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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.

Low-frequency vibrations of a thin-walled functionally graded cylinder (plane strain problem) (2022)
Journal Article
Ege, N., Erbas, B., Kaplunov, J., & Noori, N. (2022). Low-frequency vibrations of a thin-walled functionally graded cylinder (plane strain problem). Mechanics of Advanced Materials and Structures, https://doi.org/10.1080/15376494.2022.2028948

Low frequency vibrations of a thin walled functionally graded cylinder are considered within the plane strain framework. The dynamic relations in elasticity are subject to asymptotic analysis over cylinder cross section resulting in a consistent appr... Read More about Low-frequency vibrations of a thin-walled functionally graded cylinder (plane strain problem).

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.

Bridging Waves on a Membrane: An Approach to Preserving Wave Patterns (2021)
Book Chapter
Wootton, P., & Kaplunov, J. Bridging Waves on a Membrane: An Approach to Preserving Wave Patterns. In Modern Trends in Structural and Solid Mechanics 2: Vibrations (203-229). Wiley. https://doi.org/10.1002/9781119831860.ch9

This chapter introduces a novel metamaterial intended to “bridge” a gap between two membranes using a periodic array of strings, with the aim of identically reproducing an incident wave form on the other side of the void. It also introduces an elasti... Read More about Bridging Waves on a Membrane: An Approach to Preserving Wave Patterns.

Antiplane shear of an asymmetric sandwich plate (2021)
Journal Article
Prikazchikova, L., Kaplunov, J., & Alkinidri, M. (2021). Antiplane shear of an asymmetric sandwich plate. Continuum Mechanics and Thermodynamics, 33, 1247–1262. https://doi.org/10.1007/s00161-021-00969-6

AbstractAn asymmetric three-layered laminate with prescribed stresses along the faces is considered. The outer layers are assumed to be much stiffer than the inner one. The focus is on long-wave low-frequency anti-plane shear. Asymptotic analysis of... Read More about Antiplane shear of an asymmetric sandwich plate.

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.

Rayleigh-type waves on a coated elastic half-space with a clamped surface (2019)
Journal Article
Kaplunov, & Prikazchikov. (2019). Rayleigh-type waves on a coated elastic half-space with a clamped surface. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, https://doi.org/10.1098/rsta.2019.0111

Elastodynamics of a half-space coated by a thin soft layer with a clamped upper face is considered. The focus is on the analysis of localised waves that do not exist on a clamped homogeneous halfspace. Non-traditional effective boundary conditions a... Read More about Rayleigh-type waves on a coated elastic half-space with a clamped surface.

Composite dynamic models for periodically heterogeneous media (2019)
Journal Article
Kaplunov. (2019). Composite dynamic models for periodically heterogeneous media. Mathematics and Mechanics of Solids, 2663-2693. https://doi.org/10.1177/1081286518776704

Propagation of elastic waves through discrete and continuous periodically heterogeneous media is studied. A two-scale asymptotic procedure allows us to derive macroscopic dynamic equations applicable at frequencies close to the resonant frequencies o... Read More about Composite dynamic models for periodically heterogeneous media.

The edge bending wave on a plate reinforced by a beam (L). (2019)
Journal Article
Kaplunov. (2019). The edge bending wave on a plate reinforced by a beam (L). Journal of the Acoustical Society of America, 1061 - ?. https://doi.org/10.1121/1.5121315

The edge bending wave on a thin isotropic semi-infinite plate reinforced by a beam is considered within the framework of the classical plate and beam theories. The boundary conditions at the plate edge incorporate both dynamic bending and twisting of... Read More about The edge bending wave on a plate reinforced by a beam (L)..

An asymptotic hyperbolic-elliptic model for flexural-seismic metasurfaces. (2019)
Journal Article
Wootton, P., Kaplunov, J., & Colquitt, D. (2019). An asymptotic hyperbolic-elliptic model for flexural-seismic metasurfaces. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475(2227), https://doi.org/10.1098/rspa.2019.0079

We consider a periodic array of resonators, formed from Euler-Bernoulli beams, attached to the surface of an elastic half-space. Earlier studies of such systems have concentrated on compressional resonators. In this paper, we consider the effect of t... Read More about An asymptotic hyperbolic-elliptic model for flexural-seismic metasurfaces..

A composite hyperbolic equation for plate extension (2019)
Journal Article
Kaplunov. (2019). A composite hyperbolic equation for plate extension. Mechanics Research Communications, 64-67. https://doi.org/10.1016/j.mechrescom.2019.06.008

A fourth-order inhomogeneous hyperbolic equation modeling the symmetric motion of a thin elastic plate subject to shear stresses prescribed along its faces is derived. The shortened forms of this equation govern the quasi-front, i.e. dispersive wave-... Read More about A composite hyperbolic equation for plate extension.

