Outputs (51)

Seismic metasurface on an orthorhombic elastic half-space (2023)
Journal Article

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

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

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

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

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

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

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.

Preface to "Advances in mathematical theory of thin structures" in memory of Professor Petr E. Tovstik (2022)
Journal Article

On The Derivation Of A String Equation (2022)
Journal Article

Elastodynamics of a coated half-space under a sliding contact (2022)
Journal Article

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

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

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

Explicit model for bending edge wave on an elastic orthotropic plate supported by the Winkler–Fuss foundation (2021)
Journal Article

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

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

Near-resonant regimes of the moving load on a pre-stressed incompressible elastic half-space (2021)
Journal Article

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

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

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

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

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

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.

Adhesive contact problems for a thin elastic layer: Asymptotic analysis and the JKR theory (2019)
Journal Article

Contact problems for a thin compressible elastic layer attached to a rigid support are studied. Assuming that the thickness of the layer is much less than the characteristic dimension of the contact area, a direct derivation of asymptotic relations f... Read More about Adhesive contact problems for a thin elastic layer: Asymptotic analysis and the JKR theory.

Elastic contact of a stiff thin layer and a half-space (2019)
Journal Article

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

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.

Asymptotic strategy for matching homogenized structures. Conductivity problem (2018)
Journal Article

The paper is concerned with application of the homogenization theory to bodies containing macroinhomogeneities or bodies, parts of which cannot be homogenized (partial homogenization). This situation arises, in particular, for problems of joining hom... Read More about Asymptotic strategy for matching homogenized structures. Conductivity problem.

Hyperbolic-elliptic model for surface wave in a pre-stressed incompressible elastic half-space (2018)
Journal Article

The paper aims at derivation of the asymptotic model for surface wave propagating in a pre-stressed incompressible elastic half-space, subject to prescribed surface loading. The approach relies on the slow-time perturbation procedure, extending the p... Read More about Hyperbolic-elliptic model for surface wave in a pre-stressed incompressible elastic half-space.

On Higher Order Effective Boundary Conditions for a Coated Elastic Half-Space (2018)
Book Chapter

Free vibrations of nonlocally elastic rods (2018)
Journal Article

Several of the Eringen’s nonlocal stress models, including two-phase and purely nonlocal integral models, along with the simplified differential model, are studied in case of free longitudinal vibrations of a nanorod, for various types of boundary... Read More about Free vibrations of nonlocally elastic rods.

Justification and refinement of Winkler-Fuss hypothesis (2018)
Journal Article

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.

Explicit formulation for the Rayleigh wave field induced by surface stresses in an orthorhombic half-plane (2018)
Journal Article

We develop an explicit asymptotic model for the Rayleigh wave field arising in case of stresses prescribed on the surface of an orthorhombic elastic half-plane. The model consists of an elliptic equation governing the behaviour within the half-plane,... Read More about Explicit formulation for the Rayleigh wave field induced by surface stresses in an orthorhombic half-plane.

An edge moving load on an orthotropic plate resting on a Winkler foundation (2017)
Journal Article

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.

Dispersion of elastic waves in laminated glass (2017)
Journal Article

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

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.

Asymptotic Theory for Rayleigh and Rayleigh-Type Waves (2017)
Book Chapter

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.

Lowest Vibration Modes of Strongly Inhomogeneous Elastic Structures (2017)
Book Chapter

Dispersion of elastic waves in a strongly inhomogeneous three-layered plate (2017)
Journal Article

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.

On steady-state moving load problems for an elastic half-space (2016)
Conference Proceeding

Edge bending wave on a thin elastic plate resting on a Winkler foundation (2016)
Journal Article

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.

Edge bending waves on an orthotropic elastic plate resting on the Winkler-Fuss foundation (2016)
Journal Article

The propagation of bending edge waves on an orthotropic plate supported by the Winkler-Fuss foundation subject to free edge boundary conditions is investigated. A dispersion relation is derived, with the analysis revealing a cut-off frequency and a l... Read More about Edge bending waves on an orthotropic elastic plate resting on the Winkler-Fuss foundation.

Buckling of a spherical shell under external pressure and inward concentrated load: asymptotic solution (2016)
Journal Article

An asymptotic solution is suggested for a thin isotropic spherical shell subject to uniform external pressure and concentrated load. The pressure is the main load and a concentrated lateral load is considered as a perturbation that decreases buckling... Read More about Buckling of a spherical shell under external pressure and inward concentrated load: asymptotic solution.

Multi-parametric analysis of the lowest natural frequencies of strongly inhomogeneous elastic rods (2015)
Journal Article

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.

Remarks on explicit strong ellipticity conditions for anisotropic or pre-stressed incompressible solids. (2015)
Journal Article

We present a set of explicit conditions, involving the components of the elastic stiffness tensor, which are necessary and sufficient to ensure the strong ellipticity of an orthorhombic incompressible medium. The derivation is based on the procedure... Read More about Remarks on explicit strong ellipticity conditions for anisotropic or pre-stressed incompressible solids..

On the 3D Rayleigh wave field on an elastic half-space subject to tangential surface loads (2015)
Journal Article

This study is concerned with analysis of the Rayleigh wave field in a 3D isotropic elastic half-space subject to in-plane surface loading. The approach relies on the slow time perturbation of the general representation for the Rayleigh wave eigensolu... Read More about On the 3D Rayleigh wave field on an elastic half-space subject to tangential surface loads.

The near-resonant regimes of a moving load in a three-dimensional problem for a coated elastic half-space (2014)
Journal Article

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

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.

On the near-resonant regimes of the moving load in case of a coated elastic half-space (2014)
Conference Proceeding

Explicit Models for Surface, Interfacial and Edge Waves (2013)
Book Chapter

On a 3D moving load problem for an elastic half space (2013)
Journal Article

Rayleigh waves of arbitrary profile in anisotropic media (2013)
Journal Article

The paper deals with surface wave propagation in an orthorhombic elastic half-plane. The general profile of the wave is considered, incorporating the anisotropy effects within the known representation in terms of a single plane harmonic function.

The Rayleigh wave field in mixed problems for a half-plane (2012)
Journal Article