Lamb waves in discrete homogeneous and heterogeneous systems: Dispersion properties, asymptotics and non-symmetric wave propagation

In this paper, we study Lamb waves propagating in a discrete strip, whose microstructure is represented by either a monatomic or a diatomic triangular lattice. In considering the in-plane vector problem, we derive an analytical solution for the dispersion relation of Lamb waves. Additionally, we investigate the main features of the eigenmodes of the system, which describe how the lattice strip vibrates at different frequencies. Further, we discuss how the dispersion properties depend on the number of the lattice's rows and on the chosen boundary conditions. For heterogeneous systems, we focus the attention on the internal stop-band and on the flat bands appearing in the dispersion diagram. Different asymptotic models are employed to approximate the low-frequency behaviour of the lattice strip, starting from the classical Euler–Bernoulli beam. The effective behaviour of a lattice strip with dense microstructure is also investigated, and we present a comparative numerical analysis with the analogous continuum for which the classical Lamb wave problem is posed. The theory developed is exploited here to design a structured medium capable of manipulating wavemodes, and, through conversion and selection, generating uni-directional wave phenomena. We envisage that the present work can fill a gap in the research field related to the analytical study of dispersive waves in microstructured media, whose dynamic performance is influenced by the presence of multiple external boundaries

Forcing the silence of the Lamb waves: Uni-directional propagation in structured gyro-elastic strips and networks

In this paper, we propose an innovative design of an elastic network, which is capable of channelling the energy supplied by an external source towards any of its endpoints, that can be chosen arbitrarily and in advance. This system, named Mechanical Switching Network (MSN), consists of an interconnected array of branches, each of which is represented by a lattice strip endowed with gyroscopic spinners. The latter make the system non-reciprocal and, hence, are responsible for the preferential directionality exhibited by the network. We formulate and solve the forced problem for the gyro-elastic strip in the analytical form and compare the derived solutions with the results of independent finite element simulations, showing an excellent agreement. Additionally, we carry out a parametric analysis to evaluate the influence of the main parameters of the system on the uni-directional wave propagation of Lamb waves. We envisage that the proposed model can have important implications in many engineering applications, where control and tunability of guided waves play a key role

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

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)'

Rayleigh waves in micro-structured elastic systems: Non-reciprocity and energy symmetry breaking

Rayleigh waves are analysed in elastic lattices incorporating inertial devices that couple in-plane displacements. The vector problems of elasticity for a triangular lattice and its long-wavelength/low-frequency continuum approximation are considered. The analytical procedure for the derivation of the Rayleigh dispersion relation is fully detailed and, remarkably, explicit solutions for the Rayleigh waves for both the discrete and continuous systems are found. The dispersion at low wavenumbers and the softening induced by the presence of in-plane inertial coupling are shown. Despite the symmetry of the dispersion curves with respect to the wavenumber, the introduction of the inertial coupling breaks the symmetry of the eigenmodes and makes the system non-reciprocal. Such an uncommon effect is demonstrated in a set of numerical computations, where a point force applied on the boundary generates surface and bulk waves that do not propagate symmetrically from the source

Insulinoma : a Rare Cause of Hypoglycemia in Childhood

Rare disease. Insulinomas are pancreatic neuroendocrine tumors that cause non-ketotic hypoglycemia due to hyperinsulinism; they are extremely rare, especially in children. We present a case of a sporadic insulinoma in an 11-year-old boy who had episodes of self-limited drowsiness and behavior changes over a 3-month period, thought to be caused by psychological issues. Non-ketotic hypoglycemia was confirmed at our center. A fasting blood test found inappropriately elevated insulin levels during hypoglycemia, undetectable β-hydroxybutyrate, and increased C-peptide levels in line with insulin levels. Anti-insulin antibodies were negative and antidiabetic drugs untraceable. The glucagon-stimulation test was positive. Growth hormone, adrenocorticotropin hormone, and phosphorus and calcium metabolism were normal. Dual-phase computed tomography detected a lesion compatible with an insulinoma. Endoscopic ultrasound showed a homogenous lesion at the junction of the body and tail of the pancreas. Histologic analysis of a fine-needle aspiration biopsy was compatible with neuroendocrine neoplasia. Preoperatively, a fractional diet avoiding fast-absorbing carbohydrates maintained normal glucose blood levels. Enucleation was not possible, so the lesion was resected along with portions of the body and tail of the pancreas. The well-differentiated tumor measured 15×13 mm. Postoperative blood glucose levels were correct, allowing a normal diet. In children with unspecific symptoms compatible with hypoglycemia, blood glucose must be evaluated to confirm low blood glucose levels. Determining blood ketone levels is important for the differential diagnosis. The diagnostic approach to pediatric insulinoma represents a challenge for multidisciplinary teamwork

