Theoretical Solid Mechanics

We carry out research in elastic waves and vibrations in waveguides; the mathematical theory of nonlinear elasticity; structural vibrations induced
by fluid flow; the mathematics of thin elastic layers; ground vibrations produced by high speed trains; and waves in multi-layered elastic media.

Research Overview

The subject of solid dynamics and elasticity theory has a surprisingly rich mathematical theory, which is put to use all the time in the computer codes which design aircraft,bridges, nuclear reactors, sky-scrapers, and indeed anything solid which we hope will not break, either under its own weight or under the impact of forces from air, water, or earthquakes. In the Mathematics Department at Keele, we have world authorities on this theory, who apply their mathematical knowledge every day in their research work on practical problems.

Much of our research involves waves supported by elastic media, for example the Rayleigh waves which transmit earthquake energy around the Earth, or waves in thin structures, which transmit much of the energy from machinery through metal surfaces and supports, to be radiated ultimately as sound. We carry out research on railway noise, both inside the carriages and generated by, for example, the friction between the wheels and the rails.

A subject related to wave generation is the theory of structural instability, of which a familiar type is buckling under load. We do advanced mathematical work on many types of structural instability, which often involve subtle nonlinear eff ects.

Many parts of the human body are elastic, for example the walls of blood vessels and the heart. Even solid parts of the body, such as bones, can be subject to extreme dynamical events, such as fracture. Thus elasticity and solid dynamics are major underpinning disciplines in our related theme of Biomechanics.


Academic Staff

  • C. J. Chapman
  • Professor Y. Fu
  • Professor J. D. Kaplunov
  • Dr D. Prikazchikov
  • Professor G. A. Rogerson

Post-doctoral researcher

  • Dr V. Danishevsky


  • Waves in layered and curved media (Professsor C. J. Chapman)
  • Surface instabilities of bodies under stress (Professor Y. Fu)
  • The asymptotic theory of thin elastic structures (Professor J. D. Kaplunov)
  • Reduced models of surface waves (Dr D. Prikazchikov)
  • Waves in composite materials (Professor G. A. Rogerson, Dr V. Danishevsky)

PhD students

(Supervisors in parentheses)

  • S. Althobaiti (D. Prikazchikov)
  • R. Chebakov (J. D. Kaplunov)
  • A. Chorozoglou (J. D. Kaplunov, D. Prikazchikov)
  • A. Gheetamala (Y. Fu)
  • O. Sergushova (D. Prikazchikov)


  • A. Shestakova (2015)


  • Professor S. V. Sorokin (Aalborg University, Denmark)



FU, Y. B. & OGDEN, R. W. (eds.) (2001) Nonlinear Elasticity: Theory and Applications (London Mathematical Society Lecture Note Series). Cambridge University Press.

KAPLUNOV, J. D., KOSSOVITCH, E. & NOLDE, E. (1997) Dynamics of thin-walled elastic bodies. Academic Press.

Papers and articles

Chapman, CJ and Sorokin, SV  (2016) A class of reduced-order models in the theory of waves and stability.  PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 472 (2186).   ISSN 1364-5021 

SOROKIN, S.V. & CHAPMAN, C.J. (2014) A hierarchy of high-order theories for symmetric modes in an elastic layer, Journal of Sound and Vibration 333, pp. 3501-3522.

CHAPMAN, C. J. (2013) An asymptotic decoupling method for waves in layered media, Proceedings of the Royal Society of London A 469, Article Number: 20120659 DOI:10.1098/rspa.2012.0659 Published: May 8 2013.

SOROKIN, S.V. & CHAPMAN, C.J. (2011) A hierarchy of rational Timoshenko dispersion relations, Journal of Sound and Vibration 330, pp. 5460-5473.

CHAPMAN, C.J. & SOROKIN, S. V. (2010) The nite-product method in the theory of waves and stability, Proceedings of the Royal Society of London A 466, pp. 471-491.

For further publications by C.J Chapman, see the Fluid Dynamics and Acoustics page.