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Multimode long-wave approximation for a viscoelastic coating subject to antiplane shear (2024)
Journal Article
Erbaş, B., Itskov, M., Kaplunov, J., & Prikazchikov, D. (2024). Multimode long-wave approximation for a viscoelastic coating subject to antiplane shear. Zeitschrift für angewandte Mathematik und Physik, 75(6), Article 234. https://doi.org/10.1007/s00033-024-02382-w

A general asymptotic approach involving multimode long-wave approximations is illustrated by a 2D time-harmonic scalar problem for the dynamic antiplane shear of a viscoelastic coating. For the first time, a 1D equation of motion with the coefficient... Read More about Multimode long-wave approximation for a viscoelastic coating subject to antiplane shear.

Low-frequency propagating and evanescent waves in strongly inhomogeneous sandwich plates (2024)
Journal Article
Prikazchikova, L., Rege, A., Kaplunov, J., & Prikazchikov, D. (2024). Low-frequency propagating and evanescent waves in strongly inhomogeneous sandwich plates. Zeitschrift für angewandte Mathematik und Physik, 75, 1-14. https://doi.org/10.1007/s00033-024-02347-z

The paper aims at studying dispersion of elastic waves in a sandwich plate with the parameters, characteristic of aerogel core and hard skin layers, typical for aerospace applications including optimal design of fuselage structural components. The pr... Read More about Low-frequency propagating and evanescent waves in strongly inhomogeneous sandwich plates.

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.

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
Mubaraki, A., & Prikazchikov, D. (2022). On Rayleigh wave field induced by surface stresses under the effect of gravity. Mathematics and Mechanics of Solids, 27(9), 1771-1782. 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.

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.

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.

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.