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.

The lowest vibration spectra of multi-component structures with contrast material properties (2019)
Journal Article
Prikazchikov, & Kaplunov. (2019). The lowest vibration spectra of multi-component structures with contrast material properties. Journal of Sound and Vibration, 132 -147. https://doi.org/10.1016/j.jsv.2019.01.013

The paper is concerned with the lowest vibration modes of multi-component rods and cylinders with alternating high contrast material properties of the components. It is demonstrated that these modes correspond to almost rigid body motions of the “sti... Read More about The lowest vibration spectra of multi-component structures with contrast material properties.

Dispersion of elastic waves in a layer interacting with a Winkler foundation (2018)
Journal Article
Kaplunov. (2018). Dispersion of elastic waves in a layer interacting with a Winkler foundation. Journal of the Acoustical Society of America, https://doi.org/10.1121/1.5079640

ABSTRACT Dispersion of plane harmonic waves in an elastic layer interacting with a one- or two-sided Winkler foundation is analyzed. The long-wave low-frequency polynomial approximations of the full transcendental dispersion relations are derived fo... Read More about Dispersion of elastic waves in a layer interacting with a Winkler foundation.

Asymptotic analysis of an anti-plane dynamic problem for a three-layered strongly inhomogeneous laminate (2018)
Journal Article
Prikazchikova, L., Ece Aydın, Y., Erbaş, B., & Kaplunov, J. (2018). Asymptotic analysis of an anti-plane dynamic problem for a three-layered strongly inhomogeneous laminate. Mathematics and Mechanics of Solids, 25(1), 3-16. https://doi.org/10.1177/1081286518790804

Anti-plane dynamic shear of a strongly inhomogeneous dynamic laminate with traction-free faces is analysed. Two types of contrast are considered, including those for composite structures with stiff thick or thin outer layers. In both cases, the valu... Read More about Asymptotic analysis of an anti-plane dynamic problem for a three-layered strongly inhomogeneous laminate.

Composite wave models for elastic plates (2018)
Journal Article
Kaplunov. (2018). Composite wave models for elastic plates. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, https://doi.org/10.1098/rspa.2018.0103

The long-term challenge of formulating an asymptotically motivated wave theory for elastic plates is addressed. Composite two-dimensional models merging the leading or higher-order parabolic equations for plate bending and the hyperbolic equation for... Read More about Composite wave models for elastic plates.

An asymptotic higher-order theory for rectangular beams (2018)
Journal Article
Nolde, E., Pichugin, A., & Kaplunov, J. (2018). An asymptotic higher-order theory for rectangular beams. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474(2214), https://doi.org/10.1098/rspa.2018.0001

A direct asymptotic integration of the full three-dimensional problem of elasticity is employed to derive a consistent governing equation for a beam with the rectangular cross section. The governing equation is consistent in the sense that it has the... Read More about An asymptotic higher-order theory for rectangular beams.

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.

Dispersion of elastic waves in laminated glass (2017)
Journal Article
Kaplunov, J., Prikazchikov, D., & Prikazchikova, L. (2017). Dispersion of elastic waves in laminated glass. Procedia Engineering, 199, 1489 -1494. https://doi.org/10.1016/j.proeng.2017.09.428

Elastic sandwich-type structures with high-contrast material and geometrical properties have numerous applications in modern engineering, including, in particular, laminated glass, photovoltaic panels, precipitator plates in gas filters, etc. Multi-p... Read More about Dispersion of elastic waves in laminated glass.

On surface wave fields arising in soil-structure interaction problems (2017)
Journal Article
Ege, N., Erbas, B., Chorozoglou, A., Kaplunov, J., & Prikazchikov, D. A. (2017). On surface wave fields arising in soil-structure interaction problems. Procedia Engineering, 199, 2366 -2371. https://doi.org/10.1016/j.proeng.2017.09.253

Abstract The paper aims at generalization of the specialized formulation, originally developed for the surface wave fields induced by prescribed surface stresses. We extend this formulation to soil-structure interaction problems with unknown contact... Read More about On surface wave fields arising in soil-structure interaction problems.

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.

