Free-end Conditions Research Articles

A wind tunnel investigation of the effects of end and laminar/turbulent inflow conditions on cylinder vortex-induced vibrations

The influence of end and inflow conditions on the vortex-induced vibrations of a cylinder is studied on the basis of wind tunnel experiments, combining measurements of the body displacement and flow velocity in its wake. The cylinder of length-to-diameter aspect ratio 5.5 has one end exposed to the current. It is elastically mounted in the cross-flow direction, with low damping. The structure to displaced fluid mass ratio is close to 1000. The behavior of the system is explored over a range of values of the reduced velocity, U⋆, defined as the inverse of the oscillator natural frequency, non-dimensionalized by the inflow velocity (U∞) and the cylinder diameter (D), typically between 4 and 8, at a Reynolds number of the order of 104, based on U∞ and D. Three end conditions are examined: two free-end conditions with either a flat or a hemispherical shape, and a condition where a fixed plate is placed close to the flat end. Three inflow states are considered: a laminar condition and two grid-generated turbulent conditions of different turbulence intensity levels (up to 10%) and comparable integral length scales, around 30% of D. Vibrations characterized by bell-shaped evolutions of their magnitude with U⋆ develop, under flow-body synchronization (lock-in), in all conditions, with peak amplitudes ranging from 4% to 12% of D. The free end causes a shift of the response bell-shaped curve towards higher U⋆ values. The shift may be such that there is no overlap between the vibration domains in the end-plate and free-end conditions. The passage from laminar to turbulent inflow conditions is found to attenuate this shift. A clear reduction of vibration amplitude is observed when the end plate is removed, and the amplitude is further reduced when the flat end is replaced by the hemispherical one. On the other hand, turbulent inflows induce a global enhancement of the vibration amplitudes, which may reach +45% relative to the laminar stream condition. The end/inflow conditions are also shown to impact the regularity of the structural responses.

Analytical solution for longitudinal seismic response of immersed tunnel connecting artificial islands crossing different strata

Immersed tunnels typically pass through zones with different soil properties and may be subjected to earthquake threats. This paper presents a theoretical model using two flexible joints and three tube-elements for the longitudinal seismic response analysis of immersed tunnel connecting artificial islands. According to the reaction displacement method, the governing equations for bending of the immersed tunnel are established. Based on the matrix transfer principle, the end boundary conditions and the joint continuity conditions were considered in the analytical model. The analytical solutions were verified using finite element simulation results. Results indicate that the fixed and hinged end conditions have large shear forces on both ends, while the fixed end conditions have large bending moments. The free and roller end conditions have large vertical displacements on both ends, while the hinged end conditions have large rotation angles. The free end conditions can better reflect the boundary conditions of immersed tunnel connecting artificial islands. The flexible element joints can significantly reduce the shear forces at the interface of different strata, but also produce larger deformations at the joints. However, this amount of deformations can be accommodated by the flexible joints themselves, thus minimizing the damage to the immersed tunnel under seismic loading.

Analysis of the wake flow behind concave curved cylinders with velocity measurements by particle image velocimetry and modal decomposition

The properties of the wake flow behind concave curved cylinders have been investigated analyzing simultaneously the mean velocity profiles extracted along concentric arcs parallel to the cylinder axis and the dynamically most relevant coherent structures obtained by spectral proper orthogonal decomposition. These analyzes have allowed us to determine the position, the extension, and the evolution of the different wake regimes. The velocity measurements have been obtained through the stereo particle image velocimetry (stereo-PIV) technique. The study considers various Reynolds numbers, based on cylinder diameter (240<Re<840), and curvatures. The quarter-of-ring cylinder is first analyzed. Near the cylinder root, the flow exhibits a topology dominated by an oblique vortex shedding, contrary to what is observed in the literature for similar geometric configurations. We attribute this disagreement to differences in the treatment of the free-end conditions that play a role in triggering the shedding regime. We find that the local shedding inclination is driven by the axial velocity, whereas its extension and wavelength depend mainly on the Reynolds number. The near free-end region presents, instead, two counter-rotating standing vortices that induce a cross-wise velocity directed toward the cylinder root and a tip vortex that expands evolving downstream. As the Reynolds number increases, the wake presents irregularities and the shedding spreads becoming nearly normal to the incoming flow. At smaller curvatures, the cylinder free-end becoming more inclined with respect to the incoming flow, and the free-end effects are enhanced. The interaction with the vortex sheets of the standing vortices that develop at the leeward side weakens. As a consequence, these vortices stretch in the stream-wise direction giving rise to the trailing vortices that stem from the cylinder surface and affect the cross-wise velocity distributions.

