ABSTRACT
The dynamic response of elastic waveguides is important for a wide range of applications that involve dispersive waves as well as wave localization. In particular, a case of special interest relates to waveguides subjected to moving loads. In the case where the elongated structure includes a sequence of built-in resonators, the range of resonance regimes may be extended accordingly. The present paper gives an overview of several mathematical formulations that connect Floquet theory to the dynamic response of multi-scale waveguides, which include inertial sub-structures subjected to external forces. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.
ABSTRACT
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)'.
ABSTRACT
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)'.
ABSTRACT
This paper presents a unified approach to the modelling of elastic solids with embedded dynamic microstructures. General dependences are derived based on Green's kernel formulations. Specifically, we consider systems consisting of a master structure and continuously or discretely distributed oscillators. Several classes of connections between oscillators are studied. We examine how the microstructure affects the dispersion relations and determine the energy distribution between the master structure and microstructures, including the vibration shield phenomenon. Special attention is given to the comparative analysis of discrete and continuous distributions of the oscillators, and to the effects of non-locality and trapped vibrations. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 2)'.
