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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.