Evaluation of static and dynamic responses considering thickness stretching effect for layered composite and sandwich arches using exponential shear and normal deformation theory

Present theory investigates the dimensionless vibration frequencies, deformations, and stresses for multilayered and sandwich arches using exponential shear and normal deformation theory (ESNDT). Present studies consider the effect of [1+(z/R)]radius of curvature while selecting the displacement field of arches under the action of uniform load. It includes the effects of transverse shear (γxz≠0) and transverse normal deformation(εz≠0)i.e., effect of thickness stretching. The governing relations are obtained using the Navier's method, and Hamilton's virtual work principle. The proposed layered arches are completely free from shear correction, and its top and bottom surfaces is satisfies zero traction free end conditions. Present study obtained very accurate natural frequencies for layered sandwich arches than other theories because, available literature not considered the thickness stretching effect i.e.,(εz=0). Hence, the present scientific investigation accounts the effect of thickness stretching i.e.,(εz≠0). However, the non-availability of exact elasticity results of bending and dynamic responses for layered sandwich arches. Present theory is obtained vibration frequencies, displacements, and stresses of layered composite and sandwich arches; the results are compared and validates through prior published literature.

Novel test method to determine shear properties of lattices: Test set-up and data analysis

In order to determine shear response for lattices, relevant standards for other similar materials were studied. A V-notched beam shear test set-up was developed, including design of a fixture and a V-notched lattice specimen as well as determining test procedure and data analysis method. Followings are some of the considerations and features. Sufficient number of cells are required to obtain representative properties for a given lattice. The free-end condition for installation and gripping of the specimen on fixture arms guarantees loading in pure shear. The overall geometry and presence of a V-notch smooth the shear stress variation across the notch section. It was demonstrated that using Digital Image Correlation (DIC) method improves the accuracy of measured shear strain by removing the deformation of cells adjacent to the notch, as well as the deflection of fixture components. Following the proposed method, shear properties including shear chord modulus of elasticity, offset shear strength, and shear ultimate strength/strain can be determined. These data can be used for material specification, quality assurance, research and development, and structural design and analysis of lattices.

Enhancing the physical and structural properties of poly(glycolide-co-trimethylene carbonate-co-ε-caprolactone) copolymer fibers.

Nowadays, due to the methodological needs in the application of internal surgery new methods evolving novel design for surgical suture are recommended. In this work, the effect of cold drawing process and the thermal annealing process on the different optical and structural properties of surgical suture fibers were studied. For the thermal annealing process, samples of Monosyn monofilaments suture fibers were thermally annealed at temperatures ranging from 50 to 100 for annealing time=120 min. The thermal treatment was carried out under free end condition. For the cold drawing process, an Instron was used to mechanically draw and measures the tensile stress strain curve of Monosyn samples. Using differential scanning calorimetry, X-ray diffraction techniques, and optical polarizing microscope the different properties of the tested sutures, such as the crystallinity, sample radius, birefringence, molecular orientation, and tensile properties were measured. From the resulting data, there was a marked increase in the physical and structural properties during the thermal annealing and cold drawing processes. This means that a new reorientation of Monosyn suture molecular chains were performed and approved by calculating the different orientations f(θ) and fc . This is an important improvement for these biodegradable materials to widen their medical use and improve their clinical results. RESEARCH HIGHLIGHTS: The stress-strain curve for Monosyn surgical fiber is J shape and identical to the human tissue stress-stain curve. The different orientation calculated improve that the drawing process affect directly on the fiber chain orientations. The fiber chains orientation due to the cold drawing process causes strain induced crystallinity.

ANALYTICAL SOLUTION FOR NONLINEAR INTERACTION OF EULER BEAM RESTING ON A TENSIONLESS SOIL

The nonlinear interaction between an elastic Euler beam and a tensionless soil foundation is studied. Exact analytical solutions of the challenging problem are rather complicated. The basic obstacle is imposing compatibility conditions at lift-off points. These points are determined as a part of the solution although being needed to get the solution itself. In the current work, solutions are derived using the approximate Rayleigh-Ritz method. The principal of vanishing variation of potential energy is adopted. The solution is approximated using a set of suitable trial functions. Lift-off points are identified through an iterative procedure and compatibility conditions are satisfied implicitly. Results are presented for various cases, including clamped support and free end condition. Various distributed loading conditions are analyzed. Exact solutions are revised briefly. Accurate high order approximate analytical solutions are obtained using MAXIMA symbolic manipulator. The convergence of approximate solutions towards the exact solutions is verified. For each case detailed results of deflection, bending moment and shear are presented.

