All Outputs (65)

Elastic waves in periodically anisotropic heterogeneous media: bridge the gap between rigorous and phenomenological approaches (2024)
Conference Proceeding
Andrianov, I., Danishevskyy, V., Kaplunov, J., & Kirichek, Y. (2024). Elastic waves in periodically anisotropic heterogeneous media: bridge the gap between rigorous and phenomenological approaches. . https://doi.org/10.1088/1742-6596/2647/25/252034

Despite the growing capacity of computer codes, analytical solutions are still of great interest. As a rule, they are based on certain asymptotic approximations. In our work, we use a two-scale asymptotic procedure. Anti-plane shear waves in a layere... Read More about Elastic waves in periodically anisotropic heterogeneous media: bridge the gap between rigorous and phenomenological approaches.

Transverse compression of a thin elastic disc (2024)
Journal Article
Alzaidi, A. S. M., Kaplunov, J., Nikonov, A., & Zupančič, B. (2024). Transverse compression of a thin elastic disc. Zeitschrift für angewandte Mathematik und Physik, 75(3), Article 116. https://doi.org/10.1007/s00033-024-02238-3

The mathematical formulations for transverse compression of a thin elastic disc are considered, including various boundary conditions along the faces of the disc. The mixed boundary conditions corresponding to the loading by normal stresses in absenc... Read More about Transverse compression of a thin elastic disc.

A revisit to the plane problem for low-frequency acoustic scattering by an elastic cylindrical shell (2024)
Journal Article
Yücel, H., Ege, N., Erbaş, B., & Kaplunov, J. (in press). A revisit to the plane problem for low-frequency acoustic scattering by an elastic cylindrical shell. Mathematics and Mechanics of Solids, https://doi.org/10.1177/10812865241233737

The proposed revisit to a classical problem in fluid–structure interaction is due to an interest in the analysis of the narrow resonances corresponding to a low-frequency fluid-borne wave, inspired by modeling and design of metamaterials. In this cas... Read More about A revisit to the plane problem for low-frequency acoustic scattering by an elastic cylindrical shell.

Elastic bending and transverse compression of a thin plate with density-dependent Young’s modulus (2024)
Journal Article
Erbaş, B., Kaplunov, J., & Rajagopal, K. R. (2024). Elastic bending and transverse compression of a thin plate with density-dependent Young’s modulus. International Journal of Non-Linear Mechanics, 160, Article 104651. https://doi.org/10.1016/j.ijnonlinmec.2024.104651

The equilibrium equation governing the plane strain static problem for a thin elastic layer is studied using asymptotic analysis for a material with generalized Young’s modulus weakly dependent on the mass density. Within the context of the adopted s... Read More about Elastic bending and transverse compression of a thin plate with density-dependent Young’s modulus.

The Lowest Eigenfrequencies of an Immersed Thin Elastic Cylindrical Shell (2023)
Book Chapter
Yücel, H., Erbaş, B., Ege, N., & Kaplunov, J. (2023). The Lowest Eigenfrequencies of an Immersed Thin Elastic Cylindrical Shell. In Advances in Linear and Nonlinear Continuum and Structural Mechanics (559-571). Springer. https://doi.org/10.1007/978-3-031-43210-1_31

The plane strain time-harmonic motion of an immersed cylindrical elastic shell is considered. The revisit to this classical problem is motivated by modern technical applications, including the investigation of low-frequency band gaps arising at acous... Read More about The Lowest Eigenfrequencies of an Immersed Thin Elastic Cylindrical Shell.

A hierarchy of asymptotic models for a fluid-loaded elastic layer (2023)
Journal Article
Kaplunov, J., Prikazchikova, L., & Shamsi, S. (in press). A hierarchy of asymptotic models for a fluid-loaded elastic layer. Mathematics and Mechanics of Solids, https://doi.org/10.1177/10812865231201573

A hierarchy of asymptotic models governing long-wave low-frequency in-plane motion of a fluid-loaded elastic layer is established. In contrast to a layer with traction-free faces, modelled by Neumann boundary conditions, a fluid-loaded one assumes mo... Read More about A hierarchy of asymptotic models for a fluid-loaded elastic layer.

Discovering asymptotic expansions for problems in mechanics using symbolic regression (2023)
Journal Article
Abdusalamov, R., Kaplunov, J., & Itskov, M. (in press). Discovering asymptotic expansions for problems in mechanics using symbolic regression. Mechanics Research Communications, 133, Article 104197. https://doi.org/10.1016/j.mechrescom.2023.104197

Recently, symbolic regression (SR) has demonstrated its efficiency for discovering basic governing relations in physical systems. A major impact can be potentially achieved by coupling symbolic regression with asymptotic methodolog... Read More about Discovering asymptotic expansions for problems in mechanics using symbolic regression.

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.

