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Julius Kaplunov's Outputs (77)

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.

Edge bending wave on a thin elastic plate resting on a Winkler foundation (2016)
Journal Article
Kaplunov, J., Prikazchikov, D., & Rogerson, G. (2016). Edge bending wave on a thin elastic plate resting on a Winkler foundation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472(2190), https://doi.org/10.1098/rspa.2016.0178

This paper is concerned with elucidation of the general properties of the bending edge wave in a thin linearly elastic plate that is supported by a Winkler foundation. A homogeneous wave of arbitrary profile is considered, and represented in terms of... Read More about Edge bending wave on a thin elastic plate resting on a Winkler foundation.

Vibrations of an elastic cylindrical shell near the lowest cut-off frequency (2016)
Journal Article
Kaplunov, J., Manevitch, L., & Smirnov, V. (2016). Vibrations of an elastic cylindrical shell near the lowest cut-off frequency. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472(2189), https://doi.org/10.1098/rspa.2015.0753

A new asymptotic approximation of the dynamic equations in the two-dimensional classical theory of thin-elastic shells is established for a circular cylindrical shell. It governs long wave vibrations in the vicinity of the lowest cut-off frequency. A... Read More about Vibrations of an elastic cylindrical shell near the lowest cut-off frequency.

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.

Multi-parametric analysis of the lowest natural frequencies of strongly inhomogeneous elastic rods (2015)
Journal Article
Prikazchikov, D., Kaplunov, J., & Sergushova, O. (2016). Multi-parametric analysis of the lowest natural frequencies of strongly inhomogeneous elastic rods. Journal of Sound and Vibration, 366, 264-276. https://doi.org/10.1016/j.jsv.2015.12.008

The results of a multi-parametric analysis of the near-rigid body motions of a three-component strongly inhomogeneous elastic rod are presented. It is demonstrated that the values of the associated lowest natural frequencies tend to zero at large/sma... Read More about Multi-parametric analysis of the lowest natural frequencies of strongly inhomogeneous elastic rods.

Celebrating the Centenary of Timoshenko's Study of Effects of Shear Deformation and Rotary Inertia (2015)
Journal Article
Elishakoff, I., Kaplunov, J., & Nolde, E. (2015). Celebrating the Centenary of Timoshenko's Study of Effects of Shear Deformation and Rotary Inertia. Applied Mechanics Reviews, 67(6), Article ARTN 060802. https://doi.org/10.1115/1.4031965

This study revisits Timoshenko beam theory (TBT). It discusses at depth a more consistent and simpler governing differential equation. The so-called second spectrum is also addressed. Then, we provide the asymptotic justification of the aforementione... Read More about Celebrating the Centenary of Timoshenko's Study of Effects of Shear Deformation and Rotary Inertia.

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 near-resonant regimes of a moving load in a three-dimensional problem for a coated elastic half-space (2014)
Journal Article
Erbaş, B., Kaplunov, J., Prikazchikov, D. A., & Şahin, O. (2014). The near-resonant regimes of a moving load in a three-dimensional problem for a coated elastic half-space. Mathematics and Mechanics of Solids, 22(1), https://doi.org/10.1177/1081286514555451

This paper deals with the three-dimensional analysis of the near-resonant regimes of a point load, moving steadily along the surface of a coated elastic half-space. The approach developed relies on a specialized hyperbolic–elliptic formulation for th... Read More about The near-resonant regimes of a moving load in a three-dimensional problem for a coated elastic half-space.

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.