Numerical and experimental verification of a method of identification of localized damages in a rod by natural frequencies of longitudinal vibration

A method for identification of multiple transverse cracks and other localized defects in a rod by means of two spectra of longitudinal vibrations that correspond to free–free and fixed–free end conditions is presented. A numerical algorithm is developed that implements the method. The algorithm was tested on experimental data obtained on a cylindrical sample of aluminum alloy D16 with the created localized damages. The experiments were carried out on a rod with free ends. The created damages were ring grooves symmetrically located relative to the middle of the rod. With the help of such experiments, natural frequencies were obtained that correspond to two types of boundary conditions for a half-length rod. The experimental data were processed using the developed algorithm. The results showed that the model on which the developed algorithm is based describes well the longitudinal vibrations of the rod with localized damages in a fairly wide frequency range, and the algorithm enables to reconstruct multiple damages accurately enough.

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.

Dynamic responses of laminated composite sandwich beam with double-viscoelastic core layers

In this paper, the dynamic responses of double-core sandwich composite beam has been performed using experimental and numerical methods. The numerical model of the laminated composite single-core and double-core sandwich beams has been modelled using ANSYS software. An experimental modal test has been carried for single-core and double-core sandwich beams under clamped clamped (CC) and clamped free (CF) end conditions. The developed single-core and double-core numerical model is verified with experimental results. The analysis results clearly shows that the stiffness of the double-core composite sandwich beam are higher than those of single-core composite sandwich beam due to the higher stiffness offered by double-core. Further, the parametric study was performed to analyze the effect on a laminated composite double-core sandwich beam of different fiber angle orientation, thickness ratios and aspect ratios.

Mechanical characterization and experimental modal analysis of 3D Printed ABS, PC and PC-ABS materials

Additive manufacturing (AM) process builds the parts, layer by layer precisely from Computer-Aided Design (CAD) models, whereas traditional subtractive manufacturing process removes layers from materials to attain the desired shape. Of late Rapid prototyped (RP) parts are used for the direct production of components for manufacturing and testing in the industries. Understanding material, machine used along with the process variables that affect the strength of the final part gains importance as the parts can be printed directly from CAD data and effectively integrated into structures. The main aim of this investigation is to present the mechanical characterization and free vibration analysis of various 3D printed Engineering Plastic Materials. Acrylonitrile Butadiene Styrene (ABS), Polycarbonate (PC), and Polycarbonate–Acrylonitrile Butadiene Styrene (PC-ABS) materials are used in this study. Spools are prepared from plastic pellets using wire extruder. Tensile tests have been performed on dog bone specimens to evaluate strength, fractured specimen’s surfaces which are further evaluated using Field Emission Scanning Electron Microscope (FESEM) to explore fracture of the raster and bonding between layers. From the experimental results it’s noticed that the PC-ABS material exhibits improved elastic limit and load-carrying capacity compared with ABS and PC. Three types of beams are fabricated using different materials and modal analysis has been conducted to predict the stiffness of beams in terms of natural frequencies under clamped free (CF) and clamped clamped (CC) end conditions. Higher natural frequencies observed with PC-ABS is compared with the rest of the materials.

On the solution of the purely nonlocal theory of beam elasticity as a limiting case of the two-phase theory

In the recent literature stance, purely nonlocal theory of elasticity is recognized to lead to ill-posed problems. Yet, we show that, for a beam, a meaningful energy bounded solution of the purely nonlocal theory may still be defined as the limit solution of the two-phase nonlocal theory. For this, we consider the problem of free vibrations of a flexural beam under the two-phase theory of nonlocal elasticity with an exponential kernel, in the presence of rotational inertia. After recasting the integro-differential governing equation and the boundary conditions into purely differential form, a singularly perturbed problem is met that is associated with a pair of end boundary layers. A multi-parametric asymptotic solution in terms of size-effect and local fraction is presented for the eigenfrequencies as well as for the eigenforms for a variety of boundary conditions. It is found that, for simply supported end, the weakest boundary layer is formed and, surprisingly, rotational inertia affects the eigenfrequencies only in the classical sense. Conversely, clamped and free end conditions bring a strong boundary layer and eigenfrequencies are heavily affected by rotational inertia, even for the lowest mode, in a manner opposite to that brought by nonlocality. Remarkably, all asymptotic solutions admit a well defined and energy bounded limit as the local fraction vanishes and the purely nonlocal model is retrieved. Therefore, we may define this limiting case as the proper solution of the purely nonlocal model for a beam. Finally, numerical results support the accuracy of the proposed asymptotic approach.

