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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.