Elastic Line Research Articles

NUMERICAL DIFFERENTIATION OF COMPLEX BEND FORMS OF LONG ROTATING RODS

The technique of numerical differentiation of the complex bend forms of long rotating rods is presented. This technique is based on search for new bend forms of the rotating rod by solving the equations of oscillations with using the Houbolt time integration method and the polynomial functions (splines) that are described the current bend form. In it, the spline functions are found by current bend form approximation where each of the found functions is responsible to certain point of rod elastic line and describes the position of nearby points. Described technique was realized in a computer program with graphic user interface that is developed by author. Program allows to monitor for dynamics of the oscillatory motion of the modeled system in real-time by calculating and drawing the current band forms of the rotating rod during the oscillation. The results of investigation of the oscillations of long rotating rod are shown. This rod is modeling the drill string operation. Results are shown by possible bend forms at different moments of time after system had been out of equilibrium. It is noted that the action of an axial compressive force that is pointed to the lower end of the vertical heavy rod leads to the effect of twisting to a spiral of its lower part. This effect arises via action of gyroscopic moments, which begin to appear when the lower part of the rod starts to bend and this bending have been growing. It happens because the growth of bending leads to increase the angles of rod cross-sections’ turn, the velocity of change of which is part of the gyroscopic moment. The displayed instance shows, that the considered technique and developed on its basis software allows to investigate the dynamics of the objects which are modeled by heavy long rods.

The parametric oscillations of rotating rods under action of the axial beat load

The paper presents the results of investigation of the axial beat loads’ influence on the transverse rotating rods’ oscillations and their stability. The perforator's long drills are considered as objects of investigation.The analysis of different author’s papers that are studded the dynamics of oscillations of shafts and rotating rods is carried out. The relevance of the research topic is substantiated. The model of the considered dynamic system is described and equations of oscillations in space are given.The technique for investigation is presented. This technique is based on search for new bend forms of rotating rod by solving the equations of oscillations with using the Hubbolt time integration method and the polynomial functions (splines) that are described the current bend form. In it, the spline functions are found by current bend form approximation where each of the found functions is responsible to certain point of rod elastic line and describes the position of nearby points.Described technique was realized in a computer program with graphic user interface that is developed by author. Program allows to monitor for dynamics of the oscillatory motion of the modeled system in real-time by calculating and drawing the current band forms of the rotating rod during the oscillation.Diagrams with regions of stable and instable motion of the rods, that were found by different parameters and boundary conditions are shown. The analysis of the results is obtained and the conclusion about possibility of operating the equipment in certain frequency ranges is done. The space oscillating process of rotating rods is considered with account of the gyroscopic loads and geometric nonlinearity.

A preliminary numerical study of the wake effects on the fatigue load for wind farm based on elastic actuator line model

Abstract Wake effect commonly exists in the current large wind farms, which will cause not only 10–20% decline of whole power production but also 5–15% increase of fatigue loading on the wind turbine rotor. As a result, it is an important topic to quantify wake-induced fatigue damage in wind farm. In the current research, coupled with precursor method, elastic actuator line model was employed to simulate the fatigue damage loading on the wind turbine blades in wind farm. An obvious peak shift can be found between the power spectrum of upstream and downstream wind turbines, which is induced by the wake turbulence. From the simulation results, it was found that the high amplitude loading cycles of downstream wind turbine is much higher than that of upstream one, which will definitely cause the fatigue damage on the blades. This research work is a preliminary research for the wake-induced fatigue damage by elastic actuator line model. More quantitative study about the wake-induced fatigue damage will be carried out in the future work.

Experimental investigation on characteristic change of a scale-extendable chain-type floating structure

The present paper reports an experimental investigation in order to understand the characteristic evolution of a chain-type floating system with increasing number of modules up to five. Semi-submersible modules are fabricated, connected by hinges and constrained by elastic mooring lines for experimental tests in a wave flume. The module responses of floating structures in various configurations are measured and analyzed in different wave periods and wave heights. In general, the response in longitudinal direction of multi-modular floating structure can be significantly improved by the increasing number of modules, while the effects of increasing modules on the heave and pitch responses are negligible. Based on the rigid module flexible connector (RMFC) model, validated by the experimental data, the connector loads of the experimental prototypes are assessed. The results indicate that longitudinal hinge loads increase doubly as modular number is added up to four, and afterwards increases very slow for further additional modules. The maximum longitudinal load usually occurs on the interior connectors, not on the connectors near the bow and stern. The level of vertical shear load mainly depends on the wave period rather than the number of modules in the floating platform. More detailed remarks are listed in conclusions.

