Elastic Line Research Articles

Failure analysis and structural optimization of unequal-parameter metal bellows in resistance to bending and torsional composite deformation

In practical engineering applications, metal bellows are subjected to complex environmental conditions, and they usually deform under the combined effects of tension, bending and torsion. In this paper, the bending and torsion composite deformation of unequal parameter metal bellows arranged alternately by large wave and wavelet is studied. Firstly, the finite element model of metal bellows is constructed, and the finite element simulation analysis of its mechanical properties is carried out. Taking the simulation results as samples, the multi-objective structural optimization of unequal parameter metal bellows under the condition of bending and torsion composite deformation is carried out. Combined with the bending-torsion composite deformation test and fracture microscopic characterization, the bending-torsion composite deformation characteristics and fracture failure mechanism of equal-parameter metal bellows (EPMB) and unequal-parameter metal bellows (Un-EPMB) were compared and analyzed. The results show that under the same deformation conditions, compared with the EPMB, the elastic limit bending line displacement and elastic limit torsion angle displacement of Un-EPMB are increased by 52.94 %, and the bending and torsional stiffness are greatly improved, moreover, the alternating waveform arrangement led to relatively gradual stress transfer through the Un-EPMB during the bending-torsion composite deformation process, thereby reducing stress concentration. Thus, the Un-EPMB exhibited more favorable mechanical properties. Unlike in the EPMB, which underwent fracture along the grain boundary, the cracks in the Un-EPMB appeared in the middle layer and propagated to both sides in a wavelike pattern. The dimples were distributed in the middle layer of the fracture, which indicates ductile behavior.

A theoretical framework for robust implementation of in situ measurements of ocean currents and waves in dynamics of mooring systems

We develop an approximated method to solve analytically the equations of motion that describe mooring line dynamics in a one-dimensional model. For the first time, we derive integral closed-form expressions to compute dynamic properties of mooring lines subject to ocean currents and waves of arbitrary time and spatial dependence, in terms of modified Bessel functions. This is done by decomposing the mooring line in three regions where different approximations and mathematical techniques of solution are carried out. Our analytical results provide a robust framework to simulate and analyze extreme realistic oceanic events when data from in situ ocean observation systems are available, regardless of the resolution or coarseness of subsurface measurements and even for long acquisition times. In order to prove the advantages of this approach, we have processed data from two stations in the National Data Buoy Center of the National Oceanic and Atmospheric Administration. From simulations with ocean currents data, we have gained insights into the coupling of the spatial modulation of ocean currents with the characteristic wavelengths of elastic lines. From simulations with ocean waves data, we have defined a scheme to analyze wave data and identify the contribution of each subset of frequency peaks to the net fluctuation of mooring line tension. This could be useful for classification of irregular waves based on their impact on mooring line tension. The development of better tools that integrate theoretical and experimental findings is necessary for the assessment of marine structures under the environmental conditions associated with climate change.

The dynamic response of a pressure transducer for measurements in water

Dynamic pressure measurements are indispensable in the field of fluid mechanics. Attaching tubing as a transmission line to the pressure transducer is often unavoidable but significantly reduces the usable bandwidth of the measurement system. Complex fluid-wall interactions and potential outgassing of air are present within systems with water-filled tubes. Comprehensive studies aiding researchers in selecting suitable transmission line parameters (i.e., material, length, and diameter) are not available. A simple calibration apparatus is designed for the frequency response characterization of multiple pressure transducers simultaneously applying a pressure step. The setup is thoroughly characterized and a detailed description is provided to optimize the bandwidth. A piezoresistive pressure transducer attached to water-filled tubes, as commonly used in hydrodynamic experiments, is characterized in the low-frequency range (i.e., f≤300\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f \\le {300}$$\\end{document} Hz). Tube-related effects, such as length, diameter, and material are investigated. The impact of entrapped air within the tubing is analyzed. The feasibility of substituting water with silicone oil to fill the tubes is explored. To optimize the usable bandwidth of the pressure measurement system for dynamic applications, it is essential to maintain short tubing that is as rigid as possible and free from entrapped air. Pressure wave propagation speed is reduced by two orders of magnitude in elastic transmission lines made of silicone. Pressure corrections through dynamic calibration are challenging due to the system’s sensitivity to various parameters affecting the dynamic response.