Experimental study on geosynthetic-reinforced sand fill over marine clay with or without deep cement mixed soil columns under different loadings

Geosynthetics and deep cement mixed (DCM) soil columns have been widely used to improve soft soil grounds in many countries and regions. This paper presents an experimental study on a geosynthetic-reinforced sand fill over marine clay with or without DCM columns under different loadings. Two tests were conducted on the sand fill reinforced with fixed-end and free-end geosynthetics over marine clay under three-stage local loading to investigate the effects of the boundary conditions of geosynthetic reinforcement on reducing settlements. It is observed that the fixed-end geosynthetic sheet is more effective in reducing settlements than the free-end condition under identical local loading. Another test was conducted on the fixed-end geosynthetic-reinforced sand fill over the marine clay improved by DCM columns under single-stage uniform loading. The vertical stresses on the marine clay and on the DCM columns, as well as the tensile strains of the geosynthetic sheet in the overlying sand fill, were measured. The results revealed that the stress concentration ratio increases with an increase in consolidation settlements, and the maximum tensile strain of the geosynthetic sheet occurs near the edge rather than at the center of the top surface of the DCM columns.

The ‘hanging flag’ problem: on the heaving motion of a thin filament in the limit of small flexural stiffness

We investigate the fluid–structure interaction of a vertically hanging filament immersed in uniform incompressible high Reynolds number flow. The filament is subject to small-amplitude harmonic heaving at its upstream edge, and to a gravity-induced (‘hanging chain’) tension force. We focus on the limit of small bending rigidity to examine the differences between a highly elastic beam (where bending rigidity is small but finite) and a membrane (where bending rigidity vanishes). The problem is analysed by means of thin airfoil theory, in conjunction with a discrete vortex model for the downstream wake. Denoting the filament non-dimensional rigidity (normalized by the tension force) by $\bar{\unicode[STIX]{x1D700}}$, it is first verified that the beam deflection and associated flow field converge to the membrane solution at $\bar{\unicode[STIX]{x1D700}}\rightarrow 0$. At low actuation frequencies, the differences between the membrane and beam motions are small, and both follow a nearly rigid-body motion parallel to the upstream-edge actuation. With increasing frequency, the differences between the beam and membrane become visible at increasingly lower values of $\bar{\unicode[STIX]{x1D700}}$, and the stabilizing effect of beam flexural rigidity, resulting in reduced flapping amplitudes, is apparent. Examining the beam motion near its edge points at non-small frequencies, semi-analytic approximations for the associated time-periodic displacements are obtained. Close to the actuated end, a layer of width $\bar{\unicode[STIX]{x1D700}}^{1/2}$ is found, where the flexural rigidity term in the equation of motion is balanced by the tension term. Here, the differences between the beam and membrane deflections are attributed to the additional zero-slope condition satisfied by the former. In the vicinity of the free end, a local Taylor expansion is carried out. A balance between the bending and inertia terms results in a layer of width $\propto \bar{\unicode[STIX]{x1D700}}^{1/4}/\bar{\unicode[STIX]{x1D714}}_{h}^{1/2}$, where $\bar{\unicode[STIX]{x1D714}}_{h}$ denotes the scaled heaving frequency. The layer is therefore thicker than the upstream layer for $\bar{\unicode[STIX]{x1D714}}_{h}\approx 1$, and becomes thinner with increasing $\bar{\unicode[STIX]{x1D714}}_{h}$. Within the layer, the beam deflects linearly with the distance from the edge, in marked difference from a membrane and in accordance with the free-end conditions satisfied by the former.

On the dynamics of perching manoeuvres with low-aspect-ratio planforms

The dynamics of a simple perching manoeuvre are investigated using circular and aspect-ratio-two elliptical flat plates, as abstractions of low-aspect-ratio planforms observed in highly-manoeuvrable birds. The perching kinematic investigated in this study involves a pitch-up motion from an angle of attack of to , while simultaneously decelerating. This motion is defined by the shape change number, , which acts as a measure of the relative contributions of added-mass and circulatory effects. This motion has been observed in natural flyers during controlled landings, and has recently been explored through the use of a nominally two-dimensional airfoil. The parameter space of low-aspect-ratio plates therefore serves to elucidate how realistic free-end conditions affect the timescales of vortex evolution, and therefore the relative contributions between added mass and circulation. The results presented herein suggest that for the low-aspect-ratio plates, the shedding of vortices occurs more rapidly than for equivalent two-dimensional cases, and therefore faster pitching motions are required to compensate for the lower levels of lift and drag. Furthermore, the vortex topology and instantaneous forces that arise during the rapid-area changes show no sensitivity to aspect ratio, and strong collapse is observed between both flat plates. Similar aerodynamic advantages may therefore be exploited during perching manoeuvres by birds of various scale regardless of wing aspect ratio.