2D Asymptotic Analysis of a Thin Elastic Beam with Density-Dependent Generalized Young’s Modulus (2023)
Book Chapter
Erbaş, B., Kaplunov, J., & Rajagopal, K. R. (2023). 2D Asymptotic Analysis of a Thin Elastic Beam with Density-Dependent Generalized Young’s Modulus. In Mechanics of Heterogeneous Materials (501-513). Springer. https://doi.org/10.1007/978-3-031-28744-2_22

The elastic equilibrium of a thin elastic beam is studied using asymptotic analysis starting from a 2D formulation within the context of plane elasticity. The aim of the paper is to elucidate the influence of density and hence small volume strain of... Read More about 2D Asymptotic Analysis of a Thin Elastic Beam with Density-Dependent Generalized Young’s Modulus.

Asymptotic corrections to the low-frequency theory for a cylindrical elastic shell (2023)
Journal Article
Kaplunov. (2023). Asymptotic corrections to the low-frequency theory for a cylindrical elastic shell. Zeitschrift für Angewandte Mathematik und Physik, https://doi.org/10.1007/s00033-022-01933-3

AbstractThe general scaling underlying the asymptotic derivation of 2D theory for thin shells from the original equations of motion in 3D elasticity fails for cylindrical shells due to the cancellation of the leading-order terms in the geometric rela... Read More about Asymptotic corrections to the low-frequency theory for a cylindrical elastic shell.

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.

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.

Dispersion of the Bending Wave in a Fluid-loaded Elastic Layer (2022)
Book Chapter
Kaplunov, J., Prikazchikova, L., & Shamsi, S. (2022). Dispersion of the Bending Wave in a Fluid-loaded Elastic Layer. In Advances in Solid and Fracture Mechanics (127 - 134). (1). Springer. https://doi.org/10.1007/978-3-031-18393-5_8

A plane strain problem is considered for an elastic layer immersed into a compressible fluid. The dispersion relation for anti-symmetric waves is studied. The associated three-term long-wave low-frequency expansion for a fluid-borne bending wave is d... Read More about Dispersion of the Bending Wave in a Fluid-loaded Elastic Layer.

Asymptotic analysis of 3D dynamic equations in linear elasticity for a thin layer resting on a Winkler foundation (2022)
Journal Article
Kaplunov. (2022). Asymptotic analysis of 3D dynamic equations in linear elasticity for a thin layer resting on a Winkler foundation. IMA Journal of Applied Mathematics, 707 - 721. https://doi.org/10.1093/imamat/hxac023

Abstract A 3D dynamic problem for a thin elastic layer resting on a Winkler foundation is considered. The stiffness of the layer is assumed to be much greater than that of the foundation in order to allow low-frequency bending motion. The leading lon... Read More about Asymptotic analysis of 3D dynamic equations in linear elasticity for a thin layer resting on a Winkler foundation.

The effect of contact conditions on the performance of flexural seismic metasurfaces (2022)
Journal Article
Alzaidi, A. S., Kaplunov, J., Prikazchikova, L., Wootton, P., & Nikonov, A. (2022). The effect of contact conditions on the performance of flexural seismic metasurfaces. Zeitschrift für angewandte Mathematik und Physik, 73, Article 194. https://doi.org/10.1007/s00033-022-01822-9

AbstractPlane-strain motion of a flexural seismic metasurface in the form of a regular array of thin Kirchhoff plates attached to the surface of an elastic half-space is analysed. Two types of contact conditions, including simply supported plates and... Read More about The effect of contact conditions on the performance of flexural seismic metasurfaces.

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

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 differential mo... Read More about On non-locally elastic Rayleigh wave.

Asymptotic derivation of 2D dynamic equations of motion for transversely inhomogeneous elastic plates (2022)
Journal Article
Kaplunov. (2022). Asymptotic derivation of 2D dynamic equations of motion for transversely inhomogeneous elastic plates. International Journal of Engineering Science, https://doi.org/10.1016/j.ijengsci.2022.103723

The 3D dynamic equations in elasticity for a thin transversely inhomogeneous plate are subject to asymptotic analysis over the low-frequency range. The leading and first order approximations are derived. The former is given by a biharmonic equation o... Read More about Asymptotic derivation of 2D dynamic equations of motion for transversely inhomogeneous elastic plates.

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.

Homogenized equation of second-order accuracy for conductivity of laminates (2022)
Journal Article
Kaplunov, J., Prikazchikova, L., & Panasenko, G. (2022). Homogenized equation of second-order accuracy for conductivity of laminates. Applicable Analysis, 101(11), 1 - 9. https://doi.org/10.1080/00036811.2022.2027387

The high order homogenization techniques potentially generate the so-called infinite order homogenized equations. Since long ago, the coefficients at higher order derivatives in these equations have been calculated within various refined theories for... Read More about Homogenized equation of second-order accuracy for conductivity of laminates.