Pocket‐creation method with pulley clip elastic line traction for large rectal tumors

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Elastic beam line with noticeable deflection

Two differential equations are considered in the article. They describe the elasticity line of a curved beam. The second is obtained from the first if the derivative of the deviation function of the beam axis from the straight line is negligible. The question of the proximity of both solutions is studied. The literature considers many options for deviations from ordinary conditions, such as composite beams, complex deformations, too much bending. In our case, the hypothesis of Kirchhoff is supposed to be fulfilled.The following cases are considered: 1) a beam supported by two supports, and 2) a cantilever beam. The load is distributed evenly. Graphs of solutions are constructed for both equations at different load densities and beam stiffness. A parameter is found, knowing which, we can indicate from the table below how many percent these two solutions differ in. Our task is to find out the limits of application of conventional calculation methods for strong beam bending.

Theory and model implementation for analyzing line structures subject to dynamic motions of large deformation and elongation using the absolute nodal coordinate formulation (ANCF) approach

This paper presents the theory development and numerical implementation of a new gradient-deficient-based ANCF (Absolute Nodal Coordinate Formulation) model applied to perform the nonlinear dynamic analysis of elastic line structures subject to large stretching and deformation. The derivations of model equations, introduced numerical approaches, and result validations are the focuses of this study. Different from the traditional rod theory for small stretching consideration, the present model implements the line structures’ large elongation concepts into both the control mechanisms of constitutive formulations and equations of motion. The effect of external hydrodynamic forces on structures is also included in the model formulations. Based on the conservation of energy, the line model developed in this study covers the variation in strain and takes a full account of the bending effect with large stretching. A finite-element-based implicit scheme according to a modified Newmark-beta method is employed to solve the assembled system equations with unknown variables of nodal position vectors, their tangential derivatives, and strains. Selected cases with dynamic motions, such as nonlinear oscillation of a compound pendulum, free falling of a horizontal elastic beam in air with two different settings of gravity, free falling of a submerged horizontal tether with and without an attached concentrated mass, and a submerged vertical tether with a prescribed translational motion, are simulated to verify the developed model by comparing the results with analytical solutions and published experimental data and numerical results. It is found the present ANCF model, as noticed with good matched results with analytical solutions, measurements and other published solutions, is demonstrated to be able to provide converged and reasonably accurate predictions on the responses of line structures subject to large dynamic motions.

Analysis of the Finite Differences Numerical Method and Method Analysis of Successive Integrations in the study of a simply supported beam subjected to distributed load

In the present article a study is presented between the methods: analytical and numerical (Finite Difference Method “MDF”). In the analysis, the elastic line and bending moment of a beam were studied in both methods. The simply supported beam submitted to a distributed loading represents one of the most important examples in engineering. Deformation analysis is an important procedure in Structural Engineering. Initially, the Differential Equation of a beam is presented, and we tried to find the analytical and numerical solutions. Subsequently, the results are presented using tables and graphs for both methods and it was concluded that the numerical method provides satisfactory results.

Biaxial flexural response of Strain-Hardening UHPFRC circular slab elements

The biaxial flexural response of strain-hardening UHPFRC circular slab element is investigated experimentally and analytically using the ring-on-ring test. The Digital Image Correlation (DIC) technology is applied to capture the 3D full-field of strain and deflection of the tensile surface through the whole loading process. Based on DIC analysis, a quasi-elastic limit is determined additionally to characterize the flexural response of UHPFRC under biaxial stress condition. The random and uniform distribution of matrix discontinuities in UHPFRC in the quasi-elastic domain, as well as multiple fictitious crack formation in hardening domain, is highlighted. In addition, ring-on-ring test and Four-Point Bending Test (4PBT) results are compared with special emphasis on flexural strength and characteristics of matrix discontinuity development. The results show higher ultimate flexural strength and energy absorption capacity at ultimate limit from the ring-on-ring test, and almost same flexural strength at the quasi-elastic limit for both tests. Finally, a simplified inverse analysis is proposed for the ring-on-ring test based on the elastic slab bending and yield line theories. The calculation results indicate a 19% lower tensile elastic limit stress of the UHPFRC, while an almost equivalent value of tensile strength is obtained from the ring-on-ring test, compared with the 4PBT results.

