Free-end Boundary Conditions Research Articles

Global Responses Analysis of Submerged Floating Tunnel Considering Hydroelasticity Effects

To investigate the applicability and differences in wave loads and the dynamic response calculation principles for SFT on an entire-length scale, two numerical models of entire-length SFT with identical dimensions and parameters were established. These models are employed by a 3D diffraction method based on rigid-body assumptions, the potential flow theory and the Dummy-Connection-Mass (DCM) method based on the lumped mass method and Morison equation while considering hydroelasticity effects. The applicability of the potential flow theory and Morison equation for wave load calculation of SFT is presented along with the differences in their dynamic response calculation, which aim to explore the impact on SFT dynamic responses considering hydroelasticity by comparing the numerical calculation results. Furthermore, a comparison between free-end boundary and fixed-end boundary models, established using the DCM method, is conducted to examine the reasonableness of the commonly adopted free-end boundary condition.

Structural response of submerged floating tunnels with free-end boundary condition based on an analytical approach

Until now, the investigation of structural behavioral characteristics of submerged floating tunnels (SFTs) has primarily relied on numerical methods that demand intensive calculations. This preference stems from the challenges in deriving an analytical solution, given the complexity of the structural system and applied loadings. To address this, an analytical approach based on practical assumptions has been developed to assess the structural responses of SFTs. Mainly, to mitigate excessive internal forces in tunnel segments and facilitate an analytical approach, a free-end boundary condition is assumed. Under these assumptions, the analytical approach can effectively determine the structural response of SFTs in the time domain. The proposed approach was validated by a hydrodynamics-based numerical analysis using the finite element method program ABAQUS/AQUA. In the harsh wave conditions of the Messina Strait, this approach matches well with numerical analyses, except in cases of extremely low submergence depth or exceptionally large tunnel diameter compared to mooring stiffness. This analytical approach can rapidly and accurately evaluate the structural behavior of SFTs, especially when considering the specific environment and design loads at the basic design stage. Therefore, this method is practically valuable. However, its application should be carefully exercised due to the several limitations.

Laboratory Experiments Qualify Bit Influence on High-Frequency Torsional Oscillations

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 212566, “Qualifying Bit Influence on High-Frequency Torsional Oscillations Based on Full-Scale Laboratory Experiments,” by Armin Kueck, Eliah Everhard, and Xu Huang, Baker Hughes, et al. The paper has not been peer reviewed. _ High-frequency torsional oscillations (HFTOs) generate dynamic loads that can damage drilling tools, resulting in cracks, twistoffs, or broken electronics. Recently, a full-scale drilling test rig was proven to generate verified HFTO behavior under laboratory conditions. This rig allows for a comprehensive study of the influences of bit characteristics on HFTO. The complete paper presents methods to qualify bit features to suppress HFTO. Laboratory Rig Setup Test-Rig Design. The full-scale laboratory test rig drills rocks in a pressurized rock chamber. Rate of penetration (ROP), weight on bit (WOB), rotational speed, pressure, bit type, and rock type can be varied. The simulator consists of an open-loop mud-circulation system with capacity for 200 bbl of fluid, two 1,000-hp triplex pumps capable of up to 500 gal/min, a hoisting mechanism for raising and loading the drillstring up to 10,000 lbf, a 1,000-hp rotary drive capable of up to 10,000 ft-lbf, and a pressure vessel rated to 10,000 psi. High-frequency measurement instrumentation, including in-bit vibration sensors, records the tangential accelerations and dynamic torque at various positions in the BHA. The mounted device can be seen in the top left photo in Fig. 1. Measurement. To initially characterize the frequency response of the system, an impact test was performed on the system in a suspended nonoperating state with roving accelerometers (sensors) positioned as indicated by the blue lines in Fig. 1. Also indicated are the free-end and fixed-end boundary conditions at the bit (left) and drive (right), respectively, as well as the point of reference impact. The data from each pair of sensors are then processed to separate the torsional motions from lateral. Because HFTO is a self-excited vibration, it must be validated that this type of vibration is actually excited in the laboratory setup. To demonstrate that the excitation mechanism is representative for the field, one of the test results was used as a reference. A laboratory investigation showed that the measured vibration matches characteristics of self-excited vibrations. Investigations in the laboratory will, therefore, lead to valid solutions in the field.

