Wave Characterisation in a Dynamic Elastic Lattice: Lattice Flux and Circulation

A novel characterisation of dispersive waves in a vector elastic lattice is presented in the context of wave polarisation. This proves to be especially important in analysis of dynamic anisotropy and standing waves trapped within the lattice. The operators of lattice flux and lattice circulation provide the required quantitative description, especially in cases of intermediate and high frequency dynamic regimes. Dispersion diagrams are conventionally considered as the ultimate characteristics of dynamic properties of waves in periodic systems. Generally, a waveform in a lattice can be thought of as a combination of pressure-like and shear-like waves. However, a direct analogy with waves in the continuum is not always obvious. We show a coherent way to characterise lattice waveforms in terms of so-called lattice flux and lattice circulation. In the long wavelength limit, this leads to well-known interpretations of pressure and shear waves. For the cases when the wavelength is comparable with the size of the lattice cell, new features are revealed which involve special directions along which either lattice flux or lattice circulation is zero. The cases of high frequency and wavelength comparable to the size of the elementary cell are considered, including dynamic anisotropy and dynamic neutrality in structured solids

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)’

Periodically fighting shake, rattle and roll

How easy is it to suppress shake, rattle and roll in a long bridge or a skyscraper? Most practical structures are designed so that long wave resonance vibrations can be avoided. However, there are recent examples, such as the Millennium Bridge in London or the Volga Bridge in Volgograd, which show that unexpected external forces may result in large scale unwanted shake and rattle. Full scale alteration of a bridge (or a skyscraper) would not be considered as an acceptable option, unless the structure has collapsed. Can we fix this by examining a representative part of the structure only and making small lightweight changes? We will do it here and illustrate an idea linking the engineering analysis to elastic waveguides.Comment: 19 pages, 6 figure

REFINED ASSESSMENT OF SEISMIC MICROZONATION WITH A PRIORI DATA OPTIMISATION

The work is devoted to the issues of seismic microzonation representativeness, which is amongst the mandatory assessments that precedes civil and industrial construction. In addition to the practical approach and in accordance with the normative documentation, the authors propose parametric interpretation of the remote basis by means of tracing geodynamic zones and elements of the geoblock structure, where the leading marker of seismogenic risk zones is the anomaly of spatial variability of the geofield, coinciding with the discordant intersection of localised land structures. Verification of this marker is achieved by displaying a cartographic distribution image within the range of the seismic point increment, detailed on the basis of approximation dependencies

Transformation cloaking and radial approximations for flexural waves in elastic plates

It is known that design of elastic cloaks is much more challenging than that of acoustic cloaks, cloaks of electromagnetic waves or scalar problems of antiplane shear. In this paper, we address fully the fourth-order problem and develop a model of a broadband invisibility cloak for channelling flexural waves in thin plates around finite inclusions. We also discuss an option to employ efficiently an elastic pre-stress and body forces to achieve such a result. An asymptotic derivation provides a rigorous link between the model in question and elastic wave propagation in thin solids. This is discussed in detail to show connection with non-symmetric formulations in vector elasticity studied in earlier work

Theoretical foundations of hot spots policing and crime mapping features

The study is devoted to one of the ways to solve the problem of reducing the crime rate in the region due to the concentration of police forces and means in correctly defined places of criminal activity. The purpose of the study is to determine the content of the concept of police activity in places where criminal activity is concentrated in “hot spots” and examine the features of crime mapping. The key methods used are system and structural analysis, dogmatic analysis, synthesis method, modelling method, and structural-functional and formal-logical methods. It is determined that the problems of criminal activity, for the most part, are concentrated in a small number of places of an administrative- territorial unit, which continue to be dangerous for a long time in the absence of police intervention. It is proved that different types of “hot spots” require the development of individual police countermeasures, and the analysis of “hot spots” should be based on a logical and systematic approach and depends on understanding the theory of the origin of different types of analysed criminal offences and choosing the way to display the results. A reservation is made that arbitrary analysis by an analyst, or the use of only software algorithms is excluded because they can lead to a subjective perception of a “hot spot”, which may not turn out to be an accumulation of criminal activity. It is proved that the analysis of “hot spots” , in addition to simply identifying places with high crime rates, is crucial for solving problems in these places and choosing the most effective police response measures. The practical value of the proposed study is to generalise and adapt international developments to improve the theoretical and practical foundations for improving the efficiency of criminal analysis units of the National Police of Ukraine in the field of visualisation of information about criminal activity, introducing international experience in crime mapping into the practical activities of criminal analysis units of the National Police of Ukrain