Design of Mixing Device Shafts Based on a Proposed Calculation Method Supported by Finite Element Method Analysis

The elasticity of bearings as well as their clearance have an essential influence on the total arrow and, therefore, on their own pulsation. In most of the literature, this elasticity is neglected in the calculation of shaft deflections. In some work, the elasticity of the bearings has been taken into account when calculating the deflection of the mixing device shaft, but this has been carried out on the basis of a high degree of customization: the behavior of the bearings has been considered linearly elastic, which does not correspond to reality because according to the elastic response of the bearing, it is a nonlinear function of the radial displacement. When the shaft of a mixing device operates in a pressure vessel, at the outlet of the pressure vessel, the shaft is provided with a sealing device, which can be considered a third bearing. This aspect is also not taken into account in the calculation of the shaft’s deflection, which leads to a certain degree of error in its determination. This study aims to highlight the influence of the elasticity of the bearings and the sealing device on the stiffness of the shaft and to propose a method that supports a calculation program for calculating the elastic line of a vertical cantilever shaft, considering the role played by the bearings in the case that they behave nonlinearly and the sealing device as the third bearing. This problem was solved both by applying our own method and with the help of the FEM.

Anomalous scaling of heterogeneous elastic lines: A picture from sample-to-sample fluctuations.

We study a discrete model of an heterogeneous elastic line with internal disorder, submitted to thermal fluctuations. The monomers are connected through random springs with independent and identically distributed elastic constants drawn from p(k)∼k^{μ-1} for k→0. When μ>1, the scaling of the standard Edwards-Wilkinson model is recovered. When μ<1, the elastic line exhibits an anomalous scaling of the type observed in many growth models and experiments. Here we derive and use the exact probability distribution of the line shape at equilibrium, as well as the spectral properties of the matrix containing the random couplings, to fully characterize the sample to sample fluctuations. Our results lead to scaling predictions that partially disagree with previous works, but that are corroborated by numerical simulations. We also provide an interpretation of the anomalous scaling in terms of the abrupt jumps in the line's shape that dominate the average value of the observable.

A novel algorithm for finding convex hull of a generic polygon with simulation of progressively supporting elastic lines

A novel algorithm for finding convex hull of a generic polygon with simulation of progressively supporting elastic lines

Utjecaj ekscentrične porivne sile na odabir statvenog kliznog ležaja

Stern tube slide bearing of the shaft line of the ship's propulsion system causes losses during operation. Friction and material wear of the tribosystem occur. One of the reasons is the different navigating regimes of the ship, which have an influence on the formation of the velocity field on the ship's propeller. The variable velocity field defines the magnitude and the position of the thrust force. The methodology presented in this paper is based on the fact of the existence of the eccentricity of the thrust force, i.e. loads due to the action of the moment of the eccentric thrust force. Due to the changing position of the thrust force, the curvature of the elastic line of the sleeve inside the stern tube bearing, which is mostly spatial, changes. Spatial elastic line of the sleeve has an influence on the working area of the slide bearing. Therefore, the importance of a sufficient thickness of the lubricant layer for lubrication in relation to these changes was highlighted. In this paper, this is the initial criterion for the selection of materials and lubricants of the stern tube bearing. An equally important criterion would be to define the possible harmful impact of lubricant leakage with particles of bearing bush material on the ecosystem. In order to facilitate the whole process, the simplified analytical model is presented, which can be used in the initial stage of stern tube bearing selection. Such a model allows a simpler analysis of the influence of the elastic line on the condition of the stern tube bearing due to the loading by the weight of the ship's propeller and by the moment of the eccentric thrust force. The procedure for the initial selection of the stern tube bearing created by this methodological approach could have its practical application. For this reason, the paper analyzed different navigating regimes and their influence on the working area of the stern tube slide bearing. The obtained results can be useful in the selection of materials and lubricants for the stern tube bearing tribosystem.