Aeroelastic Performance Analysis of Wind Turbine in the Wake with a New Elastic Actuator Line Model

The scale of a wind turbine is getting larger with the development of wind energy recently. Therefore, the effect of the wind turbine blades deformation on its performances and lifespan has become obvious. In order to solve this research rapidly, a new elastic actuator line model (EALM) is proposed in this study, which is based on turbinesFoam in OpenFOAM (Open Source Field Operation and Manipulation, a free, open source computational fluid dynamics (CFD) software package released by the OpenFOAM Foundation, which was incorporated as a company limited by guarantee in England and Wales). The model combines the actuator line model (ALM) and a beam solver, which is used in the wind turbine blade design. The aeroelastic performances of the NREL (National Renewable Energy Laboratory) 5 MW wind turbine like power, thrust, and blade tip displacement are investigated. These results are compared with some research to prove the new model. Additionally, the influence caused by blade deflections on the aerodynamic performance is discussed. It is demonstrated that the tower shadow effect becomes more obvious and causes the power and thrust to get a bit lower and unsteady. Finally, this variety is analyzed in the wake of upstream wind turbine and it is found that the influence on the performance and wake flow field of downstream wind turbine becomes more serious.

Second magnetization peak effect and the vortex phase diagram of V0.0015NbSe2 single crystal

Effect of the weak point disorder on vortex matter phase diagram is studied by incorporation of V atoms through magnetic and magnetoresistance measurement in layered NbSe2 single crystal. We observe that the point disorder introduces fishtail effect and the second magnetization peak (SMP) in the M-H curve of V0.0015NbSe2 at magnetic field far below upper critical field (Hc2). 3D Collective creep of elastic flux line lattice (FLL) support the vortex motion below the onset of SMP. However, the crossover from collective to plastic deformation of FLL support the occurrence of SMP effect. Presence of the peak effect in pinning force density near irreversible magnetic field (Hirr) indicates the 2D to 3D distortion of FLL due to lattice softening associated with the rapid reduction of elastic modulus. Magneto transport measurement shows the glassy transition near the zero resistance region. In the glassy region, the flux line shows 2D characteristics. Above zero resistive region, thermally activated flux flow region is well described by Arrhenius relation. It is seen that the activation energy is decreased significantly by the incorporation of V atoms in NbSe2. The magnetic field dependence of activation energy follows a power law of U0(H) ~ H-α where the exponent α changed from 0.5 to a 0.9 at a crossover field of Hcr = ~ 0.7 T, indicating the transition from weak plastic deformation of FLL to the strong entangled state in vortex liquid phase. Finally a vortex phase diagram is constructed demonstrating all the different phases of vortex lattice of V0.0015NbSe2 at different magnetic fields and temperatures.

Crack detection in a beam using wavelet transform and photographic measurements

An optimistic attempt for the detection of a crack in a beam using discrete wavelet transform is proposed. Finite element model of the simply supported beam with a transverse open crack is considered. Crack in a beam causes a slope discontinuity in the elastic line. The deflection of the beam is used to locate the slope discontinuity using wavelet transform. The effect of measurement noise on the wavelet decomposition level is studied. An inexpensive digital image based technique is employed to obtain the deflection of the cracked beam for experimental investigations. White pixels due to dust particles are removed using connected component algorithm. A suitable edge detection technique is selected for finding the edged image on the basis of peak signal to noise ratio values. The deflection of the non-cracked edge of the beam is used as an input signal for wavelet transform to detect the crack location. Detection of a crack in the beam with different crack depths is investigated experimentally. The proposed method works well with numerically simulated as well as experimentally measured cracked beam deflections.

Vibroprotective mechanism with the quasizero stiffness for seats of operators of construction and road machines

The paper considers vibration isolation device with a quasi-zero stiffness, which nonlinear element is made in the form of a closed elastic rod, an elastic line described by the circle. The authors list the features of stiffness and strength characteristics of the device, and select the parameters that ensure the full protection on a portion of the suspension.

