arXiv subjects

Alexander B. Movchan

Publications and source records attributed to Alexander B. Movchan.

At least 19 recordsLinked to original sources

arXiv2025

When the Earth and Sky Dance: Seismic Shakes Meet Weather Patterns

A new modelling approach shows how the Earth's hidden vibrations may drive global weather dynamics and atmospheric pressure variations, hinting that the planet's own beat could be imprinted on our climate. The atmospheric rotational patterns of the mean sea level pressure, in connection to the development of powerful storms, are shown to be caused by Earth's rotational elastic dynamics and earthquake-induced oscillations. These seismic excitations are discussed in relation to storm formation and the global atmospheric patterns of high-pressure regions.

physics.ao-ph↗

arXiv2025

Global lattice models of a rotating planet -- view on shake, rattle and roll

A new approach, based on the analysis of a spectral problem for a discrete gyroscopic system, to modelling earthquakes on a rotating planet is presented in this paper. The eigenmodes of gyroscopic three-dimensional icosahedron-dodecahedron lattices are used for the discrete approximations of Earth's vibrations. Related model of the gyroscopic centred icosahedron lattice reveals new results about the motion of Earth's core. The vibrations of the tectonic plate boundaries, inducing shear and longitudinal motions of the ground, are described through the oscillations of the nodal elements within the discrete gyroscopic models. The theoretical analysis is complemented with the illustrative numerical examples linked to natural resonant vibrations observed during large earthquakes.

physics.geo-ph↗

arXiv2025

Coupled dynamics of chiral waves and gyroscopic systems with applications to atmospheric phenomena

The present paper introduces the notion of chiral gravitational elastic waves and explores their connections to equatorial and planetary waves. The analysis of the gravity-induced waveforms in gyroscopic systems composed of gyropendulums provides important insights into the dynamics of waves in the vicinity of the equatorial belt. We show that the direction of motion of the chiral waveforms can be controlled by choosing the orientation of the spinners. The presence of gravity is shown to affect the stop band frequencies for such structures, providing an additional control parameter for the chiral waveguides. The effect of the Coriolis force is demonstrated for chiral continuum models describing waves in the equatorial region and the polar regions on a rotating sphere. Additional asymptotic features of equatorial waves are presented in this paper. We show that the shape of a ridge of a polar vortex can be approximated by the governing equations of a gyropendulum. The theoretical work is accompanied by illustrative examples.

physics.class-ph↗

arXiv2024

A mechanical analogue of electromagnetic induction for waves in a chiral elastic structure

Classical Faraday's law on electromagnetic induction states that a change of magnetic field through a coil wire induces a current in the wire. A mechanical analogue of the Lorentz force, induced by a magnetic field on an electric charge, is the gyroscopic force. Here, we demonstrate a mechanical analogy with a chiral elastic waveguide subjected to gyroscopic forcing. We study waves in an infinite mass-spring `gyrocore helix', which consists of a helix and a central line (gyroscopic elastic core). The helicoidal geometric chirality is considered in conjunction with a physical chirality, induced by gyroscopic forces. It is shown that the interplay between these two chiral inputs leads to the breaking of symmetry of the associated dispersion diagram, resulting in a unidirectional waveform with the direction of propagation being tunable through the gyricity.

physics.class-ph↗

arXiv2021

Axisymmetric deformation of compressible, nearly incompressible, and incompressible thin layers between two rigid surfaces

Accurate asymptotic solutions are presented for axisymmetric deformation of thin layers constrained by either two rigid plates or two rigid spheres. Those solutions are developed using Saint-Venant's principle and the layer thinness as the only assumptions. The solutions are valid in the entire range of Poisson's ratios, and allow one to distinguish among compressible, nearly incompressible, and incompressible layers. That classification involves both material and geometric parameters.

math.AP↗

arXiv2019

Scattering from a non-linear structured interface

We review the scattering from non-linear interfaces containing buckling elastic beams. An illustrative example is discussed here of scattering of linear elastic pressure waves from a two-mass system connected by a non-linear structured interface modelled as elastica. In the first instance, the interaction between the masses is linearised. This allows for the study of a time-harmonic transmission model problem in the subcritical regime. Subsequently, we consider the transient problem associated with a non-linear ineraction within the interface. The effect of non-linearity is shown to suppress the transmission resonance observed in the linearised formulation.

