Julius Kaplunov's Outputs (89)

Low-Frequency Vibrations of a High-Contrast Orthotropic Lattice (2025)
Working Paper
Andrianov, I., Danishevskyy, V., & Kaplunov, J. Low-Frequency Vibrations of a High-Contrast Orthotropic Lattice

The study of long-wave propagation in lattices or in composite and layered structures is usually carried out using a single small parameter characterising the ratio of the wavelength to some characteristic size. Ratios of rigidity or density paramete... Read More about Low-Frequency Vibrations of a High-Contrast Orthotropic Lattice.

On the refined boundary condition at the edge of a thin elastic strip supported by a Winkler-type foundation under antiplane shear deformation (2024)
Journal Article
Prikazchikova, L., Nolde, E., Miszuris, W., & Kaplunov, J. (2024). On the refined boundary condition at the edge of a thin elastic strip supported by a Winkler-type foundation under antiplane shear deformation. International Journal of Engineering Science, 205, Article 104152. https://doi.org/10.1016/j.ijengsci.2024.104152

The derivation of the boundary conditions is the most challenging part of the asymptotic techniques underlying low-dimensional models for thin elastic structures. At the moment, these techniques do not take into consideration the effect of the enviro... Read More about On the refined boundary condition at the edge of a thin elastic strip supported by a Winkler-type foundation under antiplane shear deformation.

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.

Response of a thin coating of a porous elastic material whose generalised Young’s modulus depends on the density (2024)
Journal Article
Erbaş, B., Itskov, M., Kaplunov, J., & Rajagopal, K. R. (in press). Response of a thin coating of a porous elastic material whose generalised Young’s modulus depends on the density. Mathematics and Mechanics of Solids, https://doi.org/10.1177/10812865241286482

Mechanics of a thin elastic coating is analysed using nonlinear constitutive relations based on the concept of a density-dependent Young’s modulus. In contrast to previous considerations on the subject, the proposed framework does not assume weak non... Read More about Response of a thin coating of a porous elastic material whose generalised Young’s modulus depends on the density.

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.

Transverse Compression of a Thin Inhomogeneous Elastic Layer (2024)
Journal Article
Alzaidi, A. S. M., Kaplunov, J., Zupančič, B., & Nikonov, A. (in press). Transverse Compression of a Thin Inhomogeneous Elastic Layer. Mathematics, 12(16), Article 2502. https://doi.org/10.3390/math12162502

A 3D problem in linear elasticity is considered for a thin inhomogeneous layer subject to transverse compression. For the first time, the effect of arbitrary vertical inhomogeneity is elucidated. Two sets of boundary conditions along the faces of the... Read More about Transverse Compression of a Thin Inhomogeneous Elastic Layer.

Asymptotic Derivation of Consistent thin Shell Equations for a Fluid-Loaded Elastic Annulus (2024)
Journal Article
Yücel, H., Kaplunov, J., Ege, N., & Erbaş, B. (in press). Asymptotic Derivation of Consistent thin Shell Equations for a Fluid-Loaded Elastic Annulus. Journal of Applied Mechanics and Technical Physics, https://doi.org/10.1134/s0021894424020147

The classical time-harmonic plane strain problem for a fluid-loaded cylindrical elastic shell is revisited. The results of the low-frequency asymptotic analysis, including explicit formulae for eigenfrequencies, are presented. A refined version of th... Read More about Asymptotic Derivation of Consistent thin Shell Equations for a Fluid-Loaded Elastic Annulus.

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.

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

<jats:title>Abstract</jats:title><jats:p>The 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-... 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.