Flux expulsion in niobium superconducting radio-frequency cavities of different purity and essential contributions to the flux sensitivity

Magnetic flux trapped during the cooldown of superconducting radio-frequency cavities through the transition temperature due to incomplete Meissner state is known to be a significant source of radio-frequency losses. The sensitivity of flux trapping depends on the distribution and the type of defects and impurities which pin vortices, as well as the cooldown dynamics when the cavity transitions from a normal to superconducting state. Here we present the results of measurements of the flux trapping sensitivity on 1.3 GHz elliptical cavities made from large-grain niobium with different purity for different cooldown dynamics and surface treatments. The results show that lower purity material results in a higher fraction of trapped flux and that the trapped flux sensitivity parameter $S$ is significantly affected by surface treatments but without much change in the mean free path $l$. We discuss our results within an overview of published data on the dependencies of $S(l,f)$ on $l$ and frequency $f$ using theoretical models of rf losses of elastic vortex lines driven by weak rf currents in the cases of sparse strong pinning defects and collective pinning by many weak defects. Our analysis shows how multiscale pinning mechanisms in cavities can result in a maximum in $S(l)$ similar to that observed by the FNAL and Cornell groups and how pinning characteristics can be extracted from the experimental data. Here the main contribution to $S$ come from weak pinning regions at the cavity surface, where dissipative oscillations along trapped vortices perpendicular to the surface propagate into the bulk well beyond the layer of rf screening current. However, the analysis of $S$ as a function of only the mean free path is incomplete since cavity treatments change not only $l$ but pinning characteristics as well. The effect of cavity treatments on pinning is primarily responsible for the change of $S$ without much effect on $l$ observed in this work. It also manifests itself in different magnitudes and peak positions in $S(l)$, and scatter of the $S$-data coming from the measurements on different cavities which have undergone different treatments affecting both $l$ and pinning. Optimizations of flux pinning to reduce flux sensitivity at low rf fields is discussed.

TLS for Dynamic Measurement of the Elastic Line of Bridges

The evaluation of the structural health of a bridge and the monitoring of its bearing capacity are performed by measuring different parameters. The most important ones are the displacements due to fixed or mobile loads, whose monitoring can be performed using several methods, both conventional and innovative. Terrestrial Laser Scanner (TLS) is effectively used to obtain the displacements of the decks for static loads, while for dynamic measurements, several punctual sensors are in general used. The proposed system uses a TLS, set as a line scanner and positioned under the bridge deck. The TLS acquires a vertical section of the intrados, or a line along a section to be monitored. The instantaneous deviations between the lines detected in dynamic conditions and the reference one acquired with the unloaded bridge, allow to extract the displacements and, consequently, the elastic curve. The synchronization of TLS acquisitions and load location, obtained from a Global Navigation Satellite System GNSS receiver or from a video, is an important feature of the method. Three tests were carried out on as many bridges. The first was performed during the maneuvers of a heavy truck traveling on a bridge characterized by a simply supported metal structure deck. The second concerned a prestressed concrete bridge with cantilever beams. The third concerned the pylon of a cantilever spar cable-stayed bridge during a load test. The results show high precision and confirm the usefulness of this method both for performing dynamic tests and for monitoring bridges.

МАТЕМАТИЧНА МОДЕЛЬ МІЖФАЗНОЇ ТРІЩИНИ В ПЛАСТИНЦІ З ПІДСИЛЕНИМ КРУГОВИМ КОНТУРОМ ПРИ ЇЇ ЗГИНІ

Побудовано математичну модель задачі про підсилення замкненим пружним ребром контуру кругового отвору в нескінченній ізотропній пластинці, яка перебуває в умовах циліндричного згину на нескінченності, за наявності на межі поділу матеріалів міжфазної тріщини (розрізу), береги якої в процесі деформації не контактують. Наближений розв’язок системи сингулярних інтегрально-диференціальних рівнянь задачі здійснено методом механічних квадратур і колокації. Розглянуто числовий приклад.

