Static Case Research Articles

Impulsive consensus tracking for leader-following multi-AUV system with sampled information

In this paper, impulsive consensus tracking for a leader-following multiple autonomous underwater vehicles (multi-AUV) system with sampled information is studied. Two novel impulsive consensus protocols are proposed to address both the multi-AUV system recovery problem with the static leader and the formation tracking problem with the dynamic leader. It is worth noting that the proposed control protocols do not require continuous information exchange between AUVs. For the static leader case, each AUV only needs to exchange position information with its neighbors at sampling instants. For the dynamic leader case, only partial follower AUVs can obtain position information of the leader AUV at sampling instants. By using the stability theory of impulsive systems and algebraic graph theory, sufficient conditions to guarantee the leader-following consensus of the multi-AUV system are obtained. Furthermore, both the proposed algorithms can save the bandwidth of underwater acoustic communication and improve the robustness of the system. Finally, two numerical simulations are provided to demonstrate the effectiveness of the proposed theoretical analysis.

Solution of the Dynamic Lame Problem

The well-known Lame problem, posed in 1852, involves solving the static equilibrium of a parallelepiped with free side surfaces subjected to action of opposite end forces. In this article, the same problem for a more complicated case of impacts of end forces is considered. An exact analytical solution of this problem is found. Emphasizing the particular difficulty of solving this problem, Lamé, in his book “Leçons sur la thorie mathematique de Ielasticite des corps solides” (Paris, 1852), wrote: “C’est une sorte d’engine aussi digne d’exercer la sagasite des analystes que le fameux problem des trios corps de la Mécanique celeste”,—“This is a kind of drive, as worthy of training the clairvoyance of analysts as the famous three-body problem of celestial mechanics.” At that time, this problem was the subject of a prize from the Paris Academy of Sciences, that was intended for the one who solved the Lamé problem. Despite this, to date, no solution has been found even for a static case of this problem, not to mention the complicated version of the problem.

CORRELATION FUNCTIONS AND QUASI-DETERMINISTIC SIGNALS

When processing data on random functions, they are most often limited to constructing an empirical correlation function. In this regard, the problem arises of constructing a random function (a quasi-deterministic signal) determined by a finite set of random variables and having a given correlation function. Moreover, a random function can often be considered Gaussian, since in many cases a random signal is obtained at the output of the system, which is fairly well approximated by a Gaussian. For stationary random processes and for random fields, this problem has been considered. For random sequences and discrete random fields, as well as for non-stationary random signals, the problem remained open. The article considers the problem of restoring a random sequence from known mathematical expectation and correlation function. Such a model random sequence is constructed, in which the mathematical expectation and correlation function coincide with the given ones. The mathematical expectation and the correlation function are the simplest probabilistic numerical characteristics, but they do not uniquely determine the corresponding set of probability distribution densities that satisfy the conditions of normalization and consistency, provided that for each fixed integer value of the parameter, the random sequence is a continuous random variable. The article considers the restoration of a quasi-deterministic signal in stationary and non-stationary cases. For the stationary case, three examples are given for constructing a quasi-deterministic discrete signal EMBED Equation.DSMT4 , provided that the spectral density has three different forms. For the non-stationary case, the corresponding quasi-deterministic signal was obtained for various cases of the spectrum. The use of a random function model determined by a finite number of parameters makes it possible to significantly simplify the analysis of applied problems, the solution of which is associated with differential equations with random coefficients, which are such quasi-deterministic signals. In this case, there is no need to use a complex apparatus of stochastic differential equations, since the solution of such an equation simply depends on random variables as on parameters.

