Julius Kaplunov's Outputs (92)

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.

Cellulose-Aerogele als multifunktionale und nachhaltige Alternativen für Flugzeugkabinenelemente (2023)
Presentation / Conference Contribution
Aney, S., Schestakow, M., Prikazchikova, L., Milow, B., Prikazchikov, D., Kaplunov, J., Voggenreiter, H., & Rege, A. Cellulose-Aerogele als multifunktionale und nachhaltige Alternativen für Flugzeugkabinenelemente. Presented at German Aerospace Congress 2022, Dresden, German Aerospace Society - Lilienthal-Oberth eV, Bonn, 202

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.

Some aspects of wave propagation in a fluid-loaded membrane (2022)
Book Chapter
Kaplunov, J., Prikazchikova, L., & Shamsi, S. (2022). Some aspects of wave propagation in a fluid-loaded membrane. . Elsevier. https://doi.org/10.1016/b978-0-32-390543-5.00015-3

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

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

<jats:title>Abstract</jats:title><jats:p>Plane-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, incl... 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

<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.

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.

On The Derivation Of A String Equation (2022)
Journal Article
Kaplunov, J., & Prikazchikov, D. A. (in press). On The Derivation Of A String Equation. Natsional'naya Akademiya Nauk Armenii. Izvestiya. Seriya Mekhanika / Proceedings of NAS RA: Mechanics, 75(1), 163-168. https://doi.org/10.54503/0002-3051-2022.75.1-2-163

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.

Dynamic Sliding Contact for a Thin Elastic Layer (2022)
Book Chapter
Kaplunov, J., Prikazchikov, D. A., & Savšek, T. (2022). Dynamic Sliding Contact for a Thin Elastic Layer. In Recent Approaches in the Theory of Plates and Plate-Like Structures (103-114). Springer. https://doi.org/10.1007/978-3-030-87185-7_9

Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation (2021)
Journal Article
Erbas, B., Kaplunov, J., & Elishakoff, I. (2022). Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation. Mathematics and Mechanics of Solids, 27(9), 1638-1648. https://doi.org/10.1177/10812865211023885

A two-dimensional mixed problem for a thin elastic strip resting on a Winkler foundation is considered within the framework of plane stress setup. The relative stiffness of the foundation is supposed to be small to ensure low-frequency vibrations. As... Read More about Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation.

Modern Trends in Structural and Solid Mechanics 1: Statics and Stability (Ed. J Kaplunov) (2021)
Book
Kaplunov, J. (2021). N. Challamel, J. Kaplunov, & I. Takewaki (Eds.). Modern Trends in Structural and Solid Mechanics 1: Statics and Stability (Ed. J Kaplunov). Wiley. https://doi.org/10.1002/9781119831891

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

<jats:title>Abstract</jats:title><jats:p>An 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-pla... Read More about Antiplane shear of an asymmetric sandwich plate.