Alternating strain regimes for failure propagation in flexural systems

We consider both analytical and numerical studies of a steady-state fracture process inside a discrete mass-beam structure, composed of periodically placed masses connected by Euler-Bernoulli beams. A fault inside the structure is assumed to propagate with a constant speed and this occurs as a result of the action of a remote sinusoidal, mechanical load. The established regime of fracture corresponds to the case of an alternating generalised strain regime. The model is reduced to a Wiener-Hopf equation and its solution is presented. We determine the minimum feeding wave energy required for the steady-state fracture process to occur. In addition, we identify the dynamic features of the structure during the steady-state fracture regime. A transient analysis of this problem is also presented, where the existence of steady-state fracture regimes, revealed by the analytical model, are verified and the associated transient features of this process are discussed

A gyro-elastic device for cloaking of elastic waves in micro-structured materials

The design of a structured gyro-elastic system capable of being used as a cloaking device for a discrete medium is discussed. The efficiency of the gyro-elastic cloak, composed of springs connecting periodically placed masses, attached to gyroscopic spinners, is examined in the transient regime. An important effect encountered shows that the speed of the reconstructed field can be altered by tuning the gyroscopes

Gyro-elastic beams for the vibration reduction of long flexural systems

The paper presents a model of a chiral multi-structure incorporating gyro-elastic beams. Floquet–Bloch waves in periodic chiral systems are investigated in detail, with the emphasis on localization and the formation of standing waves. It is found that gyricity leads to low-frequency standing modes and generation of stop-bands. A design of an earthquake protection system is offered here, as an interesting application of vibration isolation. Theoretical results are accompanied by numerical simulations in the time-harmonic regime

Dynamic characterization of a periodic microstructured flexural system with rotational inertia.

We consider the propagation of waves in a flexural medium composed of massless beams joining a periodic array of elements, elastically supported and possessing mass and rotational inertia. The dispersion properties of the system are determined and the influence and interplay between the dynamic parameters on the structure of the pass and stop bands are analysed in detail. We highlight the existence of three special dynamic regimes corresponding to a low stiffness in the supports and/or low rotational inertia of the masses; to a high stiffness and/or high rotational inertia regime; and to a transition one where dispersion degeneracies are encountered. In the low-frequency regime, a rigorous asymptotic analysis shows that the structure approximates a continuous Rayleigh beam on an elastic foundation. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 1)'

Asymptotic analysis of in-plane dynamic problems for elastic media with rigid clusters of small inclusions.

We present formal asymptotic approximations of fields representing the in-plane dynamic response of elastic solids containing clusters of closely interacting small rigid inclusions. For finite densely perforated bodies, the asymptotic scheme is developed to approximate the eigenfrequencies and the associated eigenmodes of the elastic medium with clamped boundaries. The asymptotic algorithm is also adapted to address the scattering of in-plane waves in infinite elastic media containing dense clusters. The results are accompanied by numerical simulations that illustrate the accuracy of the asymptotic approach. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'

“Deflecting elastic prism” and unidirectional localisation for waves in chiral elastic systems

For the first time, a design of a “deflecting elastic prism” is proposed and implemented for waves in a chiral medium. A novel model of an elastic lattice connected to a non-uniform system of gyroscopic spinners is designed to create a unidirectional wave pattern, which can be diverted by modifying the arrangement of the spinners within the medium. This important feature of the gyro-system is exploited to send a wave from a point of the lattice to any other point in the lattice plane, in such a way that the wave amplitude is not significantly reduced along the path. We envisage that the proposed model could be very useful in physical and engineering applications related to directional control of elastic waves

Analytical treatment of the transient motion of inertial beams attached to coupling inertial resonators

This paper presents, for the first time, an analytical formulation to determine the transient response of an elastic beam possessing distributed inertia and connected to a coupling inertial resonator, represented by a gyroscopic spinner. The latter couples the transverse displacement components of the beam in the two perpendicular directions, thus producing roto-flexural vibrations. A detailed parametric study is presented that illustrates the effects of the beam’s distributed inertia and of the resonator’s characteristics. The limit case of massless beam is examined and it is shown that in some situations the distributed inertia in the beam should not be neglected. Analytical results are also validated by finite element computations. An illustration is also presented that demonstrates the effectiveness of using the considered inertial devices to mitigate hazardous vibrations in structural systems. It is envisaged that this paper may be useful in the analysis of flexural waveguides and metamaterials consisting of inertial elastic beam elements

Flexural vibration systems with gyroscopic spinners

In this paper, we study the spectral properties of a finite system of flexural elements connected by gyroscopic spinners. We determine how the eigenfrequencies and eigenmodes of the system depend on the gyricity of the spinners. In addition, we present a transient numerical simulation that shows how a gyroscopic spinner attached to the end of a hinged beam can be used as a ‘stabilizer’, reducing the displacements of the beam. We also discuss the dispersive properties of an infinite periodic system of beams with gyroscopic spinners at the junctions. In particular, we investigate how the band-gaps of the structure can be tuned by varying the gyricity of the spinners

Interfacial waveforms in chiral lattices with gyroscopic spinners

We demonstrate a new method of achieving topologically protected states in an elastic hexagonal system of trusses by attaching gyroscopic spinners, which bring chirality to the system. Dispersive features of this medium are investigated in detail, and it is shown that one can manipulate the locations of stop-bands and Dirac points by tuning the parameters of the spinners. We show that, in the proximity of such points, uni-directional interfacial waveforms can be created in an inhomogeneous lattice and the direction of such waveforms can be controlled. The effect of inserting additional soft internal links into the system, which is thus transformed into a heterogeneous triangular lattice, is also investigated, as the hexagonal lattice represents the limit case of the heterogeneous triangular lattice with soft links. This work introduces a new perspective in the design of periodic media possessing non-trivial topological features

Design of a chiral elastic structure supporting interfacial waveforms

An infinite heterogeneous elastic triangular lattice connected to a non-uniform array of gyroscopic spinners is considered. An algorithm is described for generating interfacial waves that propagate along the boundaries of subdomains containing inhomogeneities in the spinner array. The interfacial waveforms have preferential directions that can be controlled through adjusting the frequency of excitation or the arrangement of the spinners