Three-dimensional edge waves in plates

This paper describes the propagation of three-dimensional symmetric waves localized near the traction-free edge of a semi-infinite elastic plate with either traction-free or fixed faces. For both types of boundary conditions, we present a variational proof of the existence of the low-order edge waves. In addition, for a plate with traction-free faces and zero Poisson ratio, the fundamental edge wave is described by a simple explicit formula, and the first-order edge wave is proved to exist. Qualitative variational predictions are compared with numerical results, which are obtained using expansions in three-dimensional Rayleigh–Lamb and shear modes. It is also demonstrated numerically that for any non-zero Poisson ratio in a plate with traction-free faces, the eigenfrequencies related to the first-order wave are complex valued

Eigenvalue of a semi-infinite elastic strip

A semi-infinite elastic strip, subjected to traction free boundary conditions, is studied in the context of in-plane stationary vibrations. By using normal (Rayleigh–Lamb) mode expansion the problem of existence of the strip eigenmode is reformulated in terms of the linear dependence within infinite system of normal modes. The concept of Gram's determinant is used to introduce a generalized criterion of linear dependence, which is valid for infinite systems of modes and complex frequencies. Using this criterion, it is demonstrated numerically that in addition to the edge resonance for the Poisson ratio ν=0, there exists another value of ν≈0.22475 associated with an undamped resonance. This resonance is best explained physically by the orthogonality between the edge mode and the first Lamé mode. A semi-analytical proof for the existence of the edge resonance is then presented for both described cases with the help of the augmented scattering matrix formalism

Condon Domain Phase Diagram for Silver

We present the Condon domain phase diagram for a silver single crystal measured in magnetic fields up to 28 T and temperatures down to 1.3 K. A standard ac method with a pickup coil system is used at low frequency for the measurements of the de Haas-van Alphen effect (dHvA). The transition point from the state of homogeneous magnetization to the inhomogeneous Condon domain state (CDS) is found as the point where a small irreversibility in the dHvA magnetization arises, as manifested by an extremely nonlinear response in the pickup voltage showing threshold character. The third harmonic content in the ac response is used to determine with high precision the CDS phase boundary. The experimentally determined Condon domain phase diagram is in good agreement with the theoretical prediction calculated by the standard Lifshitz-Kosevich (LK) formula

First year engineering mathematics: the London South Bank University experience

This short article describes an innovative approach to teaching mathematics to first year undergraduates on a variety of B. Eng. courses offered in the Faculty of Engineering, Science and Built Environment (FESBE) of London South Bank University (LSBU)

A Numerical Approach for Calculation of Characteristics of Edge Waves in Three-Dimensional Plates

© 2020 World Scientific Publishing CompanySurface waves have been extensively studied in earthquake seismology. Surface waves are trapped near an infinitely large surface. The displacements decay exponentially with depth. These waves are also named Rayleigh and Love waves. Surface waves are also used for nondestructive testing of surface defects. Similar waves exist in finite width three-dimensional plates. In this case, displacements are no longer constant in the direction perpendicular to the wave propagation plane. Wave energy could still be trapped near the edge of the three-dimensional plate, and hence the term edge waves. These waves are thus different to the two-dimensional Rayleigh and Love waves. This paper presents a numerical model to study dispersion properties of edge waves in plates. A two-dimensional semi-analytical finite element method is developed, and the problem is closed by a perfectly matched layer adjacent to the edge. The numerical model is validated by comparing with available analytical and numerical solutions in the literature. On this basis, higher order edge waves and mode shapes are presented for a three-dimensional plate. The characteristics of the presented edge wave modes could be used in nondestructive testing applications.Peer reviewe

Investigation into the problem of characterization of the HF ionospheric fluctuating channel of propagation: construction of a physically based HF channel simulator