Elastic Chiral Waveguides with Gyro-Hinges

This article presents a novel chiral structure, consisting of Euler–Bernoulli beams connected to gyroscopic spinners.Anew type of boundary condition is introduced, which is referred to as a gyrohinge. In this system, flexural waves are coupled with rotational motion.Time-harmonic conditions are derived by assuming small nutation angles of the spinners. It is shown that the eigenfrequencies of a finite beam with gyro-hinges at one or both ends change dramatically with the moments of inertia and the spin and precession rates of the spinners. The formulation is then extended to elastic beams with periodically-spaced gyro-hinges, whose dispersion properties are investigated in detail. In particular, it is shown how stop-bands and standing modes are affected by the introduction of gyroscopic spinners at the junctions. It is also demonstrated that a periodic system composed of beams connected by gyro-hinges represents a good approximation of a gyrobeam, a theoretical structural element consisting of an elastic beam possessing a continuous distribution of stored angular momentum. The gyricity coefficient of a gyrobeam is then interpreted in terms of the physical parameters of the system of beams with gyroscopic spinners. This article opens a new perspective on the design and practical implementation of chiral mechanical systems

Models and data analysis tools for the Solar Orbiter mission

Context. The Solar Orbiter spacecraft will be equipped with a wide range of remote-sensing (RS) and in situ (IS) instruments to record novel and unprecedented measurements of the solar atmosphere and the inner heliosphere. To take full advantage of these new datasets, tools and techniques must be developed to ease multi-instrument and multi-spacecraft studies. In particular the currently inaccessible low solar corona below two solar radii can only be observed remotely. Furthermore techniques must be used to retrieve coronal plasma properties in time and in three dimensional (3D) space. Solar Orbiter will run complex observation campaigns that provide interesting opportunities to maximise the likelihood of linking IS data to their source region near the Sun. Several RS instruments can be directed to specific targets situated on the solar disk just days before data acquisition. To compare IS and RS, data we must improve our understanding of how heliospheric probes magnetically connect to the solar disk.Aims. The aim of the present paper is to briefly review how the current modelling of the Sun and its atmosphere can support Solar Orbiter science. We describe the results of a community-led effort by European Space Agency's Modelling and Data Analysis Working Group (MADAWG) to develop different models, tools, and techniques deemed necessary to test different theories for the physical processes that may occur in the solar plasma. The focus here is on the large scales and little is described with regards to kinetic processes. To exploit future IS and RS data fully, many techniques have been adapted to model the evolving 3D solar magneto-plasma from the solar interior to the solar wind. A particular focus in the paper is placed on techniques that can estimate how Solar Orbiter will connect magnetically through the complex coronal magnetic fields to various photospheric and coronal features in support of spacecraft operations and future scientific studies.Methods. Recent missions such as STEREO, provided great opportunities for RS, IS, and multi-spacecraft studies. We summarise the achievements and highlight the challenges faced during these investigations, many of which motivated the Solar Orbiter mission. We present the new tools and techniques developed by the MADAWG to support the science operations and the analysis of the data from the many instruments on Solar Orbiter.Results. This article reviews current modelling and tool developments that ease the comparison of model results with RS and IS data made available by current and upcoming missions. It also describes the modelling strategy to support the science operations and subsequent exploitation of Solar Orbiter data in order to maximise the scientific output of the mission.Conclusions. The on-going community effort presented in this paper has provided new models and tools necessary to support mission operations as well as the science exploitation of the Solar Orbiter data. The tools and techniques will no doubt evolve significantly as we refine our procedure and methodology during the first year of operations of this highly promising mission.Peer reviewe

The Solar Orbiter Science Activity Plan: translating solar and heliospheric physics questions into action

Solar Orbiter is the first space mission observing the solar plasma both in situ and remotely, from a close distance, in and out of the ecliptic. The ultimate goal is to understand how the Sun produces and controls the heliosphere, filling the Solar System and driving the planetary environments. With six remote-sensing and four in-situ instrument suites, the coordination and planning of the operations are essential to address the following four top-level science questions: (1) What drives the solar wind and where does the coronal magnetic field originate?; (2) How do solar transients drive heliospheric variability?; (3) How do solar eruptions produce energetic particle radiation that fills the heliosphere?; (4) How does the solar dynamo work and drive connections between the Sun and the heliosphere? Maximising the mission’s science return requires considering the characteristics of each orbit, including the relative position of the spacecraft to Earth (affecting downlink rates), trajectory events (such as gravitational assist manoeuvres), and the phase of the solar activity cycle. Furthermore, since each orbit’s science telemetry will be downloaded over the course of the following orbit, science operations must be planned at mission level, rather than at the level of individual orbits. It is important to explore the way in which those science questions are translated into an actual plan of observations that fits into the mission, thus ensuring that no opportunities are missed. First, the overarching goals are broken down into specific, answerable questions along with the required observations and the so-called Science Activity Plan (SAP) is developed to achieve this. The SAP groups objectives that require similar observations into Solar Orbiter Observing Plans, resulting in a strategic, top-level view of the optimal opportunities for science observations during the mission lifetime. This allows for all four mission goals to be addressed. In this paper, we introduce Solar Orbiter’s SAP through a series of examples and the strategy being followed