A Study On Flight Vibration Environmental Test of Unmanned Aerial Vehicle using Dual Electric Vibration Exciters

Analysis of dynamic characteristics and flight vibration test for unmanned aerial vehicles was studied by using dummy test body. The FEM model for dummy test body was supplemented by results of modal and random vibration test. The free end boundary condition to simulate flight environments was made by test setup using bungee cable. Prior to the flight vibration test using a dual electric vibration exciters, the test procedure to calculate quantitative vibration level was studied by using military specification. The actual test was successfully done by using the analysis and pretest results. From the analysis results, it was possible to determine the feasibility of the test by predicting the excitation force of the flight vibration test and to get the response of any point which could not be measured by the test. The results of this study will much contribute to the Test and Evaluation of unmanned aerial vehicles.

Shear vibration modes of granular structures: Continuous and discrete approaches

AbstractThis work is dedicated to the study of shear vibration modes of one‐dimensional granular microstructured beams using a discrete Cosserat model. The dynamic response of the one‐dimensional granular beam (discrete beam) is investigated for various boundary conditions, through the analytical resolution of an exact discrete eigenvalue problem. For an infinite number of grains, the dynamic behavior of the discrete problem converges towards a Bresse–Timoshenko continuum beam model. First, the effective modeling parameters, the constitutive equations and the governing equations of motion are derived in a difference form. For simply supported granular beams, the appearance of pure shear modes of vibration is highlighted (vibration modes without deflection), a phenomenon which is already known in the free vibration of a continuous Bresse–Timoshenko beam problem. The eigenfrequencies of these pure shear modes for the discrete granular beam coincide with the critical frequencies of the discrete system. These pure shear modes may appear for granular beams composed of few grains, which give a physical support of a phenomenon well studied in the literature from a continuum beam model. The eigenfrequencies of the discrete granular beam are also calculated for various boundary conditions, including clamped, hinge and free end boundary conditions. Based on the discrete element method (DEM), several numerical simulations of dynamic tests in some representative examples have been performed. The responses of the numerical approach are accurately compared against the exact results of the analytical solutions based on the difference eigenvalue problem, which illustrates the relevance of the proposed approach.

A Study on the Flight Vibration Environmental Specification of Unmanned Flying Vehicle using Random Vibration Test and Analysis Methods

In this study, analysis of dynamic characteristics and flight vibration was performed to unmanned aerial vehicles. The analysis model was supplemented by performing a dynamic characteristic test and a random vibration test using manufactured dummy aerial vehicle. For the dynamic characteristic test, a bungee cable was used to implement the free end boundary condition. Prior to the flight vibration test using a multiple electric shaker, a random vibration test was performed to predict the excitation force during the actual flight vibration test. It was judged that the actual test could be predicted more accurately by supplementing the analysis model from the test results. In addition, it was possible to determine the feasibility of the test by predicting the excitation force of the flight vibration test.

Decoupling bi-directional fluid–structure interactions by the Koopman theory: Actualizing one-way subcases and the role of crosswind structure motion

We propose a novel thinking of decoupling bi-directional fluid–structure interactions (bi-FSI) into simpler mono-directional components for analytical insights. The decoupling aims to overcome nonlinearity by the Koopman theory and transform bi-FSI into a linear superposition of the fluid-to-structure, structure-to-fluid, and interactive subcases. This first of a serial effort presents the wind tunnel experimental and computational fluid dynamics numerical actualizations of the fluid-to-structure and structure-to-fluid subcases via rigid and forced vibration models, which are indispensable requisites to the forthcoming Koopman analysis. The results have been analyzed with respect to flow field phenomenology, and the role of forced vibration, hence cross-structure motion alone, has been isolated and elucidated. Compared with the rigid case, crosswind motion weakens leading-edge separation, promotes shear layer curvature and the impingement of the asymmetric wall jets, and hastens reattachment. Consequently, it causes premature shedding of the roll substructure and delays the formation of the rib substructure, effectively altering the Kármán shedding frequency. It also reduces three-dimensional suppression of the Kármán shedding near the fix- and free-end boundary conditions, overarchingly devolumizing wake coherent structures and weakening the Kármán street's intensity. Results also suggest that increasing the wind speed from the characteristic speed of the vortex-induced vibration (VIV) to that of galloping intensifies vortical activities but causes no fundamental change in flow field phenomenology. Therefore, the underlying causes of VIV and galloping are not attributed to the flow field nor structure motion alone but to the interactive mechanisms unique to bi-FSI.