Cyclic torsion behavior and the related thermal response of 316L stainless steel tube: Experiments and FE simulations

In a previous work, the author has systemically investigated the thermo-mechanical coupling response of 316L stainless steel tube under cyclic tension/compression condition. In this work, such thermo-mechanical coupling behaviors of the material were experimentally studied under strain-controlled cyclic free-end torsion condition. It is concluded from the experimental results that: the material presents a cyclic hardening-softening response in strain-controlled cyclic torsion; a temperature oscillation with the period of half a cycle time was observed during cyclic deformation; the heat source vanishes in elastic torsion while it is non-vanishing in elastic tension/compression reported in the previous work. Then, the experimental results were simulated by a pre-developed thermo-mechanically coupled cyclic constitutive model. It is shown that the simulations match the experimental data reasonably.

Low-velocity impact to transmission line conductors

This combined experimental and numerical study addresses mechanical effects associated with the energy dissipation from transverse low-velocity impacts on a novel High Temperature Low Sag (HTLS) transmission line conductor, subjected to either free or constrained end conditions and large axial tensile loads. Impact experiments were conducted on one type of Polymer Composite Core Conductor (PCCC) belonging to the family of HTLS designs. The experimental work performed using an original approach was supported by non-linear static and dynamic finite element analysis.Despite their geometrical simplicity, the numerical models provided useful information regarding the response of the conductor to both static and dynamic conditions. Most importantly it has been determined that the PCCC exhibits good resistance to impact under constrained end conditions with and without initial axial tension. It was also identified that the most damaging condition under impact is when the conductor had free ends and was thus subjected to severe bending. It has been shown in this work that the suggested approach to the impact testing of transmission lines could result in useful predictions of their structural integrity after low-velocity impact either during installation or in service.

Local-distortional buckling interaction on cold-formed steel lipped channel beams

This paper deals with the ultimate strength, post-buckling behaviour and design of cold-formed steel lipped channel beams affected by local-distortional buckling mode interaction, subjected to uniform bending of the major axis. The cross-sectional dimensions and length of the beams were chosen to have almost equal local and distortional critical buckling stresses by using the GBTUL-2.0β and CUFSM software. The beams are analysed under pinned with warping free end conditions. 12 sections were selected for this study. The selected sections satisfy the geometric limitations for pre-qualified sections in AISI-S100:2007. Elastic buckling and non-linear finite element analyses were carried out using ABAQUS. The results were compared with corresponding results from experiments available in the literature. The numerical parametric study of 60 analyses of different geometries and yield stress values was undertaken. Based on the comparison of ultimate strengths obtained from the finite element analysis and Direct Strength Method (DSM), a design equation is proposed for lipped channel sections which have their elastic local and distortional buckling moments nearly equal.

Crack identification in non-uniform rods by two frequency data

We consider the inverse problem of identifying a single open crack in a longitudinally vibrating rod having non-uniform smooth profile. Without any a priori assumption on the smallness of the damage and assuming that the rod profile is symmetric with respect to the mid-point of the rod axis, we present a constructive diagnostic algorithm from minimal frequency data. We show that the crack can be uniquely identified, up to a symmetric position, from the first two positive natural frequencies of the rod under free–free end conditions. We also show that the non-uniqueness of the damage location can be removed by using as data the first positive resonant frequency of the free–free rod and the first antiresonant frequency of the driving-point frequency response evaluated at one end of the rod. The results of numerical simulations and of applications of the method to experimental data agree well with the theory.

The impact of particle form on the packing and shear behaviour of some granular materials: an experimental study

This paper reports the results of experiments carried out to explore the effects of particle form, sometimes referred to as sphericity, on the depositional density and subsequent shear behaviour of granular material. Previous experimental studies have generally neglected this important control, considering only rotund or bulky particles. However, the results of a few numerical studies have suggested its importance. Pluviated granular materials were tested in triaxial compression under free-end conditions, achieved using enlarged lubricated platens, which allowed specimens to be taken to high axial strain levels without strain localisation. Strains were measured locally. The results show that the limiting void ratios, \(e_{max}\) and \(e_{min}\), the void ratio range (\(e_{max}- e_{min})\) and the depositional anisotropy increase as particles become platy. Almost all aspects of behaviour during shear are significantly affected by particle form, including mobilised friction at the onset of dilation, peak state and ultimate (or critical) state, dilation and particle breakage. For extremely platy material it appears that dilatancy may be completely suppressed, even for dense packings of particles.