All Outputs (38)

Asymptotic strategy for matching homogenized structures. Conductivity problem (2018)
Journal Article
Kolpakov, A. G., Andrianov, I. V., & Prikazchikov, D. A. (2018). Asymptotic strategy for matching homogenized structures. Conductivity problem. Quarterly Journal of Mechanics and Applied Mathematics, 71(4), 519-535. https://doi.org/10.1093/qjmam/hby017

The paper is concerned with application of the homogenization theory to bodies containing macroinhomogeneities or bodies, parts of which cannot be homogenized (partial homogenization). This situation arises, in particular, for problems of joining hom... Read More about Asymptotic strategy for matching homogenized structures. Conductivity problem.

Hyperbolic-elliptic model for surface wave in a pre-stressed incompressible elastic half-space (2018)
Journal Article
Khajiyeva, L., Prikazchikov, D., & Prikazchikova, L. (2018). Hyperbolic-elliptic model for surface wave in a pre-stressed incompressible elastic half-space. Mechanics Research Communications, 92, 49-53. https://doi.org/10.1016/j.mechrescom.2018.07.006

The paper aims at derivation of the asymptotic model for surface wave propagating in a pre-stressed incompressible elastic half-space, subject to prescribed surface loading. The approach relies on the slow-time perturbation procedure, extending the p... Read More about Hyperbolic-elliptic model for surface wave in a pre-stressed incompressible elastic half-space.

Free vibrations of nonlocally elastic rods (2018)
Journal Article
Mikhasev, G., Avdeichik, E., & Prikazchikov, D. (2019). Free vibrations of nonlocally elastic rods. Mathematics and Mechanics of Solids, 24(5), 1279-1293. https://doi.org/10.1177/1081286518785942

Several of the Eringen’s nonlocal stress models, including two-phase and purely nonlocal integral models, along with the simplified differential model, are studied in case of free longitudinal vibrations of a nanorod, for various types of boundary... Read More about Free vibrations of nonlocally elastic rods.

Justification and refinement of Winkler-Fuss hypothesis (2018)
Journal Article
Kaplunov, J., Prikazchikov, D., & Sultanova, L. (2018). Justification and refinement of Winkler-Fuss hypothesis. Zeitschrift für Angewandte Mathematik und Physik, 69, Article 80. https://doi.org/10.1007/s00033-018-0974-1

Two-parametric asymptotic analysis of the equilibrium of an elastic half-space coated by a thin soft layer is developed. The initial scaling is motivated by the exact solution of the plane problem for a vertical harmonic load. It is established that... Read More about Justification and refinement of Winkler-Fuss hypothesis.

Explicit formulation for the Rayleigh wave field induced by surface stresses in an orthorhombic half-plane (2018)
Journal Article
Nobili, A., & Prikazchikov, D. A. (2018). Explicit formulation for the Rayleigh wave field induced by surface stresses in an orthorhombic half-plane. European Journal of Mechanics - A/Solids, 70, 86-94

We develop an explicit asymptotic model for the Rayleigh wave field arising in case of stresses prescribed on the surface of an orthorhombic elastic half-plane. The model consists of an elliptic equation governing the behaviour within the half-plane,... Read More about Explicit formulation for the Rayleigh wave field induced by surface stresses in an orthorhombic half-plane.

An edge moving load on an orthotropic plate resting on a Winkler foundation (2017)
Journal Article
Althobaiti, S. N., Kaplunov, J., & Prikazchikov, D. A. (2017). An edge moving load on an orthotropic plate resting on a Winkler foundation. Procedia Engineering, 199, 2579-2584. https://doi.org/10.1016/j.proeng.2017.09.340

Steady-state motion of a bending moment along the edge of a semi-infinite orthotropic Kirchhoff plate supported by a Winkler foundation is considered. The analysis of the dispersion relation reveals a local minimum of the phase velocity, coinciding w... Read More about An edge moving load on an orthotropic plate resting on a Winkler foundation.

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 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.

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.

Edge bending waves on an orthotropic elastic plate resting on the Winkler-Fuss foundation (2016)
Journal Article
Prikazchikov, D., & Altobaiti, S. (2016). Edge bending waves on an orthotropic elastic plate resting on the Winkler-Fuss foundation

The propagation of bending edge waves on an orthotropic plate supported by the Winkler-Fuss foundation subject to free edge boundary conditions is investigated. A dispersion relation is derived, with the analysis revealing a cut-off frequency and a l... Read More about Edge bending waves on an orthotropic elastic plate resting on the Winkler-Fuss foundation.

Buckling of a spherical shell under external pressure and inward concentrated load: asymptotic solution (2016)
Journal Article
Evkin, A., Kolesnikov, M., & Prikazchikov, D. A. (2016). Buckling of a spherical shell under external pressure and inward concentrated load: asymptotic solution. Mathematics and Mechanics of Solids, 22(6), 1425-1437. https://doi.org/10.1177/1081286516635872

An asymptotic solution is suggested for a thin isotropic spherical shell subject to uniform external pressure and concentrated load. The pressure is the main load and a concentrated lateral load is considered as a perturbation that decreases buckling... Read More about Buckling of a spherical shell under external pressure and inward concentrated load: asymptotic solution.

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.

Remarks on explicit strong ellipticity conditions for anisotropic or pre-stressed incompressible solids. (2015)
Journal Article
Pichugin, A., & Prikazchikov, D. (2016). Remarks on explicit strong ellipticity conditions for anisotropic or pre-stressed incompressible solids. Quarterly Journal of Mechanics and Applied Mathematics, 69(1), 67-81. https://doi.org/10.1093/qjmam/hbv017

We present a set of explicit conditions, involving the components of the elastic stiffness tensor, which are necessary and sufficient to ensure the strong ellipticity of an orthorhombic incompressible medium. The derivation is based on the procedure... Read More about Remarks on explicit strong ellipticity conditions for anisotropic or pre-stressed incompressible solids..

On the 3D Rayleigh wave field on an elastic half-space subject to tangential surface loads (2015)
Journal Article
Ege, N., Erbaş, B., & Prikazchikov, D. (2015). On the 3D Rayleigh wave field on an elastic half-space subject to tangential surface loads. Zeitschrift für Angewandte Mathematik und Mechanik, 95(12), 1558-1565. https://doi.org/10.1002/zamm.201400211

This study is concerned with analysis of the Rayleigh wave field in a 3D isotropic elastic half-space subject to in-plane surface loading. The approach relies on the slow time perturbation of the general representation for the Rayleigh wave eigensolu... Read More about On the 3D Rayleigh wave field on an elastic half-space subject to tangential surface loads.

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.

Rayleigh waves of arbitrary profile in anisotropic media (2013)
Journal Article
Prikazchikov, D. (2013). Rayleigh waves of arbitrary profile in anisotropic media. Mechanics Research Communications, 50, 83 -86. https://doi.org/10.1016/j.mechrescom.2013.03.009

The paper deals with surface wave propagation in an orthorhombic elastic half-plane. The general profile of the wave is considered, incorporating the anisotropy effects within the known representation in terms of a single plane harmonic function.