Structure-preserving and helicity-conserving finite element approximations and preconditioning for the Hall MHD equations

We develop structure-preserving finite element methods for the incompressible, resistive Hall magnetohydrodynamics (MHD) equations. These equations incorporate the Hall current term in Ohm's law and provide a more appropriate description of fully ionized plasmas than the standard MHD equations on length scales close to or smaller than the ion skin depth. We introduce a stationary discrete variational formulation of Hall MHD that enforces the magnetic Gauss's law exactly (up to solver tolerances) and prove the well-posedness and convergence of a Picard linearization. For the transient problem, we present time discretizations that preserve the energy and magnetic and hybrid helicity precisely in the ideal limit for two types of boundary conditions. Additionally, we present an augmented Lagrangian preconditioning technique for both the stationary and transient cases. We confirm our findings with several numerical experiments.

STUDYING THE EFFECT OF RIFLING PARAMETERS ON THE STRESS STATE IN A GUN BARREL WALL WHEN FIRING

The problem of determining the stress state of the rifled-bore barrel when firing was presented in this article. Where the effects of rifling parameters such as the quantity of grooves n, groove width a, depth of groove t, radius of groove corner ρ were investigated. A rifled-bore barrel has been modeled and investigated by using Ansys software on the basis of finite element method. The problem has only been treated under pressure load in static case. The article can be used for reference to improve the accuracy in calculating design and manufacturing gun barrel.

Similarity-Driven Topology Optimization for Statics and Crash via Energy Scaling Method

Abstract Topology optimization (TO) is used in the initial design phase to optimize certain objective functions under given boundary conditions by finding suitable material distributions in a specified design domain. Currently available methods in the industry work very efficiently to get topologically optimized design concepts under static and dynamic load cases. However, conventional methods do not address the designer’s preferences about the final material layout in the optimized design. In practice, the final design might be required to have a certain degree of local or global structural similarity with an already present good reference design because of economic, manufacturing, and assembly limitations or the desire to re-use parts in different systems. In this article, a heuristic energy scaling method (ESM) for similarity-driven TO under static as well as dynamic loading conditions is presented and thoroughly evaluated. A 2D cantilever beam under static point load is used to show that the proposed method can be coupled with gradient-based and also heuristic, nongradient methods to get designs of varying similarity with respect to a reference design. Further testing of the proposed method for similarity-driven TO on a 2D crash test case and a large-scale 3D hood model of a car body indicates the effectiveness of the method for a wide range of problems in the industry. Finally, the application of similarity-driven TO is further extended to show that ESM also has the potential for sensitivity analysis of performance with respect to the extension of design domain.

Numerical Investigation on Drag and Vortex Induced Vibration Characteristics of Multiple Cylinders

The drag and vortex induced vibration (VIV) characteristics of a multiple cylinder are investigated using the detached eddy simulations. The multiple cylinders consist of a single main cylinder and twin auxiliary cylinders for a deep sea mining riser. Tandem and side-by-side arrangements are tested and compared with the single cylinder. The drag characteristics are investigated with the stationary case in the range of 0.5∼2.0 × 105 in Reynolds number (Re). The drag of the tandem arrangement shows smaller drag than those of the single cylinder while it’s consisted with the three cylinders. The stationary vortexes are observed at the clearance between the main and auxiliary cylinder which make the tandem arrangement become airfoil-like section as a total which induce the smallest drag than the other cases. The VIV characteristics are studied with the cases of forced oscillation in the cross-flow direction. The damping and added mass coefficients in cross-flow direction are estimated from the time series of the lift forces. Flow field analysis reveal the difference in VIV characteristics due to the variety of the arrangements and the single pipe.

Influence of Underlying Topography on Post-Monsoon Cyclonic Systems over the Indian Peninsula

During the post-monsoon cyclone season, the landfalls of westward-moving cyclonic systems often lead to extreme rainfall over the east coast of the Indian peninsula. A stationary cyclonic system over the coast can produce heavy rainfall for several days and cause catastrophic flooding. This study analyzes the dynamics of a propagating and stationary cyclonic system over the east coast, highlighting the possible cause behind the stagnation. The vorticity budgets of these two systems are presented using a reanalysis dataset. Vortex stretching and horizontal vorticity advection were the dominant terms in the budget. Vertical advection and tilting terms were significant over the orography. The horizontal advection of vorticity was positive (negative) on the western (eastern) side of the systems and, thus, favored westward propagation. Vortex stretching was confined to the upstream of orography in the stationary vortex. In the propagating vortex, the vortex stretching occurred over the orography during its passage. Data from the radiosonde soundings over a coastal station showed orographic blocking of the low-level winds in the stationary case. Conversely, the flow crossed the orographic barrier in the propagating case. Thus, the predominance of the upstream orographic convergence over the vortex circulation can be the reason for system stagnation over the coast.