physics.class-ph↗

arXiv2019

Nested Bloch waves in elastic structures with configurational forces

Small axial and flexural oscillations are analyzed for a periodic and infinite structure, constrained by sliding sleeves and composed of elastic beams. A nested Bloch-Floquet technique is introduced to treat the non-linear coupling between longitudinal and transverse displacements induced by the configurational forces generated at the sliding sleeve ends. The action of configurational forces is shown to play an important role from two perspectives. First, the band gap structure for purely longitudinal vibration is broken so that axial propagation may occur at frequencies that are forbidden in the absence of a transverse oscillation and, second, a flexural oscillation may induce axial resonance, a situation in which the longitudinal vibrations tend to become unbounded. The presented results disclose the possibility of exploiting configurational forces in the design of mechanical devices towards longitudinal actuation from flexural vibrations of small amplitude at given frequency.

physics.class-ph↗

arXiv2018

Quasi-periodicity and multi-scale resonators for the reduction of seismic vibrations in fluid-solid systems

This paper presents a mathematical model for an industry-inspired problem of vibration isolation applied to elastic fluid-filled containers. A fundamental problem of suppression of vibrations within a finite-width frequency interval for a multi-scale fluid-solid system has been solved. We have developed a systematic approach employing full fluid-solid interaction and dispersion analysis, which can be applied to finite and periodic multi-scale systems. The analytical findings are accompanied by numerical simulations, including frequency response analyses and transient regime computations.

physics.flu-dyn↗

arXiv2017

Edge waves and localisation in lattices containing tilted resonators

The paper presents the study of waves in a structured geometrically chiral solid. A special attention is given to the analysis of the Bloch-Floquet waves in a doubly periodic high-contrast lattice containing tilted resonators. Dirac-like dispersion of Bloch waves in the structure is identified, studied and applied to wave-guiding and wave-defect interaction problems. The work is extended to the transmission problems and models of fracture, where localisation and edge waves occur. The theoretical derivations are accompanied with numerical simulations and illustrations.

cond-mat.mtrl-sci↗

arXiv2016

Controlling flexural waves in semi-infinite platonic crystals

We address the problem of scattering and transmission of a plane flexural wave through a semi-infinite array of point scatterers/resonators, which take a variety of physically interesting forms. The mathematical model accounts for several classes of point defects, including mass-spring resonators attached to the top surface of the flexural plate and their limiting case of concentrated point masses. We also analyse the special case of resonators attached to opposite faces of the plate. The problem is reduced to a functional equation of the Wiener-Hopf type, whose kernel varies with the type of scatterer considered. A novel approach, which stems from the direct connection between the kernel function of the semi-infinite system and the quasi-periodic Green's functions for corresponding infinite systems, is used to identify special frequency regimes. We thereby demonstrate dynamically anisotropic wave effects in semi-infinite platonic crystals, with particular attention paid to designing systems to exhibit dynamic neutrality (perfect transmission) and localisation close to the structured interface.

physics.class-ph↗

arXiv2016

Tilted resonators in a triangular elastic lattice: chirality, Bloch waves and negative refraction

We consider a vibrating triangular mass-truss lattice whose unit cell contains a resonator of a triangular shape. The resonators are connected to the triangular lattice by trusses. Each resonator is tilted, i.e. it is rotated with respect to the triangular lattice's unit cell through an angle $\vartheta_0$. This geometrical parameter is responsible for the emergence of a resonant mode in the Bloch spectrum for elastic waves and strongly affects the dispersive properties of the lattice. Additionally, the tilting angle $\vartheta_0$ triggers the opening of a band gap at a Dirac-like point. We provide a physical interpretation of these phenomena and discuss the dynamical implications on elastic Bloch waves. The dispersion properties are used to design a structured interface containing tilted resonators which exhibit negative refraction and focussing, as in a "flat elastic lens".

physics.class-ph↗

arXiv2016

Spider-Web Inspired Mechanical Metamaterials

Spider silk is a remarkable example of bio-material with superior mechanical characteristics. Its multilevel structural organization of dragline and viscid silk leads to unusual and tunable properties, extensively studied from a quasi-static point of view. In this study, inspired by the Nephila spider orb web architecture, we propose a novel design for mechanical metamaterials based on its periodic repetition. We demonstrate that spider-web metamaterial structure plays an important role in the dynamic response and wave attenuation mechanisms. The capability of the resulting structure to inhibit elastic wave propagation in sub-wavelength frequency ranges is assessed and parametric studies are performed to derive optimal configurations and constituent mechanical properties. The results show promise for the design of innovative lightweight structures for tunable vibration damping and impact protection, or the protection of large scale infrastructure such as suspended bridges.