Волновые движения жидкого топлива в тороидальных сосудах с учетом капиллярного эффекта

A numerical approach is proposed to solve the linear sloshing problem of an incompressible inviscid liquid with account for surface tension effects, which are predominant in the low-gravity environment. A variational formulation is derived by the linearization of motion equations for the liquid near its initial equilibrium state with consideration of a pressure drop on the free surface and a free-end boundary condition on the contact line. The continuous problem domain is discretized by the finite element method. After discretization, the classical generalized eigenvalue problem is obtained, whose solutions are the natural frequencies and mode shapes. Several examples show the effect of the Bond number and the fluid-filled volume on the liquid behavior in toroidal tanks. A comparison of numerical results with experimental measurements under ground conditions reveals that under microgravity condition, the surface tension force and the boundary condition on the contact line play an important role when determining the natural frequencies and mode shapes of the liquid sloshing. Each fluid-filled volume has its own characteristic Bond number, above which the natural frequencies approximate to the experimental values obtained under ground conditions. The presented results can be used in the coupling dynamic analysis of a spacecraft with propellant tanks. The author is grateful to the supervisor associate professor A.N. Tem-nov for help in formulating the problem and discussion of the results of the work.

Investigation of Crystal Shape Controllability in the Micro-Pulling-Down Method for Low-Wettability Systems.

This study presents the criteria for shape control in the micro-pulling-down (μ-PD) method for low-wettability systems (dewetting μ-PD method), which enables us to achieve highly shape-controllable crystal growth. In the dewetting μ-PD method, the presence of the die wall inhibits the direct observation of the meniscus during the process. Therefore, in this study, the meniscus shape was calculated using the Young–Laplace equation to predict the optimal crystal growth conditions. The free-end and fixed-end boundary conditions to be satisfied for the differential equations were defined at the triple point, with the melt on the die wall. The relationship between the crystal diameter and pressure in the fixed-end condition, wherein the wetting angle (α) at the triple point of the crystal was 90°, indicated the suppression of the melt infiltration by the presence of crystals. The gap between the die and crystal was minimized for the contact angle (θ) and growth angle (αgr) in the fixed-end and free-end conditions, at which |αgr + θ – π| was minimum at a given pressure under the assumption of single-valued solutions. The results of this study will facilitate the formation of noble-metal alloys with a net shape and expand the scope for the development of new materials.

Survey of shear coupling behavior in FCC Ni and BCC Fe grain boundaries

In this study, the shear coupling behavior of 388 FCC Ni and 408 BCC Fe grain boundaries is surveyed under a wide range of temperatures (e.g., 100 – 1000 K in Ni and 100 – 1400 K in Fe) via the recently developed ramped synthetic driving force method with free end boundary conditions. It is found that there is no universal dependence of the shear coupling behavior on temperature or driving force among the grain boundaries being surveyed, i.e., an increase in temperature or driving force may make the shear coupling factor increase, decrease, or remain unchanged depending on grain boundary type. Furthermore, a continuous change in driving force is shown to generate complex shear coupling behaviors in both FCC Ni and BCC Fe bicrystals at each temperature. Observed behaviors include both smooth changes and sharp transitions in shear coupling factor within increasing driving force. Despite this complex behavior, it is found that there is no fundamental difference in the shear coupling behavior between FCC Ni and BCC Fe grain boundaries: (1) all types of transitions in shear coupling behavior that are observed in FCC Ni are also found in BCC Fe; (2) the grain boundaries with low Σ values (e.g., Σ3−Σ11) in both Ni and Fe generally show small or zero shear coupling except for a few special grain boundaries with high symmetry. Collectively, these results highlight the complexity that must be captured to construct a general model for shear coupled grain boundary migration.