Galileo-Based Doppler Shifts and Time Difference Carrier Phase: A Static Case Demonstration.

The European Commission is designing and implementing new regulations for vehicle navigation in different sectors. Commission Delegated Regulation 2017/79 defines the compatibility and performance of the 112-based eCall in-vehicle systems. The regulation has a large impact on road transportation because it requires that all cars and light duty vehicles must be equipped with eCall devices. For heavy duty vehicles, a set of new regulations has been developed, starting from EU Regulation No 165/2014, in which the concept of smart tachographs was introduced to enforce the EU legislation on professional drivers' driving and resting times. In addition, intelligent speed assistance (ISA) devices increase the safety of road users. These new devices fully exploit the Global Navigation Satellite System (GNSS) to compute position velocity and time (PVT) information. In all these systems, the velocity of the vehicle plays a fundamental role; hence, a reliable and accurate velocity estimate is of utmost importance. In this work, two methods for velocity estimation using Galileo are presented and compared. The first exploits Doppler shift measurements, while the second uses time difference carrier phase (TDCP) measurements. The Doppler-based technique for velocity estimation is widely adopted in current devices, while the TDCP technique is emerging due to its promising high accuracy. The two methods are compared considering all the Galileo signals including E1, E5a, E5b, E5 Alt BOC and E6. The methods are compared in terms of velocity errors for both horizontal and vertical components using real static data. From the tests performed, it emerged that the TDCP has increased performance with respect to the Doppler-based solution. Among the Doppler-based solutions, the most accurate solution is the one obtained with the E5 Alt BOC signal.

Convergence Analysis of the Phase-Scheduled-Command FXLMS Algorithm with Phase Error

In this paper, a phase-scheduled-command filtered-x least mean square (FXLMS) algorithm with a phase error between the disturbance and command signal is analyzed in detail. The influence of the phase error on the control effort, convergence time constant and performance of convergence is explained for both stationary and nonstationary disturbance signal cases. An estimation ratio, in both stationary and nonstationary disturbance cases, of the pseudo-error MSE convergence performance is also developed and discussed. Simulation results were collected to verify the analysis. The results show that, for both stationary and nonstationary disturbance, the phase error may heavily increase the distance of the optimum vector from the initial value, leading to a large control effort, a large convergence time constant and poor convergence performance. The estimation ratio also has a satisfactory performance for estimating the influence of the phase error.

Stochastic seepage analysis in embankment dams using different types of random fields

Random field theory has become a very popular approach for probabilistic analysis of earth dams. This study performs a stochastic analysis of seepage through an embankment dam to account for the spatial variability of hydraulic parameters. The originality of this study consists in using and comparing three types of Random Fields RFs for the seepage analysis: classical stationary RFs, conditional RFs (to consider the position of available measurements), and non-stationary RFs (to consider the mean variation with depth). The same sample of hydraulic conductivity values is considered to generate the three types of random fields. The hydraulic conductivity RFs are integrated into a Finite Element seepage analysis model to evaluate the flow velocity, hydraulic gradient, pore water pressure, and flow rate. The process is repeated by Monte Carlo simulations to characterize the spatial variability of the seepage results in terms of mean and standard deviation at each point of the studied dam and its foundation. The results show a higher dispersion for the stationary RF case and a lower dispersion for the conditional RF case. For the case study, the results also show that the use of different RFs for modelling the spatial variability of hydraulic conductivity induces differences that can be considered significant for flow velocity, moderate for hydraulic gradient and minor for pore pressure.

