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Asymptotic analysis of 3D dynamic equations in linear elasticity for a thin layer resting on a Winkler foundation (2022)
Journal Article
Kaplunov. (2022). Asymptotic analysis of 3D dynamic equations in linear elasticity for a thin layer resting on a Winkler foundation. IMA Journal of Applied Mathematics, 707 - 721. https://doi.org/10.1093/imamat/hxac023

<jats:title>Abstract</jats:title> <jats:p>A 3D dynamic problem for a thin elastic layer resting on a Winkler foundation is considered. The stiffness of the layer is assumed to be much greater than that of the foundation in order to allow low-frequenc... Read More about Asymptotic analysis of 3D dynamic equations in linear elasticity for a thin layer resting on a Winkler foundation.

The effect of contact conditions on the performance of flexural seismic metasurfaces (2022)
Journal Article
Alzaidi, A. S., Kaplunov, J., Prikazchikova, L., Wootton, P., & Nikonov, A. (2022). The effect of contact conditions on the performance of flexural seismic metasurfaces. Zeitschrift für angewandte Mathematik und Physik, 73, Article 194. https://doi.org/10.1007/s00033-022-01822-9

<jats:title>Abstract</jats:title><jats:p>Plane-strain motion of a flexural seismic metasurface in the form of a regular array of thin Kirchhoff plates attached to the surface of an elastic half-space is analysed. Two types of contact conditions, incl... Read More about The effect of contact conditions on the performance of flexural seismic metasurfaces.

On non-locally elastic Rayleigh wave (2022)
Journal Article
Kaplunov, Prikazchikov, & Prikazchikova. (2022). On non-locally elastic Rayleigh wave. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, https://doi.org/10.1098/rsta.2021.0387

<jats:p>The Rayleigh-type wave solution within a widely used differential formulation in non-local elasticity is revisited. It is demonstrated that this wave solution does not satisfy the equations of motion for non-local stresses. A modified differe... Read More about On non-locally elastic Rayleigh wave.

Asymptotic derivation of 2D dynamic equations of motion for transversely inhomogeneous elastic plates (2022)
Journal Article
Kaplunov. (2022). Asymptotic derivation of 2D dynamic equations of motion for transversely inhomogeneous elastic plates. International Journal of Engineering Science, https://doi.org/10.1016/j.ijengsci.2022.103723

The 3D dynamic equations in elasticity for a thin transversely inhomogeneous plate are subject to asymptotic analysis over the low-frequency range. The leading and first order approximations are derived. The former is given by a biharmonic equation o... Read More about Asymptotic derivation of 2D dynamic equations of motion for transversely inhomogeneous elastic plates.

Elastodynamics of a coated half-space under a sliding contact (2022)
Journal Article
Bratov, V., Kaplunov, J., Lapatsin, S., & Prikazchikov, D. (2022). Elastodynamics of a coated half-space under a sliding contact. Mathematics and Mechanics of Solids, 27(8), https://doi.org/10.1177/10812865221094425

The paper deals with elastic wave propagating in a layer on a half-space induced by a vertical force. The focus is on the effect of a sliding contact along the interface and its comparative study with a perfect one. The effective boundary conditions... Read More about Elastodynamics of a coated half-space under a sliding contact.

Homogenized equation of second-order accuracy for conductivity of laminates (2022)
Journal Article
Kaplunov, J., Prikazchikova, L., & Panasenko, G. (2022). Homogenized equation of second-order accuracy for conductivity of laminates. Applicable Analysis, 101(11), 1 - 9. https://doi.org/10.1080/00036811.2022.2027387

The high order homogenization techniques potentially generate the so-called infinite order homogenized equations. Since long ago, the coefficients at higher order derivatives in these equations have been calculated within various refined theories for... Read More about Homogenized equation of second-order accuracy for conductivity of laminates.

Low-frequency vibrations of a thin-walled functionally graded cylinder (plane strain problem) (2022)
Journal Article
Ege, N., Erbas, B., Kaplunov, J., & Noori, N. (2022). Low-frequency vibrations of a thin-walled functionally graded cylinder (plane strain problem). Mechanics of Advanced Materials and Structures, https://doi.org/10.1080/15376494.2022.2028948

Low frequency vibrations of a thin walled functionally graded cylinder are considered within the plane strain framework. The dynamic relations in elasticity are subject to asymptotic analysis over cylinder cross section resulting in a consistent appr... Read More about Low-frequency vibrations of a thin-walled functionally graded cylinder (plane strain problem).

On integral and differential formulations in nonlocal elasticity (2022)
Journal Article
Prikazchikova, L., Kaplunov, J., & Prikazchikov, D. A. (2022). On integral and differential formulations in nonlocal elasticity. European Journal of Mechanics - A/Solids, 100, Article 104497. https://doi.org/10.1016/j.euromechsol.2021.104497

The paper is concerned with comparative analysis of differential and integral formulations for boundary value problems in nonlocal elasticity. For the sake of simplicity, the focus is on an antiplane problem for a half-space for an exponential kernel... Read More about On integral and differential formulations in nonlocal elasticity.