A wideband HF simulator has been constructed that is based on a detailed physical model. It can generate an output giving a time realization of the HF wideband channel for any HF carrier frequency and bandwidth and for any given transmitter receiver path, time of day, month and year and for any solar activity/geomagnetic conditions. To accomplish this, a comprehensive solution has been obtained to the problem of HF wave propagation for the most general case of a 3D inhomogeneous ionosphere with time-varying electron density fluctuations. The solution is based on the complex phase method (Rytov s method), which has been extended to the case of an inhomogeneous medium and a point source of the field. Results of simulation obtained according to the technique developed have been presented, calculated for a single-hop path 1000 km long oriented to the south from St. Petersburg and including a horizontal electron density gradient present in the IRI model used as the basis of the ionosphere model. The fluctuations of the ionospheric electron density were characterized by an inverse power law anisotropic spatial spectrum. For this model, the random walk of the phasor at the receiver is determined and shown both for paths reflected in the E- and Fregions, being significantly larger for the latter. The oblique sounding ionogram is constructed and reveals three propagation modes: the E-mode and low and high angle F-mode paths. The time-varying field due to each of these paths is then summed at the receiving location enabling the calculation of the scattering function and also the time realization of the received signal shown as a function of both fast and slow time. This is performed both with and without the presence of the geomagnetic field; in the former case the splitting of the F2-mode into both e- and o-modes is seen. It is also shown how the scattering function can be obtained from the time realization of the channel in a way akin to experimental determination of the scattering function from channel measurements. Results from the simulations show the very significant effect of irregularities of even modest magnitude and the comparative effects due to background ionosphere dispersion and the fluctuating irregularities as well as geomagnetic mode splitting. Since the simulator is based on a physical model, it should be possible by comparison of experimental results and simulation to identify the correspondence between physical parameters (e.g., the variance and anisotropy of the electron density fluctuations, orientation of the propagation path to the magnetic meridian, bulk ionosphere motions) with observed channel parameters (e.g., Doppler spread and shift, time delay spread)

Scintillations effects on satellite to Earth links for telecommunication and navigation purposes

Radio wave scintillations are rapid fluctuations in both amplitude and phase of signals propagating through the atmosphere. GPS signals can be affected by these disturbances which can lead to a complete loss of lock when the electron density strongly fluctuates around the background ionization level at small spatial scales. This paper will present recent improvements to the theoretical Global Ionospheric Scintillation Model (GISM), particularly tailored for satellite based navigation systems such GPS coupled with Satellite Based Augmentation System (SBAS). This model has been improved in order to take into account GPS constellation, signals, and receiver response to ionospheric scintillation environments. A new modelling technique, able to describe the scintillation derived modifications of transionospheric propagating fields is shown. Results from GPS derived experimental measurements performed at high and low magnetic latitudes will show preliminary assessments of the scintillation impact on real receivers and system operations. Nevertheless, comparisons between theoretical scintillation models, such as WBMOD and GISM, with GPS derived experimental data will be shown

The efficiency of using the substrate technological module in the technology of growing potato mini-tubers

Known technologies and methods for obtaining virus-free potato mini-tubers of a required size fraction do not fully provide the highest multiplication factor, which occurs due to the insufficient productivity of an individual potato plant. On the basis of long-term experimental data (2012…2022), an assessment of the effectiveness of methods for growing potato mini-tubers in open and protected ground conditions is given. According to the number of tubers harvested from one plant, all growing methods can be divided into two large groups:  traditional (3-12 potatoes per plant) and modified (more than 40 potatoes per plant). A highly efficient method has been developed for obtaining mini-tubers of potatoes harvested as they grow on soil substrates with an average annual productivity of at least 50 mini-tubers from one micro-tuber and 40 mini-tubers from one virus-free plant (with traditional substrate methods – from 3 to 10 mini-tubers). Based on this method, there has been created a substrate technological module of a new generation harvesting tubers as they grow which makes it possible to obtain an average of 40 to 55 mini-tubers from one virus-free plant over the years, that is almost 10 times more in comparison with traditional methods of growing with a single harvest at the end of vegetation. Harvesting mini-tubers as they grow up to a required size creates the possibility of obtaining tubers of one size fraction (10-25 g), which allows later, when laying the nursery of the first field reproduction, to apply mechanized planting in the field and obtain uniform seedlings

Towards semi-automated non-destructive evaluation

A demonstrator has been developed showing feasibility of semi-automatic characterisation of large planar flaws in steel using ultrasonic transducer arrays. The unit is based on a real-time ultrasonic imager deploying National Instruments hardware and software, is connected to an IMASONIC linear phased array containing 128 elements and incorporates a novel flaw characterisation algorithm, which is a model-based variant of Total Focusing Method, taking into account undulations in inspection surface. It has been shown to process RF data collected in immersion reasonably fast and be capable of detecting and characterising with reasonable accuracy large planar defects