Regular hairy black holes through Minkowski deformation

Static and stationary regular black holes are examined under a minimal set of requirements consisting of (i) the existence of a well defined event horizon and (ii) the weak energy condition for matter sourcing the geometry. We perform our analysis by means of the gravitational decoupling approach and find hairy solutions free of curvature singularities. We identify the matter source producing a deformation of the Minkowski vacuum such that the maximum deformation is the Schwarzschild solution for the static case, and the Kerr metric for the stationary case.

Partially Coherent Cylindrical Vector Sources

A new class of stationary electromagnetic sources radiating outward from the surface of an infinitely long cylinder is introduced via vectorial coherent mode representation. First, two particular types of such sources are discussed: with either an electric or magnetic field aligned with the cylinder’s axis. The former case represents a scalar scenario, while the latter leads to the two-component electric field. The combination of these two types of sources is then considered by forming the three-component electric field vector. An extension to the stationary case is then made in which the electric field correlations are shown to be described by the intrinsically 3×3 cross-spectral density matrix. Several known theories of electromagnetic coherence and polarization are then invoked for the analysis of radiation, on and off the source surface. The results for the spectral density, degree of coherence, and degree of polarization are then discussed in detail. The effects of mutual correlation of modes are also outlined. The new family of sources is of importance for any application involving cylindrical sources with controllable radiation.

Thermodynamics of static and stationary black holes in Einstein–Gauss–Bonnet gravity with dark matter

This paper studies Einstein–Gauss–Bonnet (EGB) black holes surrounded by three phenomenological distributions of dark matter halos. The main result is obtaining the analytical solutions for the metric and all thermodynamic quantities, such as Hawking temperature, entropy, constant-volume heat capacity, and Gibbs free energy for static and stationary black hole solutions. Consequently, we determine a non-null horizon radius at which the black hole halts its evaporation by vanishing the temperature, indicating the emergence of remnants. In the stationary case, we also obtain the ergosphere regions for the found solutions and compare them. Finally, we find local and global phase transitions by studying the behavior of the heat capacity and Gibbs free energy.

Confidence Distributions for the Autoregressive Parameter

The notion of confidence distributions is applied to inference about the parameter in a simple autoregressive model, allowing the parameter to take the value one. This makes it possible to compare to asymptotic approximations in both the stationary and the nonstationary cases at the same time. The main point, however, is to compare to a Bayesian analysis of the same problem. A noninformative prior for a parameter, in the sense of Jeffreys, is given as the ratio of the confidence density and the likelihood. In this way, the similarity between the confidence and noninformative Bayesian frameworks is exploited. It is shown that, in the stationary case, asymptotically the so induced prior is flat. However, if a unit parameter is allowed, the induced prior has to have a spike at one of some size. Simulation studies and two empirical examples illustrate the ideas.

3D Modeling & Analysis Techniques for the Apollo Temple in Delphi

This paper demonstrates the application and usage of advanced 3D modeling techniques on monuments through the Apollo Temple in Delphi case study. Firstly, it combines 3D scanning and unmanned aerial vehicle (UAV) photogrammetry to produce an accurate 3D model of the monument, and afterward, it performs finite element modeling (FEM) analysis for both static and dynamic cases. Collapsing scenarios in the case of earthquakes are produced, predicting which parts would first collapse and under which regime the collapsing mechanism would be activated. From the results disclosed herein, the frequency profile of the seismic activity that could lead to resonance with the structure’s dynamic characteristics, and therefore to excessive damages or collapse, was identified. Static structural analysis pinpoints that maximum stress exhibited on the columns’ base never exceeds 0.1338 MPa. Among others, the main novelty of this paper is that it consists of an integrated and multidisciplinary paradigm that advances the available historical knowledge for a quite heavily investigated site.

