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.

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.

Rayleigh-type waves on a coated elastic half-space with a clamped surface (2019)
Journal Article
Kaplunov, & Prikazchikov. (2019). Rayleigh-type waves on a coated elastic half-space with a clamped surface. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, https://doi.org/10.1098/rsta.2019.0111

Elastodynamics of a half-space coated by a thin soft layer with a clamped upper face is considered. The focus is on the analysis of localised waves that do not exist on a clamped homogeneous halfspace. Non-traditional effective boundary conditions a... Read More about Rayleigh-type waves on a coated elastic half-space with a clamped surface.

A composite hyperbolic equation for plate extension (2019)
Journal Article
Kaplunov. (2019). A composite hyperbolic equation for plate extension. Mechanics Research Communications, 64-67. https://doi.org/10.1016/j.mechrescom.2019.06.008

A fourth-order inhomogeneous hyperbolic equation modeling the symmetric motion of a thin elastic plate subject to shear stresses prescribed along its faces is derived. The shortened forms of this equation govern the quasi-front, i.e. dispersive wave-... Read More about A composite hyperbolic equation for plate extension.

The lowest vibration spectra of multi-component structures with contrast material properties (2019)
Journal Article
Prikazchikov, & Kaplunov. (2019). The lowest vibration spectra of multi-component structures with contrast material properties. Journal of Sound and Vibration, 132 -147. https://doi.org/10.1016/j.jsv.2019.01.013

The paper is concerned with the lowest vibration modes of multi-component rods and cylinders with alternating high contrast material properties of the components. It is demonstrated that these modes correspond to almost rigid body motions of the “sti... Read More about The lowest vibration spectra of multi-component structures with contrast material properties.

Dispersion of elastic waves in laminated glass (2017)
Journal Article
Kaplunov, J., Prikazchikov, D., & Prikazchikova, L. (2017). Dispersion of elastic waves in laminated glass. Procedia Engineering, 199, 1489 -1494. https://doi.org/10.1016/j.proeng.2017.09.428

Elastic sandwich-type structures with high-contrast material and geometrical properties have numerous applications in modern engineering, including, in particular, laminated glass, photovoltaic panels, precipitator plates in gas filters, etc. Multi-p... Read More about Dispersion of elastic waves in laminated glass.

On surface wave fields arising in soil-structure interaction problems (2017)
Journal Article
Ege, N., Erbas, B., Chorozoglou, A., Kaplunov, J., & Prikazchikov, D. A. (2017). On surface wave fields arising in soil-structure interaction problems. Procedia Engineering, 199, 2366 -2371. https://doi.org/10.1016/j.proeng.2017.09.253

Abstract The paper aims at generalization of the specialized formulation, originally developed for the surface wave fields induced by prescribed surface stresses. We extend this formulation to soil-structure interaction problems with unknown contact... Read More about On surface wave fields arising in soil-structure interaction problems.

Dispersion of elastic waves in a strongly inhomogeneous three-layered plate (2017)
Journal Article
Prikazchikov, D., Kaplunov, J., & Prikazchikova, L. (2017). Dispersion of elastic waves in a strongly inhomogeneous three-layered plate. International Journal of Solids and Structures, 113-114, 169-179. https://doi.org/10.1016/j.ijsolstr.2017.01.042

Elastic wave propagation in a three-layered plate with high-contrast mechanical and geometric properties of the layers is analysed. Four specific types of contrast arising in engineering practice, including the design of stiff and lightweight structu... Read More about Dispersion of elastic waves in a strongly inhomogeneous three-layered plate.

Multi-parametric analysis of strongly inhomogeneous periodic waveguides with internal cutoff frequencies (2016)
Journal Article
Kaplunov. (2016). Multi-parametric analysis of strongly inhomogeneous periodic waveguides with internal cutoff frequencies. Mathematical Methods in the Applied Sciences, 3381-3392. https://doi.org/10.1002/mma.3900

In this paper, we consider periodic waveguides in the shape of a inhomogeneous string or beam partially supported by a uniform elastic Winkler foundation. A multi-parametric analysis is developed to take into account the presence of internal cutoff f... Read More about Multi-parametric analysis of strongly inhomogeneous periodic waveguides with internal cutoff frequencies.

Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects (2016)
Journal Article
Kaplunov. (2016). Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, https://doi.org/10.1098/rspa.2015.0800

The dynamic response of a homogeneous half-space, with a traction-free surface, is considered within the framework of non-local elasticity. The focus is on the dominant effect of the boundary layer on overall behaviour. A typical wavelength is assume... Read More about Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects.

The edge waves on a Kirchhoff plate bilaterally supported by a two-parameter elastic foundation (2015)
Journal Article
Kaplunov. (2015). The edge waves on a Kirchhoff plate bilaterally supported by a two-parameter elastic foundation. Journal of Vibration and Control, 2014-2022. https://doi.org/10.1177/1077546315606838

In this paper, the bending waves propagating along the edge of a semi-infinite Kirchhoff plate resting on a two-parameter Pasternak elastic foundation are studied. Two geometries of the foundation are considered: either it is infinite or it is semi-i... Read More about The edge waves on a Kirchhoff plate bilaterally supported by a two-parameter elastic foundation.

Low-frequency perturbations of rigid body motions of a viscoelastic inhomogeneous bar (2015)
Journal Article
Kaplunov. (2015). Low-frequency perturbations of rigid body motions of a viscoelastic inhomogeneous bar. Mechanics of Time-Dependent Materials, 135 -151. https://doi.org/10.1007/s11043-015-9256-x

This paper deals with a low-frequency analysis of a viscoelastic inhomogeneous bar subject to end loads. The spatial variation of the problem parameters is taken into consideration. Explicit asymptotic corrections to the conventional equations of rig... Read More about Low-frequency perturbations of rigid body motions of a viscoelastic inhomogeneous bar.

Anti-plane shear waves in a fibre-reinforced composite with a non-linear imperfect interface (2015)
Journal Article
Danishevs׳kyy, V. V., Kaplunov, J. D., & Rogerson, G. A. (2015). Anti-plane shear waves in a fibre-reinforced composite with a non-linear imperfect interface. International Journal of Non-Linear Mechanics, 76, 223 -232. https://doi.org/10.1016/j.ijnonlinmec.2014.12.009

The propagation of non-linear elastic anti-plane shear waves in a unidirectional fibre-reinforced composite material is studied. A model of structural non-linearity is considered, for which the non-linear behaviour of the composite solid is caused by... Read More about Anti-plane shear waves in a fibre-reinforced composite with a non-linear imperfect interface.

The edge wave on an elastically supported Kirchhoff plate (2014)
Journal Article
Kaplunov, J., Prikazchikov, D. A., Rogerson, G. A., & Lashab, M. I. (2014). The edge wave on an elastically supported Kirchhoff plate. Journal of the Acoustical Society of America, 136(4), 1487 - 1490. https://doi.org/10.1121/1.4894795

This Letter deals with an analysis of bending edge waves propagating along the free edge of a Kirchhoff plate supported by a Winkler foundation. The presence of a foundation leads to a non-zero cut-off frequency for this wave, along with a local mini... Read More about The edge wave on an elastically supported Kirchhoff plate.

Long-wave asymptotic theories: the connection between functionally graded waveguides and periodic media (2014)
Journal Article
Kaplunov. (2014). Long-wave asymptotic theories: the connection between functionally graded waveguides and periodic media. Wave Motion, 581 - 588. https://doi.org/10.1016/j.wavemoti.2013.09.007

This article explores the deep connections that exist between the mathematical representations of dynamic phenomena in functionally graded waveguides and those in periodic media. These connections are at their most obvious for low-frequency and long-... Read More about Long-wave asymptotic theories: the connection between functionally graded waveguides and periodic media.