All Outputs (52)

Two-Parametric Analysis of a Semi-Infinite Three-Layered High-Contrast Elastic Strip Under Antiplane Shear Deformation (2024)
Book Chapter
Chernomorets, I., Kaplunov, J., & Prikazchikov, D. (2024). Two-Parametric Analysis of a Semi-Infinite Three-Layered High-Contrast Elastic Strip Under Antiplane Shear Deformation. In Selected Problems of Solid Mechanics and Solving Methods (99-109). Springer. https://doi.org/10.1007/978-3-031-54063-9_7

Antiplane shear of a symmetric three-layered elastic semi-strip under the self-equilibrated edge load is studied. The arbitrary ratios of thickness and stiffness are considered, with emphasis on high-contrast scenario; in doing so, two aforementioned... Read More about Two-Parametric Analysis of a Semi-Infinite Three-Layered High-Contrast Elastic Strip Under Antiplane Shear Deformation.

Seismic metasurface on an orthorhombic elastic half-space (2023)
Journal Article
Prikazchikov, D., Sabirova, R., & Wootton, P. T. (in press). Seismic metasurface on an orthorhombic elastic half-space. Science Progress, 106(4), https://doi.org/10.1177/00368504231206320

The article is studying a seismic meta-surface in the case of an oscillatory system arranged on the surface of an orthorhombic elastic half-space. The approach is based on the asymptotic hyperbolic–elliptic formulation for the Rayleigh wave excited b... Read More about Seismic metasurface on an orthorhombic elastic half-space.

Degenerated Boundary Layers and Long-Wave Low-Frequency Motion in High-Contrast Elastic Laminates (2023)
Journal Article
Aghalovyan, L. A., Ghulghazaryan, L. G., Kaplunov, J., & Prikazchikov, D. (in press). Degenerated Boundary Layers and Long-Wave Low-Frequency Motion in High-Contrast Elastic Laminates. Mathematics, 11(18), Article 3905. https://doi.org/10.3390/math11183905

The effect of high contrast on the multiscale behaviour of elastic laminates is studied. Mathematical modelling in this area is of significant interest for a variety of modern applications, including but not limited to advanced sandwich structures an... Read More about Degenerated Boundary Layers and Long-Wave Low-Frequency Motion in High-Contrast Elastic Laminates.

Three-Dimensional Dynamic Analysis of Layered Elastic Shells (2023)
Journal Article
Aghalovyan, L. A., Ghulghazaryan, L. G., Kaplunov, J. D., & Prikazchikov, D. A. (2023). Three-Dimensional Dynamic Analysis of Layered Elastic Shells. Journal of Mathematical Sciences, 273(6), 999-1015. https://doi.org/10.1007/s10958-023-06560-5

Three-dimensional dynamic problem for a layered orthotropic elastic shell with free upper face is considered. The interfaces between the layers are assumed to be in perfect contact and the displacements of one of the interfaces are prescribed. A long... Read More about Three-Dimensional Dynamic Analysis of Layered Elastic Shells.

On a Hyperbolic Equation for the Rayleigh Wave (2023)
Journal Article
Kaplunov, J. D., Prikazchikov, D. A., & Sabirova, R. F. (2023). On a Hyperbolic Equation for the Rayleigh Wave. Доклады Академии Наук / Doklady Physics, 67(10), 424-427. https://doi.org/10.1134/S1028335822100056

A 1D hyperbolic equation is derived for the Rayleigh wave induced by prescribed surface loading. The wave operator turns out to be independent of the vertical coordinate, which appears only in the right hand side of the equation as a parameter within... Read More about On a Hyperbolic Equation for the Rayleigh Wave.

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)
Journal Article
Aney, S., Schestakow, M., Prikazchikova, L., Milow, B., Prikazchikov, D., Kaplunov, J., …Rege, A. (2023). Cellulose-Aerogele als multifunktionale und nachhaltige Alternativen für Flugzeugkabinenelemente. https://doi.org/10.25967/570245

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.

Preface to "Advances in mathematical theory of thin structures" in memory of Professor Petr E. Tovstik (2022)
Journal Article
Bauer, S. M., Mikhasev, G., & Prikazchikov, D. A. (2022). Preface to "Advances in mathematical theory of thin structures" in memory of Professor Petr E. Tovstik. Mathematics and Mechanics of Solids, 27(9), 1635-1637. https://doi.org/10.1177/10812865221108284

On The Derivation Of A String Equation (2022)
Journal Article
Kaplunov, J., & Prikazchikov, D. A. (in press). On The Derivation Of A String Equation. Natsional'naya Akademiya Nauk Armenii. Izvestiya. Seriya Mekhanika / Proceedings of NAS RA: Mechanics, 75(1), 163-168. https://doi.org/10.54503/0002-3051-2022.75.1-2-163

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 Rayleigh wave field induced by surface stresses under the effect of gravity (2022)
Journal Article
Prikazchikov, D., & Mubaraki, A. (2022). On Rayleigh wave field induced by surface stresses under the effect of gravity. Mathematics and Mechanics of Solids, 27(9), https://doi.org/10.1177/10812865221080550

The paper is concerned with development of the asymptotic formulation for surface wave field induced by vertical surface stress under the effect of gravity in the short-wave region. The approach relies on the methodology of hyperbolic-elliptic models... Read More about On Rayleigh wave field induced by surface stresses under the effect of gravity.

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.

Dynamic Sliding Contact for a Thin Elastic Layer (2022)
Book Chapter
Kaplunov, J., Prikazchikov, D. A., & Savšek, T. (2022). Dynamic Sliding Contact for a Thin Elastic Layer. In Recent Approaches in the Theory of Plates and Plate-Like Structures (103-114). Springer. https://doi.org/10.1007/978-3-030-87185-7_9

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 on an Elastic Half-Space Coated by a Thin Vertically Inhomogeneous Layer (2021)
Book Chapter
Mubaraki, A., Prikazchikov, D., & Kudaibergenov, A. (2022). Explicit Model for Surface Waves on an Elastic Half-Space Coated by a Thin Vertically Inhomogeneous Layer. . Springer International Publishing. https://doi.org/10.1007/978-3-030-77306-9_23

Near-resonant regimes of the moving load on a pre-stressed incompressible elastic half-space (2021)
Journal Article
Kudaibergenov, A., Kudaibergenov, A., & Prikazchikov, D. (2021). Near-resonant regimes of the moving load on a pre-stressed incompressible elastic half-space. Acta Mechanica et Automatica, 15(1), 30-36. https://doi.org/10.2478/ama-2021-0005

The article is concerned with the analysis of the problem for a concentrated line load moving at a constant speed along the surface of a pre-stressed, incompressible, isotropic elastic half-space, within the framework of the plane-strain assumption.... Read More about Near-resonant regimes of the moving load on a pre-stressed incompressible elastic half-space.

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.