Loss of memory of an elastic line on its way to limit cycles.

Oscillatory-driven amorphous materials forget their initial configuration and converge to limit cycles. Here we investigate this memory loss under a nonquasistatic drive in a minimal model system, with quenched disorder and memory encoded in a spatial pattern, where oscillating protocols are formally replaced by a positive-velocity drive. We consider an elastic line driven athermally in a quenched disorder with biperiodic boundary conditions and tunable system size, thus controlling the area swept by the line per cycle as would the oscillation amplitude. The convergence to disorder-dependent limit cycle is strongly coupled to the nature of its velocity dynamics depending on system size. Based on the corresponding phase diagram, we propose a generic scenario for memory formation in disordered systems under finite driving rate.

Conceptual study of a new instrument for dynamic neutron scattering measurements-The modulated intensity with diffraction analysis spectrometer (MIDAS).

Dynamic neutron scattering probes unique nanoscale dynamics via measurement of energy exchanged between a sample and the neutrons. The two spectrometers that investigate processes with characteristic times around a nanosecond are backscattering (BS) and neutron spin-echo (NSE). We present a new method for measuring dynamics using an oscillating cosine-like energy-distribution neutron-package at the sample and measure solely the portion scattered into the elastic line. This portion corresponds to elastically scattered neutrons and, in addition, inelastic components that are scattered with a probability directly proportional to the cosine Fourier-coefficients of the exchanged-energy spectrum. The counts at the detector thus correspond to the van Hove intermediate scattering function. We denote this new method as "Fourier transform neutron scattering" (FTNS), it being broadly analogous to IR and Raman spectroscopies. Here, the realization of such a concept is investigated using an oscillating incident beam produced via a precession method and a secondary spectrometer identical to a BS instrument using crystal analyzers. The instrument is denoted "Modulated Intensity with Diffraction Analysis Spectrometer" (MIDAS). However, simpler approaches, e.g., choppers, may also be used for an FTNS instrument. The theory behind MIDAS is presented, supported by numerical calculations and in silico experiments. Finally, we present a Monte Carlo simulation to compare BS and MIDAS spectrometers. This shows that MIDAS has almost 100 times more incident flux than standard BS, but due to the better signal-to-noise ratio of BS, the final information acquisition rate gain of MIDAS is approximately a factor of 2.

Dynamics of the antiferromagnetic spin ice phase in pyrochlore spinels

Motivated by the classical spin-nematic state observed in the breathing pyrochlore spinel LiGa0.95In0.05Cr4O8, we theoretically discuss spin dynamics in models of spin-lattice coupling in these materials. Semiclassical dynamical simulations successfully recover the key features of inelastic neutron-scattering experiments on LiGa0.95In0.05Cr4O8: a broad finite-energy peak alongside a continuum of scattering near the (200) wave vector that extends from the elastic line to high energies. To interpret this result, we generalize linear-spin-wave theory for conventionally ordered magnets to the disordered spin-ice-like ground states expected for moderate spin-lattice coupling, which reproduces the numerical simulation results quantitatively. In particular, we find that the inelastic peak is well explained by collective modes confined to ferromagnetic loops of the underlying nematic order. In addition, we find a sharp, linearly dispersing mode in the dynamic structure factor, which originates in long-wavelength fluctuations of the nematic director. We believe identifying this mode will be an interesting target for future experiments on these materials. We also outline potential future applications of our methods to both pyrochlore spinels and other spin-nematic systems. Published by the American Physical Society 2024

Does the Larkin length exist?

