Outputs (5)

Dispersion of elastic waves in a layer interacting with a Winkler foundation (2018)
Journal Article
Kaplunov. (2018). Dispersion of elastic waves in a layer interacting with a Winkler foundation. Journal of the Acoustical Society of America, https://doi.org/10.1121/1.5079640

ABSTRACT
Dispersion of plane harmonic waves in an elastic layer interacting with a one- or two-sided Winkler foundation is analyzed. The long-wave low-frequency polynomial approximations of the full transcendental dispersion relations are derived fo... Read More about Dispersion of elastic waves in a layer interacting with a Winkler foundation.

Asymptotic analysis of an anti-plane dynamic problem for a three-layered strongly inhomogeneous laminate (2018)
Journal Article
Prikazchikova, L., Ece Aydın, Y., Erbaş, B., & Kaplunov, J. (2018). Asymptotic analysis of an anti-plane dynamic problem for a three-layered strongly inhomogeneous laminate. Mathematics and Mechanics of Solids, 25(1), 3-16. https://doi.org/10.1177/1081286518790804

Anti-plane dynamic shear of a strongly inhomogeneous dynamic laminate with traction-free faces is
analysed. Two types of contrast are considered, including those for composite structures with stiff thick or thin outer layers. In both cases, the valu... Read More about Asymptotic analysis of an anti-plane dynamic problem for a three-layered strongly inhomogeneous laminate.

Composite wave models for elastic plates (2018)
Journal Article
Kaplunov. (2018). Composite wave models for elastic plates. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, https://doi.org/10.1098/rspa.2018.0103

The long-term challenge of formulating an asymptotically motivated wave theory for elastic plates is addressed. Composite two-dimensional models merging the leading or higher-order parabolic equations for plate bending and the hyperbolic equation for... Read More about Composite wave models for elastic plates.

An asymptotic higher-order theory for rectangular beams (2018)
Journal Article
Nolde, E., Pichugin, A., & Kaplunov, J. (2018). An asymptotic higher-order theory for rectangular beams. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474(2214), https://doi.org/10.1098/rspa.2018.0001

A direct asymptotic integration of the full three-dimensional problem of elasticity is employed to derive a consistent governing equation for a beam with the rectangular cross section. The governing equation is consistent in the sense that it has the... Read More about An asymptotic higher-order theory for rectangular beams.

Justification and refinement of Winkler-Fuss hypothesis (2018)
Journal Article
Kaplunov, J., Prikazchikov, D., & Sultanova, L. (2018). Justification and refinement of Winkler-Fuss hypothesis. Zeitschrift für Angewandte Mathematik und Physik, 69, Article 80. https://doi.org/10.1007/s00033-018-0974-1

Two-parametric asymptotic analysis of the equilibrium of an elastic half-space coated by a thin soft layer is developed. The initial scaling is motivated by the exact solution of the plane problem for a vertical harmonic load. It is established that... Read More about Justification and refinement of Winkler-Fuss hypothesis.