Natural convection and entropy generation of hybrid nanofluid in double annulus separated by a thin rotating partition under magnetic field

The present study analyzes the impacts of using a rotating partition on the natural convection and entropy generation of nanofluid filled double annulus under magnetic field by using finite volume method. Effects of various pertinent parameters such as Rayleigh number (Ra: 104 – 6×105), rotational Reynolds number (Rew: 0-100), Hartmann number (Ha: 0–60), fin height (Hf:0.1–0.5) and fin number (Nf:4–20) on the thermal performance improvements are numerically assessed. The contributions of rotations to the overall thermal performance become different depending upon the activation of rotations and magnetic field effects. Depending on whether rotations exist, magnetic field effects have different impact on the behavior of heat transport and entropy generation. Thermal performance reduction amounts become 40% without magnetic field when comparing the rotating and stationary interface cases. Fins further improve the thermal performance up to 23% depending upon the existence of magnetic field while rises with existence of magnetic field and increasing its strength for the case of non-rotating interface while it shows opposite behavior for rotating interface case. When the location of the interface becomes closer to the outer surface of the annulus, reduction of the entropy generation up to 68% can be obtained. Artificial neural network based model provides successful estimation of thermal performance and entropy generation when considering the impacts of rotating interface.

Three-dimensional nonlinear dynamics of a thin liquid film on a spinning ellipsoid

The present work investigates the three-dimensional flow of a thin liquid film distributed on the outer surface of an ellipsoid, rotating around the vertical axis at constant angular velocity. The lubrication approximation expressing the evolution of the film thickness, originally developed for stationary curved substrates, has been re-derived by including the non-inertial forces associated with the rotation. This comprehensive model, which incorporates the gravitational, centrifugal, and capillary forces, is employed for a parametric investigation via numerical simulations. The results validate and extend the conclusions of our former study covering the axisymmetric case and bring about an advanced understanding by exploring non-axisymmetric effects. The parametric analysis sheds light on the significance of rotation on a non-constant curvature substrate by comparing the thickness profiles with the static case.

On the modal characteristics and stability of translating cable: Application to an overall line of cable transport systems

Moving cables are used for many applications in engineering structures such as cable-supported transport systems that involves mobile cables suspended between supports for moving attached vehicles. Advantages of such systems in terms of cost, footprint and energy efficiency make its urban integration as one of the solutions to meet the need for new mobilities. Because of the inherent cable’s flexibility and the modification of dynamic properties during the cable movement, such systems are sensitive to the effects of perturbations and self-sustaining oscillations. The methods commonly used to describe cable dynamics are restricted to small static sag case with a predominant vertical dynamics. To accurately analyse a multi-segment mobile cable, this paper proposes an hybrid analytical–numerical strategy to deal with a general mechanical elementary model of a cable in unsteady translation formulated in curvilinear abscissa derived from the formalism of continuum mechanics. An assembly procedure permits to deal with a more complex system considering a cable loop in contact with intermediary supports and punctual loads according to different boundary conditions, considering the coupling between the vertical dynamics activated at the local scale of a span and the longitudinal dynamics activated at the scale of the whole cable loop. The translation speed and acceleration gyroscopic effects on the system’s complex modes are studied and design rules are provided to guide an optimal conception avoiding strong oscillations of the system.

Scattering of Ions at a Rippled Shock

In a collisionless shock the energy of the directed flow is converted to heating and acceleration of charged particles, and to magnetic compression. In low-Mach number shocks the downstream ion distribution is made of directly transmitted ions. In higher-Mach number shocks ion reflection is important. With the increase of the Mach number, rippling develops, which is expected to affect ion dynamics. Using ion tracing in a model shock front, downstream distributions of ions are analyzed and compared for a planar stationary shock with an overshoot and a similar shock with ripples propagating along the shock front. It is shown that rippling results in the distributions, which are substantially broader and more diffuse in the phase space. Gyrotropization is sped up. Rippling is able to generate backstreaming ions, which are absent in the planar stationary case.