The yield stress of random solid solutions is a classic theme in physical metallurgy that currently attracts a renewed interest in connection to high entropy alloys. Here, we revisit this subject using a minimal dislocation dynamics model, where a dislocation is represented as an elastic line with a constant line tension embedded in the stochastic stress field of the solutes. Our exploration of size effects reveals that the so-called Larkin length (Lc ) is not a length scale over which a dislocation can be geometrically decomposed. Instead, Lc is a crossover length scale marking a transition in dislocation behavior identifiable in at least three properties: (1) below Lc , the dislocation is close to straight, aligned in a single energy valley, while above Lc , it roughens and traverses several valleys; (2) the yield stress exhibits pronounced size-dependence below Lc but becomes size-independent above Lc ; (3) the power-spectral density of the dislocation shape changes scaling at a critical wavelength directly proportional to Lc . We show that for white and correlated stress noises, Lc and the thermodynamic limit of the yield stress can be predicted using Larkin’s model, where the noise dependence in the glide direction is neglected. Moreover, we show that our analysis is relevant beyond the minimal line tension model by comparison with atomic-scale simulations. Finally, our work suggests a practical approach for predicting yield stresses in atomistic models of random solid solutions, which only involves small-scale atomistic simulations below Lc .

Numerical and experimental investigation on crack detection in a beam using maximal overlapping discrete wavelet transform

The present study is concerned with detecting a crack in the beam numerically and experimentally using maximal overlapping discrete wavelet transform (MODWT). Slope discontinuity in the beam elastic line can reveal the presence of a crack in a beam. The MODWT is used for locating the cracks in a beam. MODWT coefficients are compared with discrete wavelet transform coefficients at different noise levels. For the experimental validation, high-resolution measurements of the cantilever beam deflection are obtained using photographic measurements. The algorithm is tested for the detection of cracks away and near the ends of a beam. Crack detection near the end of the beam is difficult due to border distortion. Border distortion suppresses the signal in that region. Isomorphism is utilized to shrink the border distortion zone. It helps in the better visualization of the spike due to the crack located away from the ends. Moving averaging is applied to the MODWT-based results for better localization of the spike near the crack position.

РАСЧЁТ НА ПРОЧНОСТЬ И ПРОВЕРКА ЖЁСТКОСТИ СТАТИЧЕСКИ ОПРЕДЕЛИМОЙ БАЛКИ ДВУТАВРОВОГО СЕЧЕНИЯ

This paper presents a strength calculation for a statically determinate I-beam. Diagrams of internal force factors (transverse forces and bending moments) are constructed and the number of the I-beam is selected according to the given external load and the values of the material strength characteristics. The given material characteristics are permissible normal stress, elastic modulus and permissible shear stress. The strength of a beam with a selected cross-section for shear stresses was tested. To construct the I-beam elastic line, the deflections of cross-sections with a unit interval along the length are calculated. The beam deflections were calculated using the universal elastic line equation. The obtained value of the maximum beam deflection made it possible to draw a conclusion about the beam sufficient hardness and operability under given external loads.

Improving the processing accuracy of the puller shaft of the cotton harvesting machine controlling the dynamic system parameters

The article is dedicated to improving the accuracy of shaft turning by controlling the elastically deformed state of the part during processing. This study is conducted on the example of a puller shaft of a cotton harvesting machine, which belongs to the class of non-rigid parts such as bodies of rotation. To evaluate the possibilities of the method and establish theoretical patterns of the behavior of the part during transverse-longitudinal bending, the equation of the elastic line of a non-rigid shaft is solved. An integral assessment is adopted as a criterion of the accuracy in controlling elastic deformations of a technological system.