A robust approach for analysing dispersion of elastic waves in an orthotropic cylindrical shell (2017)
Journal Article
Kaplunov. (2017). A robust approach for analysing dispersion of elastic waves in an orthotropic cylindrical shell. Journal of Sound and Vibration, 23 - 35. https://doi.org/10.1016/j.jsv.2017.04.028

Dispersion of elastic waves in a thin orthotropic cylindrical shell is considered, within the framework of classical 2D Kirchhoff-Love theory. In contrast to direct multi-parametric analysis of the lowest propagating modes, an alternative robust appr... Read More about A robust approach for analysing dispersion of elastic waves in an orthotropic cylindrical shell.

A nonlocal asymptotic theory for thin elastic plates (2017)
Journal Article
Kaplunov. (2017). A nonlocal asymptotic theory for thin elastic plates. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, https://doi.org/10.1098/rspa.2017.0249

The three-dimensional dynamic non-local elasticity equations for a thin plate are subject to asymptotic analysis assuming the plate thickness to be much greater than a typical microscale size. The integral constitutive relations, incorporating the va... Read More about A nonlocal asymptotic theory for thin elastic plates.

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.

Dispersion of elastic waves in a strongly inhomogeneous three-layered plate (2017)
Journal Article
Prikazchikov, D., Kaplunov, J., & Prikazchikova, L. (2017). Dispersion of elastic waves in a strongly inhomogeneous three-layered plate. International Journal of Solids and Structures, 113-114, 169-179. https://doi.org/10.1016/j.ijsolstr.2017.01.042

Elastic wave propagation in a three-layered plate with high-contrast mechanical and geometric properties of the layers is analysed. Four specific types of contrast arising in engineering practice, including the design of stiff and lightweight structu... Read More about Dispersion of elastic waves in a strongly inhomogeneous three-layered plate.

Edge bending wave on a thin elastic plate resting on a Winkler foundation (2016)
Journal Article
Kaplunov, J., Prikazchikov, D., & Rogerson, G. (2016). Edge bending wave on a thin elastic plate resting on a Winkler foundation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472(2190), https://doi.org/10.1098/rspa.2016.0178

This paper is concerned with elucidation of the general properties of the bending edge wave in a thin linearly elastic plate that is supported by a Winkler foundation. A homogeneous wave of arbitrary profile is considered, and represented in terms of... Read More about Edge bending wave on a thin elastic plate resting on a Winkler foundation.

Vibrations of an elastic cylindrical shell near the lowest cut-off frequency (2016)
Journal Article
Kaplunov, J., Manevitch, L., & Smirnov, V. (2016). Vibrations of an elastic cylindrical shell near the lowest cut-off frequency. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472(2189), https://doi.org/10.1098/rspa.2015.0753

A new asymptotic approximation of the dynamic equations in the two-dimensional classical theory of thin-elastic shells is established for a circular cylindrical shell. It governs long wave vibrations in the vicinity of the lowest cut-off frequency. A... Read More about Vibrations of an elastic cylindrical shell near the lowest cut-off frequency.

Multi-parametric analysis of strongly inhomogeneous periodic waveguides with internal cutoff frequencies (2016)
Journal Article
Kaplunov. (2016). Multi-parametric analysis of strongly inhomogeneous periodic waveguides with internal cutoff frequencies. Mathematical Methods in the Applied Sciences, 3381-3392. https://doi.org/10.1002/mma.3900

In this paper, we consider periodic waveguides in the shape of a inhomogeneous string or beam partially supported by a uniform elastic Winkler foundation. A multi-parametric analysis is developed to take into account the presence of internal cutoff f... Read More about Multi-parametric analysis of strongly inhomogeneous periodic waveguides with internal cutoff frequencies.

Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects (2016)
Journal Article
Kaplunov. (2016). Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, https://doi.org/10.1098/rspa.2015.0800

The dynamic response of a homogeneous half-space, with a traction-free surface, is considered within the framework of non-local elasticity. The focus is on the dominant effect of the boundary layer on overall behaviour. A typical wavelength is assume... Read More about Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects.

Multi-parametric analysis of the lowest natural frequencies of strongly inhomogeneous elastic rods (2015)
Journal Article
Prikazchikov, D., Kaplunov, J., & Sergushova, O. (2016). Multi-parametric analysis of the lowest natural frequencies of strongly inhomogeneous elastic rods. Journal of Sound and Vibration, 366, 264-276. https://doi.org/10.1016/j.jsv.2015.12.008

The results of a multi-parametric analysis of the near-rigid body motions of a three-component strongly inhomogeneous elastic rod are presented. It is demonstrated that the values of the associated lowest natural frequencies tend to zero at large/sma... Read More about Multi-parametric analysis of the lowest natural frequencies of strongly inhomogeneous elastic rods.