Critical scaling and aging near the flux-line-depinning transition

We utilize Langevin molecular dynamics simulations to study dynamical critical behavior of magnetic flux lines near the depinning transition in type-II superconductors subject to randomly distributed attractive point defects. We employ a coarse-grained elastic line Hamiltonian for the mutually repulsive vortices and purely relaxational kinetics. In order to infer the stationary-state critical exponents for the continuous non-equilibrium depinning transition at zero temperature T = 0 and at the critical driving current density j_c, we explore two-parameter scaling laws for the flux lines' gyration radius and mean velocity as functions of the two relevant scaling fields T and j - j_c. We also investigate critical aging scaling for the two-time height auto-correlation function in the early-time non-equilibrium relaxation regime to independently measure critical exponents. We provide numerical exponent values for the distinct universality classes of non-interacting and repulsive vortices.

Series solution of beams with variable cross-section

In structural engineering beams with non-constant cross-section or beams with variable cross-section represent a class of slender bodies, aim of practitioners’ interest due to the possibility of optimizing their geometry with respect to specific needs. Despite the advantages that engineers can obtain from their applications, non-trivial difficulties occurring in the non-prismatic beam modeling often lead to inaccurate predictions that vanish the gain of the optimization process. As a consequence, an effective non-prismatic beam modeling still represents a branch of the structural engineering of interest for the community, especially for advanced design applications in large spans elements.A straight beam of length l with variable inertia J(z) is provided in figure, subject to a generic live load condition q(z). The vertical displacement y(z) can be obtained from the solution of the differential equation of the elastic line, i.e., taking into consideration the inertia variability and neglecting, as first approximation, any shear contribution. Even if this solution is an approximate one, it is able to deal with the problem in its basic formulation.In this paper a solution for the problem stated is formulated using a series expansion of solutions, in a general load and cross section variability condition. Solution is thus obtained for a generic rectangular cross section beam with a variable height. Analytical solution is presented and evaluated using numerical evaluation of some cases of practical interest.

Monitoring system of high-rise buildings, determined from the nature of the curvature of the elastic line of vertical elements

Introduction. Issues arising from the automatic monitoring of high-rise buildings are considered. One of such issues is the necessity of minimizing the number of sensors when taking the operational patterns of such load-bearing systems. The method of sensor placement in high-rise buildings is described. Materials and methods. Different structural systems of high-rise buildings have common dependencies of longitudinal axis deformation on rigidity of vertical and horizontal load-bearing elements. Calculation of deformations from static wind load, comparison of data obtained by manual and computer calculation, and also comparison of static wind load with the wind load pulsation component are performed. Results. From the analysis of the extrema of the deformation function of the building vertical axis with the horizontal plane of the floor structure preserved, the main typical monitoring points necessary to minimize the number of sensors in high-rise buildings were determined. Based on the typical breaking points, the required number of sensors located 1/4 of the building height away from each other and the range of measured values of deformations that occur during operation were determined. Conclusions. For automatic (constant) monitoring of high-rise buildings, it is advisable to use a complex integrated method of measuring deformations of vertical load-bearing structures, frequencies and amplitudes of oscillations, and rotation angles. According to the general design theory of high-rise buildings and computer calculation models, the most efficient placement of engineering structure monitoring sensors is when they are evenly covering the perimeter of each floor and the entire height of the building. Measurements should be carried out following the outlines of the floor structures on stories located 1/4 of the building height away from each other, as well as on the stiffening core to control the integrity of floor structures and their connection to the stiffness core.

Stress-strain relationship of translucent nanocrystalline Gadolinium Zirconate ceramic with grain size below 10 nm using nanoindentation

Translucent nanocrystalline Gadolinium Zirconate (Gd2Zr2O7) ceramic with grain size below 10 nm was successfully fabricated using high pressure sintering technology at 5 GPa and low temperature of 550 °C. The bilinear compressive stress-strain relationship of this sample was firstly extracted from nanoindentation procedure based on the partial unloading method. It indicated that the plastic deformation did not originate from dislocation sliding and was controlled by the grain boundary sliding. Moreover, the compressive yield strength, σy=7.8 GPa of the translucent nanocrystalline Gd2Zr2O7 ceramic was also determined by the intersection of the theoretical elastic line and the indentation compressive stress-strain line.