Kinematically excited beam vibrations under random perturbations

There is numerous information in the technical and scientific literature that often the sources of forced kinematically excited oscillations have a clearly expressed random nature. Kinematically excited vibrations of beams are considered. Their sources are random disturbances. Steady (in a probabilistic sense) vibrations of beams are studied. As a consequence, the transverse vibrations of the beam will also be random, and it becomes necessary and expedient to switch to stochastic motion models.&#x0D; Introduction. For a random perturbation process, a spectral matrix is specified. Initial conditions for the equations are not required. The boundary conditions are similar to those used for free and kinematically excited deterministic oscillations. The task is to find the spectral matrix of the random field of beam deviations and dispersion for a given spectral matrix. The question of determining the mathematical expectation is not raised. It is argued that it can be easily reduced to known deterministic problems.&#x0D; Methods. To carry out specific calculations, a model of kinematic disturbances is used in the form of a vector N-dimensional stationary random process with stationary connected components that have hidden periodicities (characteristic frequencies). A test example was completed to determine the dispersion and standard deviation of displacements. The numerical integration step was adopted after numerical experiments. When performing calculations, the parity of the integrand was taken into account. The lower limit of integration is taken to be zero, followed by doubling of the final result.&#x0D; Results. For small values of the broadband parameter, the results of the stochastic and deterministic problems differ little. Examples are presented that are stochastic analogs of harmonic oscillations. For beams under kinematic harmonic disturbances, test examples were performed to determine dispersions and standard deviations.&#x0D; The discussion of the results. The results of calculations in the article are presented by curves having numbers that coincide with the numbers of the matrices. The first matrix corresponds to the absolute correlation of disturbances. The second matrix corresponds to the absolute correlation between the first and third, second and fourth disturbances, while these pairs are absolutely uncorrelated. The third matrix describes random perturbations when the indicated pairs, being perfectly positively correlated within, are absolutely perfectly negatively correlated between pairs. The fourth curve corresponds to the case of ideal correlation of the first three disturbances with each other, while the movements of the fourth support are in antiphase with them. In the latter case, the movements of the outer supports are in antiphase with the movements of the middle ones, which favors the greatest bending of the beam. Therefore, the elastic line has a curvature that is significantly greater than the others.

Аппроксимация статической упругой линии несущего каната при тяговом расчете однопролетных мобильных канатных дорог

During the operation of cargo and passenger aerial ropeways, carrying-traction ropes are subject to natural sagging under the influence of their own weight, transported cargo or passenger cabins, wind and temperature effects. The ability to model the geometric shape of a rope, taking into account the conditions and operating modes of ropeways, is necessary when designing and modeling work processes in the rope system, optimizing the design and characteristics of the drive and tension mechanisms. This article presents a method for determining the analytical dependence approximating the configuration of the static elastic line of the carrying-traction rope, in relation to the problem of trac-tion calculation of single-channel single-span mobile ropeways. The peculiarity of the proposed approach is to take into account the inequality of the tension forces of the carrying-traction rope at the ends of the span, which makes it possible to more adequately reflect the real situation.

Improvement on the axial force accuracy of the ANCF Euler-Bernoulli beam element with the second-order approximate function of the centerline and precise constraint equations

The conventional Euler-Bernoulli beam element of the absolute nodal coordinate formulation (ANCF) yields incorrect axial force due to the existence of the first-order approximate function of the centerline and over-constraint equations. This work aims to improve the axial force accuracy of the element by using the second-order centerline approximate function and precise constraint equations. The second-order function includes the quintic Hermite shape function and the vector of nodal coordinates containing zeroth to second-order derivatives of position. The elastic force vector of the element and its tangent stiffness were then formulated based on the decoupled elastic line method. The exact kinematic requirements of three types of constraint points were fully clarified. On this basis, the corresponding concise constraint equations, constraint Jacobian and Hessian matrices were rigorously derived in the context of ANCF, where G2 continuity was demonstrated to be satisfied at the node acted by an inclined concentrated force, the relative rotation constraint of the rigid joint was described using the dot product of the gradients on both sides of the joint, and the fixing gradient direction at the partially-clamped end was expressed by using the zero cross product of the end gradients in the initial and deformed configurations. Large deformation problems of typical beams under fixed and follower loads were solved using five types of elements, where the results of the ABAQUS B22 elements were taken as a reference for validation. It is found that when using the first- and second-order beam elements having over-constraint equations of the three types of constraint points, obvious axial force error occurs near the corresponding constraint points. In comparison, a few second-order elements containing the derived constraint equations output correct axial force consistent with ABAQUS. However, a large number of the first-order elements containing the correct constraint equations still yield inaccurate axial force in certain beam regions.