Gravity waves oscillations at semicircular and general 2D containers: an efficient computational approach to 2D sloshing problem

We compute the natural frequencies for the oscillations of the free boundary of gravity waves in contact with a solid container. First, we study the case of a semicircular shaped container. We deduce an integrodifferential evolutionary equation for the linearized free boundary and impose pinned-end and free-end boundary conditions. For both cases, the natural oscillations frequencies for the free surfaces are provided and compared with the frequencies in the absence of solid walls. Then, we study the effect of having an underwater rectangle-shaped bottom in a rectangular container and the corresponding frequencies. The method introduced can be applied to arbitrary 2D containers, with all the information on their geometry contained into a matrix (related to the conformal mapping into a half-plane) that appears as a factor in a linear system for the computation of eigenfrequencies.

Sliding paths for series of Frenkel-Kontorova models – a contribution to the concept of 1D-superlubricity

Newton trajectories are used to calculate low energy pathways for a series of Frenkel-Kontorova models with 6 and up to 69 particles thus up to a medium chain, and an expedition to 101 particles. The model is a finite chain with free-end boundary conditions. It has two competing potentials and an additional, external force. We optimize stationary structures and calculate the low energy paths between global minimums for a movement of the chain over its on-site potential, if an external tilting by a push- and/or pull direction is applied. We propose to understand a low energy path for a possibility of a superlubricity of the chain. We compare different misfit parameters. The result is that the minimums differ only little, however, the critical length of the chain, Ncr, depends on the misfit parameter. Ncr describes the end of a ‘good’ calculability of the Newton trajectory which follows the low energy pathway of the chain through the potential energy surface, for a movement of the chain along the axis. We discuss reasons for the boundary of an Ncr. However, we assume that the low energy paths exist beyond their calculability by NTs.

A model for a driven Frenkel–Kontorova chain

We study a Frenkel–Kontorova (FK) model of a finite chain with free-end boundary conditions. The model has two competing potentials. Newton trajectories are an ideal tool to understand the circumstances under a driving of an FK chain by external forces. To reach the insights we calculate some stationary structures for a chain with 23 particles. We search the lowest energy saddle points for a complete minimum energy path of the chain for a movement over the full period of the on-site potential, a sliding. If an additional tilting is set, then one is interested in barrier breakdown points (BBPs) on the potential energy surface for a critical tilting force named the static frictional force. In symmetric cases, such BBPs are often valley-ridge inflection points of the potential energy surface. We explain the theory and demonstrate it with an example. We propose a model for a DC drive, as well as an AC drive, of the chain using special directional vectors of the external force.

Newton trajectories for the tilted Frenkel–Kontorova model

ABSTRACTNewton trajectories are used for the Frenkel–Kontorova model of a finite chain with free-end boundary conditions. We optimise stationary structures, as well as barrier breakdown points for a critical tilting force were depinning of the chain happens. These special points can be obtained straight forwardly by the tool of Newton trajectories. We explain the theory and add examples for a finite-length chain of a fixed number of 2, 3, 4, 5 and 23 particles.

Effect of symmetry on electronic DOS, peierls transition and elastic modulus of carbon nanowires

A Monte Carlo arithmetic method is utilized to investigate the Peierls transition in the linear and circular carbon nanowire respectively. The carbon nanowires interacting with the 6 nearest neighbors in hexagonal structure are spaced by 0.3 nm. Despite the Peierls transition of the linear carbon nanowires is unaffected by the Van der Waal’s force, we discovered that the Peierls transition temperature of the isolated curved nanowire is raised to 910K under curvature. Based on the simulation results, the fluctuation of the atomic position of the atoms are stronger near to the free end boundary condition. Applying stress on the interstitial doped carbon nanowire array examines the elastic modulus which shows above 6TPa. The geometrical effect on the electronic density of states of the kink structural carbon chain is simulated by Harris functional in combination with Local Density Approximation. Two different lengths of branches A and B, are occupied alternatively to generate the asymmetric carbon chain. The ratio of the asymmetric branch length, RAB = A / B, plays an important role in the electronic density of states DOS around Fermi level . The highest DOS(EF) occurs if the RAB equals to 2 and while the Fermi level coincides with the Von-Hove singularity at RAB = 3.