Celebrating the Centenary of Timoshenko's Study of Effects of Shear Deformation and Rotary Inertia (2015)
Journal Article
Elishakoff, I., Kaplunov, J., & Nolde, E. (2015). Celebrating the Centenary of Timoshenko's Study of Effects of Shear Deformation and Rotary Inertia. Applied Mechanics Reviews, 67(6), Article ARTN 060802. https://doi.org/10.1115/1.4031965

This study revisits Timoshenko beam theory (TBT). It discusses at depth a more consistent and simpler governing differential equation. The so-called second spectrum is also addressed. Then, we provide the asymptotic justification of the aforementione... Read More about Celebrating the Centenary of Timoshenko's Study of Effects of Shear Deformation and Rotary Inertia.

The edge waves on a Kirchhoff plate bilaterally supported by a two-parameter elastic foundation (2015)
Journal Article
Kaplunov. (2015). The edge waves on a Kirchhoff plate bilaterally supported by a two-parameter elastic foundation. Journal of Vibration and Control, 2014-2022. https://doi.org/10.1177/1077546315606838

In this paper, the bending waves propagating along the edge of a semi-infinite Kirchhoff plate resting on a two-parameter Pasternak elastic foundation are studied. Two geometries of the foundation are considered: either it is infinite or it is semi-i... Read More about The edge waves on a Kirchhoff plate bilaterally supported by a two-parameter elastic foundation.

Low-frequency perturbations of rigid body motions of a viscoelastic inhomogeneous bar (2015)
Journal Article
Kaplunov. (2015). Low-frequency perturbations of rigid body motions of a viscoelastic inhomogeneous bar. Mechanics of Time-Dependent Materials, 135 -151. https://doi.org/10.1007/s11043-015-9256-x

This paper deals with a low-frequency analysis of a viscoelastic inhomogeneous bar subject to end loads. The spatial variation of the problem parameters is taken into consideration. Explicit asymptotic corrections to the conventional equations of rig... Read More about Low-frequency perturbations of rigid body motions of a viscoelastic inhomogeneous bar.

Anti-plane shear waves in a fibre-reinforced composite with a non-linear imperfect interface (2015)
Journal Article
Danishevs׳kyy, V. V., Kaplunov, J. D., & Rogerson, G. A. (2015). Anti-plane shear waves in a fibre-reinforced composite with a non-linear imperfect interface. International Journal of Non-Linear Mechanics, 76, 223 -232. https://doi.org/10.1016/j.ijnonlinmec.2014.12.009

The propagation of non-linear elastic anti-plane shear waves in a unidirectional fibre-reinforced composite material is studied. A model of structural non-linearity is considered, for which the non-linear behaviour of the composite solid is caused by... Read More about Anti-plane shear waves in a fibre-reinforced composite with a non-linear imperfect interface.

The near-resonant regimes of a moving load in a three-dimensional problem for a coated elastic half-space (2014)
Journal Article
Erbaş, B., Kaplunov, J., Prikazchikov, D. A., & Şahin, O. (2014). The near-resonant regimes of a moving load in a three-dimensional problem for a coated elastic half-space. Mathematics and Mechanics of Solids, 22(1), https://doi.org/10.1177/1081286514555451

This paper deals with the three-dimensional analysis of the near-resonant regimes of a point load, moving steadily along the surface of a coated elastic half-space. The approach developed relies on a specialized hyperbolic–elliptic formulation for th... Read More about The near-resonant regimes of a moving load in a three-dimensional problem for a coated elastic half-space.

The edge wave on an elastically supported Kirchhoff plate (2014)
Journal Article
Kaplunov, J., Prikazchikov, D. A., Rogerson, G. A., & Lashab, M. I. (2014). The edge wave on an elastically supported Kirchhoff plate. Journal of the Acoustical Society of America, 136(4), 1487 - 1490. https://doi.org/10.1121/1.4894795

This Letter deals with an analysis of bending edge waves propagating along the free edge of a Kirchhoff plate supported by a Winkler foundation. The presence of a foundation leads to a non-zero cut-off frequency for this wave, along with a local mini... Read More about The edge wave on an elastically supported Kirchhoff plate.

Long-wave asymptotic theories: the connection between functionally graded waveguides and periodic media (2014)
Journal Article
Kaplunov. (2014). Long-wave asymptotic theories: the connection between functionally graded waveguides and periodic media. Wave Motion, 581 - 588. https://doi.org/10.1016/j.wavemoti.2013.09.007

This article explores the deep connections that exist between the mathematical representations of dynamic phenomena in functionally graded waveguides and those in periodic media. These connections are at their most obvious for low-frequency and long-... Read More about Long-wave asymptotic theories: the connection between functionally graded waveguides and periodic media.