Modeling of suspended weightlessness on the cables of the beam system, by changing the tension forces

The problem of weightlessness simulation of beam systems suspended on inextensible cables is considered. Imitation of weightlessness means zeroing or reducing any selected force factor (for example, the reaction of the support or the moment in the support or joint), and the kinematic factor (deflection or angle of rotation). It is required to select the forces in the cables such that the sum of the squares of the deflections at the points of the elastic line of the beam is minimal. The problem is formulated as a nonlinear programming problem; the search for the minimum of the objective function with constraints, in the form of equilibrium equations, is carried out. In general, all equations written out for a geometrically variable system are linearly dependent. Parameters are selected from the system of equations, the vectors at which are entered into the basis, and the remaining parameters are considered free and are the coordinates of the objective function. The problem was reduced to the problem of quadratic programming without restrictions. Partial derivatives of coordinates give a system of linear algebraic equations that allows you to determine the coordinates taken as free parameters, and then calculate the coordinates entered into the basis. The reference plan of nonlinear optimization problems can have local minima; it is shown that for any initial basis, the optimal plan is the only one. To calculate the deflections of the beam, the method of initial parameters is used. Deflection, angle of rotation, additional angles of rotation in articulated joints are considered as initial parameters; as well as the reaction and bending moment. The continuum problem is transformed into a discrete one by limiting the number of points at which deflections are calculated. The objective function has a finite number of variables. It is determined which number of selected points on the elastic line of the beams is sufficient to ensure the convergence of the functions of deflections, angles of rotation, bending moments and transverse forces for the purpose of application to practical calculations. Optimization of deflections of a beam pivotally fixed, suspended on two cables with verification of solutions, change of basic variables and convergence study depending on the choice of the number of points at which deflections are calculated is performed. The deformation of systems of I-beams connected by hinges to each other, having linear weight in gravity conditions, is analyzed. To simulate weightlessness, the system is supported by six cables. The boundary conditions are considered: – rigid pinching; – hinge-fixed support, – sliding sealing; – free edge. Models of three-beam systems in the simulation of weightlessness, to a certain extent equivalents. The type of boundary condition affects the first beam to a greater extent; the tension forces of the cables equalize the deformed and stressed state in subsequent beams. Any of the considered systems with the presented boundary conditions can be converted into an equivalent one by changing the boundary force factors, setting torques or installing a spring with a given stiffness and adjusting the tension of the cables.

Analytical model for thermo-mechanical interaction induced residual stress distribution during multi-conditional machining Inconel 718

Residual stress induced by coupling thermo-mechanical fields cannot be completely released and remains inside the workpiece after the cutting process, which has a significant impact on the fatigue resistance, corrosion resistance and deflection of manufacturing parts. This work focused on an analytical model for thermo-mechanical fields induced residual stress distribution during multi-conditional machining superalloy Inconel 718. Based on the relationships of material properties, cutting parameters, and cutting geometric conditions, the proposed analytical model investigated the thermo-mechanical fields based on the semi-infinite space elastic mechanical line load and the uneven film thermal stress distribution under the action of moving heat sources. The development process of residual stress was examined through the changes in the stress release process from loading to unloading based on the in-plane stress assumption solution. The effects of basic cutting variables including cutting speeds, uncut chip thickness and tool wear on the thermo-mechanical fields were discussed. According to the experimental and predicted results, the residual stress distribution characteristics were evaluated including surface residual stress, reverse peak stresses, transition position, and total influence depth, indicating that the proposed analytical model could obtain the residual stress distribution characteristics with the predicted error of approximately 4.3%–11.9%, 3.9%–73.4%, 4%–33.3%, and 3.3%–25.7%, respectively. This work can provide significant theoretical support for the analysis of the residual stress generation to control surface integrity during the cutting process.

Влияние поперечной нагрузки на устойчивость сжимаемого продольной силой стержня

The work is devoted to the study of the effect of normal load&#x0D; on the stability of a rod compressed by a longitudinal force.&#x0D; Two types of boundary conditions are considered: the boundary&#x0D; conditions of rigid sealing and the conditions of hinge support.&#x0D; It is noted that in the case of the boundary conditions of&#x0D; the hinge bearing, the shape of the elastic line of the rod qualitatively&#x0D; depends on the magnitude of the longitudinal force.