Statics and dynamics of nanorods embedded in an elastic medium: Nonlocal elasticity and lattice formulations

Abstract This paper is focused on the static and the dynamic behaviour of an axial lattice (with direct neighbouring interaction) loaded by some distributed forces and in interaction with an elastic medium. Some exact analytical solutions are provided both in static and in dynamic settings, for the finite lattice system under general boundary conditions including fixed- and free-end boundary conditions. A nonlocal rod model based on the introduction of one additional length scale, is then constructed by continualization scheme of the lattice difference equations, to capture the scale effects associated with the lattice spacing. The continualized nonlocal model coincides with a phenomenological Eringen's nonlocal model, except eventually for the boundary conditions. These new continualized nonlocal boundary conditions are derived from the end lattice boundary conditions. The enriched nonlocal wave equation augmented by the elastic medium interaction has a spatial derivative which coincides with the local wave equation, thus avoiding the need of higher-order boundary conditions. The static and the dynamic responses of the equivalent nonlocal bar are also analytically studied and compared to the lattice problem. It is shown that the nonlocal solution efficiently fits the lattice one, both in static and in dynamic settings. The nonlocal model can be also introduced from variational arguments, thus leading to a nonlocal optimal Rayleigh quotient. For very high frequencies, the nonlocal model is corrected by a two-length scale model, which is shown to capture efficiently the frequency spectra of the lattice model for all frequency range.

Analytical study on stress-induced phase transitions in geometrically graded shape memory alloy layers. Part II: Analyses on geometrical shapes, loading procedures and boundary conditions

Based on the asymptotic ODE system derived in part I of this series of papers, the mechanical behaviors of geometrically graded shape memory alloy (SMA) layers with different shapes, loading procedures and boundary conditions are studied in the current paper. First, for SMA layers with concave and convex shapes, the stress-strain curves during a full loading cycle are plotted based on the analytical solutions to the asymptotic ODE system, which can capture most of the experimental features. The effects of width ratio on the responses of the SMA layers are also discussed. Second, corresponding to the inner loops of the stress-strain curves, the configurations and phase states of the SMA layers with the different shapes are simulated. The underlying mechanisms responsible for the experimental features are also investigated. Third, the effects of boundary conditions are studied, where the free end boundary conditions, the mixed boundary conditions and the clamped boundary conditions are taken into account. The corresponding analytical solutions are derived and the responses of the SMA layers are simulated, which are compared with each other to reveal the effects of boundary conditions. The results obtained in the current paper further demonstrate the validity of the analytical approach for studying the phase transitions in geometrically graded SMA specimens.

Resolvent approach to the fourier method in a mixed problem for the wave equation

The method of contour integration as applied to the resolvent of the spectral problem is used to substantiate the Fourier method in a mixed problem for the wave equation with a complex potential and boundary conditions generalizing free-end boundary conditions. Minimum smoothness assumptions are made about the initial data. Krylov’s technique of accelerating the convergence of the Fourier method is essentially employed.

Synchronization enhancement via an oscillatory bath in a network of self-excited cells

The possibility of using a dynamic environment to achieve and optimize phase synchronization in a network of self-excited cells with free-end boundary conditions is addressed in this paper. The dynamic environment is an oscillatory bath coupled linearly to a network of four cells. The boundaries of the stable solutions of the dynamical states as well as the ranges of coupling parameters leading to stability and instability of synchronization are determined. Numerical simulations are used to check the accuracy and to complement the result obtained from analytical treatment. The robustness of synchronization strategy is tested using a local and global injection of Gaussian white noise in the network. The control gain parameter of the bath coupling can modulate the occurrence of synchronization in the network without prior requirement of direct coupling among all the cells. The process of synchronization obtained through local injection is independent of the node at which noise is injected into the system. As compared to local injection, the global injection scheme increases the range of noise amplitude for which synchronization occurs in the network.

Effects of a locally injected signal on phase synchronization in a network of self-excited cells

We consider in this paper the problem of phase synchronization in a network of coupled self-excited cells with free-end boundary conditions. The eigenvalues properties are used to perform the stability boundaries of the synchronization process for pure sinusoidal and quasi-sinusoidal oscillatory states. In the case where the cells’ oscillatory states are quasi-periodic, more energy and time are required for the network to become fully synchronized, compared to the case where each cell exhibits a periodic oscillation. The influence on the stability boundaries of a periodic external excitation locally injected in the network is tackled. For both cases (with and without local injection), numerical simulations are used to check the accuracy and to complement the results derived from the analytical treatment. In this configuration, the local injection helps to drastically increase the range of the coupling parameter for which all cells become synchronized.