (2007) UK : Edge and surface
waves.
Brussels Open University (2007) Belgium : Experiments in
Space and Beyond.
BAMC (2006) Keele, UK : British applied mathematics
colloquium.
CISM advanced course (2006): Waves in non-linear
pre-stressed materials.
Back to Top Home
Publications
Formally accepted for publication, to appear
1. S.R.Amirova and G.A.Rogerson, Feb (2008), JoMMS 071031, ISSN: 1559-3959,
Long wave motion, dispersion relation analysis.
2. S.R.Amirova and G.A.Rogerson, March (2008), Mechanics of Solids, ISSN: 0025-6544,
Long wave low frequency asymptotic models in respect to neo-Hookean strain-energy function.
In prepation
1. S.R.Amirova and G.A.Rogerson,
Long wave low frequency asymptotic models in respect to most general strain-energy function.
2. S.R.Amirova and G.A.Rogerson,
The asymptotic long wave high frequency models.
Back to Top Home