Asymptotic Formulation for the Rayleigh Wave on a Nonlocally Elastic Half-Space (2023)
Journal Article
Prikazchikov, D. A. (2023). Asymptotic Formulation for the Rayleigh Wave on a Nonlocally Elastic Half-Space. Vibration, 6(1), 57-64. https://doi.org/10.3390/vibration6010005

This paper deals with the Rayleigh wave, propagating on a nonlocally elastic, linearly isotropic half-space, excited by a prescribed surface loading. The consideration develops the methodology of hyperbolic–elliptic models for Rayleigh and Rayleigh-t... Read More about Asymptotic Formulation for the Rayleigh Wave on a Nonlocally Elastic Half-Space.

Cellulose-Aerogele als multifunktionale und nachhaltige Alternativen für Flugzeugkabinenelemente (2023)
Presentation / Conference Contribution
Aney, S., Schestakow, M., Prikazchikova, L., Milow, B., Prikazchikov, D., Kaplunov, J., Voggenreiter, H., & Rege, A. Cellulose-Aerogele als multifunktionale und nachhaltige Alternativen für Flugzeugkabinenelemente. Presented at German Aerospace Congress 2022, Dresden, German Aerospace Society - Lilienthal-Oberth eV, Bonn, 202

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.

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.

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.

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.

Explicit model for bending edge wave on an elastic orthotropic plate supported by the Winkler–Fuss foundation (2021)
Journal Article
Althobaiti, S. N., Nikonov, A., & Prikazchikov, D. (2021). Explicit model for bending edge wave on an elastic orthotropic plate supported by the Winkler–Fuss foundation. Journal of Mechanics of Materials and Structures, 16(4), 543 - 554. https://doi.org/10.2140/jomms.2021.16.543

The paper is concerned with a bending edge wave on a thin orthotropic elastic plate resting on a Winkler–Fuss foundation. The main focus of the contribution is on derivation of a specialised reduced model accounting for the contribution of the bendin... Read More about Explicit model for bending edge wave on an elastic orthotropic plate supported by the Winkler–Fuss foundation.

Elastic Surface Waves Induced by Internal Sources (2021)
Journal Article
Prikazchikov, D., Chevrychkina, A., Chorozoglou, A., & Khajiyeva, L. (2021). Elastic Surface Waves Induced by Internal Sources. Journal of Mathematical Sciences, 258, 545 - 552. https://doi.org/10.1007/s10958-021-05565-2

The paper is focused on the surface wave field induced by an internal time-harmonic point source embedded in the elastic half space. By using the superposition principle, we first analyze the disturbances caused by the embedded source in an unbounded... Read More about Elastic Surface Waves Induced by Internal Sources.

Explicit model for surface waves in a pre-stressed, compressible elastic half-space (2020)
Journal Article
Prikazchikov, D. (2020). Explicit model for surface waves in a pre-stressed, compressible elastic half-space. https://doi.org/10.26577/ijmph.2020.v11.i1.02

The paper is concerned with the derivation of the hyperbolic-elliptic asymptotic model for surface wave in a pre-stressed, compressible, elastic half-space, within the framework of plane-strain assumption. The consideration extends the existing metho... Read More about Explicit model for surface waves in a pre-stressed, compressible elastic half-space.

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.

Adhesive contact problems for a thin elastic layer: Asymptotic analysis and the JKR theory (2019)
Journal Article
Borodich, F. M., Galanov, B. A., Perepelkin, N. V., & Prikazchikov, D. A. (2019). Adhesive contact problems for a thin elastic layer: Asymptotic analysis and the JKR theory. Mathematics and Mechanics of Solids, 1405-1424. https://doi.org/10.1177/1081286518797378

Contact problems for a thin compressible elastic layer attached to a rigid support are studied. Assuming that the thickness of the layer is much less than the characteristic dimension of the contact area, a direct derivation of asymptotic relations f... Read More about Adhesive contact problems for a thin elastic layer: Asymptotic analysis and the JKR theory.

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.

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.

Asymptotic Theory for Rayleigh and Rayleigh-Type Waves (2017)
Book Chapter
Kaplunov, J., & Prikazchikov, D. A. (2017). Asymptotic Theory for Rayleigh and Rayleigh-Type Waves. In Advances in Applied Mechanics (1-106). Elsevier. https://doi.org/10.1016/bs.aams.2017.01.001

Explicit asymptotic formulations are derived for Rayleigh and Rayleigh-type interfacial and edge waves. The hyperbolic–elliptic duality of surface and interfacial waves is established, along with the parabolic–elliptic duality of the dispersive edge... Read More about Asymptotic Theory for Rayleigh and Rayleigh-Type Waves.