A revisit to the plane problem for low-frequency acoustic scattering by an elastic cylindrical shell (2024)
Journal Article
Yücel, H., Ege, N., Erbaş, B., & Kaplunov, J. (in press). A revisit to the plane problem for low-frequency acoustic scattering by an elastic cylindrical shell. Mathematics and Mechanics of Solids, https://doi.org/10.1177/10812865241233737

The proposed revisit to a classical problem in fluid–structure interaction is due to an interest in the analysis of the narrow resonances corresponding to a low-frequency fluid-borne wave, inspired by modeling and design of metamaterials. In this cas... Read More about A revisit to the plane problem for low-frequency acoustic scattering by an elastic cylindrical shell.

Asymptotic corrections to the low-frequency theory for a cylindrical elastic shell (2023)
Journal Article
Kaplunov. (2023). Asymptotic corrections to the low-frequency theory for a cylindrical elastic shell. Zeitschrift für Angewandte Mathematik und Physik, https://doi.org/10.1007/s00033-022-01933-3

<jats:title>Abstract</jats:title><jats:p>The general scaling underlying the asymptotic derivation of 2D theory for thin shells from the original equations of motion in 3D elasticity fails for cylindrical shells due to the cancellation of the leading-... Read More about Asymptotic corrections to the low-frequency theory for a cylindrical elastic shell.

Cellulose-Aerogele als multifunktionale und nachhaltige Alternativen für Flugzeugkabinenelemente (2023)
Journal Article
Aney, S., Schestakow, M., Prikazchikova, L., Milow, B., Prikazchikov, D., Kaplunov, J., …Rege, A. (2023). Cellulose-Aerogele als multifunktionale und nachhaltige Alternativen für Flugzeugkabinenelemente. https://doi.org/10.25967/570245

German; Aufgrund steigender Anforderungen steht das Design von Flugzeugkabinen vor revolutionären Herausforderungen. Die Integration innovativer Konzepte und nachhaltiger Materialien bietet einen wichtigen Lösungsansatz. Entsprechend müssen die Entwi... Read More about Cellulose-Aerogele als multifunktionale und nachhaltige Alternativen für Flugzeugkabinenelemente.

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.

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.

Antiplane shear of an asymmetric sandwich plate (2021)
Journal Article
Prikazchikova, L., Kaplunov, J., & Alkinidri, M. (2021). Antiplane shear of an asymmetric sandwich plate. Continuum Mechanics and Thermodynamics, 33, 1247–1262. https://doi.org/10.1007/s00161-021-00969-6

<jats:title>Abstract</jats:title><jats:p>An asymmetric three-layered laminate with prescribed stresses along the faces is considered. The outer layers are assumed to be much stiffer than the inner one. The focus is on long-wave low-frequency anti-pla... Read More about Antiplane shear of an asymmetric sandwich plate.

Preface to a special feature dedicated to the memory of Prof. Peter Chadwick FRS. (2020)
Journal Article
Fu, & Kaplunov. (2020). Preface to a special feature dedicated to the memory of Prof. Peter Chadwick FRS. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 20200615 - ?. https://doi.org/10.1098/rspa.2020.0615

'No abstract'

A second-order asymptotic model for Rayleigh waves on a linearly elastic half plane (2020)
Journal Article
Wootton, P. T., Prikazchikov, D., & Kaplunov, J. (2020). A second-order asymptotic model for Rayleigh waves on a linearly elastic half plane. IMA Journal of Applied Mathematics, 85(1), 113 - 131. https://doi.org/10.1093/imamat/hxz037

We derive a second-order correction to an existing leading-order model for surface waves in linear elasticity. The same hyperbolic–elliptic equation form is obtained with a correction term added to the surface boundary condition. The validity of the... Read More about A second-order asymptotic model for Rayleigh waves on a linearly elastic half plane.

Reduced model for the surface dynamics of a generally anisotropic elastic half-space (2020)
Journal Article
Prikazchikov, Kaplunov, & Fu. (2020). Reduced model for the surface dynamics of a generally anisotropic elastic half-space. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 20190590 - 20190590. https://doi.org/10.1098/rspa.2019.0590

Near-surface resonance phenomena often arise in semi-infinite solids. For instance, when a moving load with a speed v close to the surface wave speed vR is applied to the surface of an elastic half-space, it will give rise to a large-amplitude distur... Read More about Reduced model for the surface dynamics of a generally anisotropic elastic half-space.

Multi-parametric dynamic analysis of lightweight elastic laminates (2019)
Journal Article
Prikazchikov, D., Kaplunov, J., & Prikazchikova, L. (2019). Multi-parametric dynamic analysis of lightweight elastic laminates. IOP Conference Series: Materials Science and Engineering, https://doi.org/10.1088/1757-899X/683/1/012014

Multi-parametric asymptotic analysis of dynamic phenomena in lightweight three-layered structures is performed. The presence of high contrast in densities of skin and core layers may lead to the small value of the lowest shear thickness resonance fre... Read More about Multi-parametric dynamic analysis of lightweight elastic laminates.

Composite dynamic models for periodically heterogeneous media (2019)
Journal Article
Kaplunov. (2019). Composite dynamic models for periodically heterogeneous media. Mathematics and Mechanics of Solids, 2663-2693. https://doi.org/10.1177/1081286518776704

Propagation of elastic waves through discrete and continuous periodically heterogeneous media is studied. A two-scale asymptotic procedure allows us to derive macroscopic dynamic equations applicable at frequencies close to the resonant frequencies o... Read More about Composite dynamic models for periodically heterogeneous media.

The edge bending wave on a plate reinforced by a beam (L). (2019)
Journal Article
Kaplunov. (2019). The edge bending wave on a plate reinforced by a beam (L). Journal of the Acoustical Society of America, 1061 - ?. https://doi.org/10.1121/1.5121315

The edge bending wave on a thin isotropic semi-infinite plate reinforced by a beam is considered within the framework of the classical plate and beam theories. The boundary conditions at the plate edge incorporate both dynamic bending and twisting of... Read More about The edge bending wave on a plate reinforced by a beam (L)..

An asymptotic hyperbolic-elliptic model for flexural-seismic metasurfaces. (2019)
Journal Article
Wootton, P., Kaplunov, J., & Colquitt, D. (2019). An asymptotic hyperbolic-elliptic model for flexural-seismic metasurfaces. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475(2227), https://doi.org/10.1098/rspa.2019.0079

We consider a periodic array of resonators, formed from Euler-Bernoulli beams, attached to the surface of an elastic half-space. Earlier studies of such systems have concentrated on compressional resonators. In this paper, we consider the effect of t... Read More about An asymptotic hyperbolic-elliptic model for flexural-seismic metasurfaces..

Elastic contact of a stiff thin layer and a half-space (2019)
Journal Article
Kaplunov, J., Prikazchikov, D., & Sultanova, L. (2019). Elastic contact of a stiff thin layer and a half-space. Zeitschrift für angewandte Mathematik und Physik, 70, Article 22. https://doi.org/10.1007/s00033-018-1068-9

The 3D problem in linear elasticity for a layer lying on a half-space is subject to a two-parametric asymptotic treatment using the small parameters corresponding to the relative thickness of the layer and stiffness of the foundation. General scaling... Read More about Elastic contact of a stiff thin layer and a half-space.

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.