cond-mat.mtrl-sci↗

arXiv2016

Propagation and filtering of elastic and electromagnetic waves in piezoelectric composite structures

In this article we discuss the modelling of elastic and electromagnetic wave propagation through one- and two-dimensional structured piezoelectric solids. Dispersion and the effect of piezoelectricity on the group velocity and positions of stop bands are studied in detail. We will also analyze the reflection and transmission associated with the problem of scattering of an elastic wave by a heterogeneous piezoelectric stack. Special attention is given to the occurrence of transmission resonances in finite stacks and their dependence on a piezoelectric effect. A 2D doubly-periodic piezoelectric checkerboard structure is subsequently introduced, for which the dispersion surfaces for Bloch waves have been constructed and analysed, with the emphasis on the dynamic anisotropy and special features of standing waves within the piezoelectric structure.

cond-mat.mtrl-sci↗

arXiv2015

Blockage, trapping and waveguide modes for flexural waves in a semi-infinite double grating

The paper presents a novel view on the scattering of a flexural wave in a Kirchhoff plate by a semi-infinite discrete system. Blocking and channelling of flexural waves are of special interest. A quasi-periodic two-source Green's function is used in the analysis of the waveguide modes. An additional "effective waveguide" approximation has been constructed. Comparisons are presented for these two methods in addition to an analytical solution for a finite truncated system.

physics.class-ph↗

arXiv2015

Dynamic interfacial trapping of flexural waves in structured plates

The paper presents new results on localisation and transmission of flexural waves in a structured plate containing a semi-infinite two-dimensional array of rigid pins. In particular, surface waves are identified and studied at the interface boundary between the homogeneous part of the flexural plate and the part occupied by rigid pins. A formal connection has been made with the dispersion properties of flexural Bloch waves in an infinite doubly periodic array of rigid pins. Special attention is given to regimes corresponding to standing waves of different types as well as Dirac-like points, that may occur on the dispersion surfaces. A single half-grating problem, hitherto unreported in the literature, is also shown to bring interesting solutions.

math.AP↗

arXiv2012

Transition wave in a supported heavy beam

We consider a heavy, uniform, elastic beam rested on periodically distributed supports as a simplified model of a bridge. The supports are subjected to a partial destruction propagating as a failure wave along the beam. Three related models are examined and compared: (a) a uniform elastic beam on a distributed elastic foundation, (b) an elastic beam which mass is concentrated at a discrete set of points corresponding to the discrete set of the elastic supports and (c) a uniform elastic beam on a set of discrete elastic supports. Stiffness of the support is assumed to drop when the stress reaches a critical value. In the formulation, it is also assumed that, at the moment of the support damage, the value of the `added mass', which reflects the dynamic response of the support, is dropped too. Strong similarities in the behavior of the continuous and discrete-continuous models are detected. Three speed regimes, subsonic, intersonic and supersonic, where the failure wave is or is not accompanied by elastic waves excited by the moving jump in the support stiffness, are considered and related characteristic speeds are determined. With respect to these continuous and discrete-continuous models, the conditions are found for the failure wave to exists, to propagate uniformly or to accelerate. It is also found that such beam-related transition wave can propagate steadily only at the intersonic speeds. It is remarkable that the steady-state speed appears to decrease as the jump of the stiffness increases.

physics.class-ph↗

arXiv2012

Vortex-type elastic structured media and dynamic shielding

The paper addresses a novel model of metamaterial structure. A system of spinners has been embedded into a two-dimensional periodic lattice system. The equations of motion of spinners are used to derive the expression for the chiral term in the equations describing the dynamics of the lattice. Dispersion of elastic waves is shown to possess innovative filtering and polarization properties induced by the vortextype nature of the structured media. The related homogenised effective behavior is obtained analytically and it has been implemented to build a shielding cloak around an obstacle. Analytical work is accompanied by numerical illustrations.

math-ph↗

arXiv2008

Achieving control of in-plane elastic waves

We derive the elastic properties of a cylindrical cloak for in-plane coupled shear and pressure waves. The cloak is characterized by a rank 4 elasticity tensor with 16 spatially varying entries which are deduced from a geometric transform. Remarkably, the Navier equations retain their form under this transform, which is generally untrue [Milton et al., New J. Phys. 8, 248 (2006)]. We numerically check that clamped and freely vibrating obstacles located inside the neutral region are cloaked disrespectful of the frequency and the polarization of an incoming elastic wave.

cond-mat.mtrl-sci↗