Flexural vibration systems with gyroscopic spinners

Controlling the motion of gravitational spinners and waves in chiral waveguides

In this paper we present a mathematical modelling framework for chiral phenomena associated with rotational motions, highlighting the combination of gyroscopic action with gravity. We discuss new ideas of controlling gravity-induced waves by a cluster of gyroscopic spinners. For an elementary gravitational spinner, the transient oscillations are accompanied by a full classification and examples, linked to natural phenomena observed in planetary motion. Applications are presented in the theory of chiral metamaterials, and of the dynamic response of such materials to external loads.

Modelling of seismic assessment for large geological systems

A new approach to seismic analysis has been introduced and demonstrated for a sequence of recent seismic events recorded in the Blackpool region of Lancashire, UK. The seismic activity, induced by an industrial hydraulic fracturing at a depth exceeding 2 km, had the extent of registered surface elastic vibrations reaching a distance exceeding 15 km. The analysis is based on the study of elastic fields, three-dimensional extrapolations of the landscape and the novel reconstruction of a three-dimensional digital model of seismic map boundaries and vertical profiles. The verification of the proposed approach is carried out via the comparison with published data of the Blackpool seismic events, combined with the new spectral analysis linked to the identified regions of seismic activity. The latter was accompanied by a finite-element simulation of vibrations for an elastic layer of variable thickness, approximating the test region. The analysis and numerical modelling have demonstrated consistency with the dynamic nature of structural stratification of the geological systems, and in addition, the predictive nature of the modelling work was demonstrated by the comparison of the model eigenmodes with the published parameters of registered earthquakes in the Blackpool area. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.

One-way interfacial waves in a flexural plate with chiral double resonators

In this paper, we demonstrate a new approach to control flexural elastic waves in a structured chiral plate. The main focus is on creating one-way interfacial wave propagation at a given frequency by employing double resonators in a doubly periodic flexural system. The resonators consist of two beams attached to gyroscopic spinners, which act to couple flexural and rotational deformations, hence inducing chirality in the system. We show that this elastic structure supports one-way flexural waves, localized at an interface separating two sub-domains with gyroscopes spinning in opposite directions, but with otherwise identical properties. We demonstrate that a special feature of double resonators is in the directional control of wave propagation by varying the value of the gyricity, while keeping the frequency of the external time-harmonic excitation fixed. Conversely, for the same value of gyricity, the direction of wave propagation can be reversed by tuning the frequency of the external excitation. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 2)'.