Amplitude Of Cylinder Research Articles

CRITICAL BEHAVIOR IN c=1 MATRIX MODEL WITH BRANCHING INTERACTIONS

In order to understand the phase structure of d>1 strings we investigate the c=1 matrix model with g′(tr M(t)2)2 interaction which is the simplest approximation of the large-N reduced model of odd-dimensional matrix field theory. We find three distinct phases: (i) an ordinary c=1 gravity phase, (ii) a branched polymer phase and (iii) an intermediate phase, and compute the disk and cylinder amplitudes in the phases (i) and (iii). Further we also analyze the model with slightly generalized [Formula: see text][Formula: see text] interaction. As a result the multi-critical versions of the phase (ii) are found.

2D quantum gravity in the proper-time gauge

A two-loop (cylinder) amplitude of the 2d pure gravity theory is obtained in the proper-time gauge ( g 00 = 1, g 01 = g 10 = 0) in the continuum formulation. The constraint T 01 = 0 is solved and used to reduce the problem of field theory to that of quantum mechanics. This reduction can also be proved by using a conformal Ward identity. The amplitude depends on the lengths l 1, l 2 of the boundaries, the proper time T and a non-negative integer m associated with winding modes around the boundaries.

Hopf Bifurcations and Hysteresis in Flow-induced Vibrations of Cylinders

Flow-induced oscillations of rigid cylinders exposed to fully developed flow can be described by a fourth order autonomous system of ordinary differential equations. Its rest solution is the only equilibrium point which is unstable in the entire regime of parameters. It turns out that Hopf bifurcations from the trivial solution occur in regions of comparatively low damping. We found that a wind speed parameter, Ω, controls the bifurcations while the other parameters have been arranged into discrete sets. In the case of two bifurcating solutions with branches of amplitudes tending towards each other, hysteresis occurred. The bifurcating solutions are unstable close to their respective bifurcation points. The branch tending to the left-hand side changes its stability and exhibits high-level amplitudes of synchronized oscillations. This type of solution can also be analysed by means of asymptotic methods. Near the location of the bifurcation, the predictions of bifurcation theory, the multiple scales approach, and numerics are in quite good agreement. As opposed to this, the branch tending to the right-hand side represents synchronized oscillations of somewhat smaller period but much smaller cylinder amplitudes, and these vibrations remain unstable in the entire regime of parameters. This means that keeping the cylinder fixed, starting the wind tunnel, and releasing the cylinder at low wind speeds would lead to a jump of its displacement amplitude from the low, unstable to the comparatively high-stable values. It is shown that the theoretical predictions are in fairly good agreement with the experimental trends of flow-induced synchronized cylinder oscillations.

Suppression of Karman Vortex Excitation of a Circular Cylinder by Another Cylinder Located Downstream in Cruciform Arrangement.

In this work, a technique to suppress the Karman vortex excitation of a circular cylinder in a uniform flow is developed by placing another cylinder in cruciform arrangement with a gap between them. When the diameters of the two cylinders are equal, the oscillation amplitude of the upstream cylinder is effectively suppressed, e. g., by less than 1% of the value without the downstream cylinder. Compared with the conventional ones, this technique has the following advantages : it is unnecessary to change the shape of the oscillating body or to remodel the supporting structure, and the flow approaching the oscillating body is virtually undisturbed.

Response characteristics of a vortex-excited cylinder at low reynolds numbers

An experimental investigation has been conducted into vortex-induced, cross-flow oscillations of a circular cylinder mounted elastically in a water channel. The Reynolds number ranged between 90 and 150, a regime where the vortex street is fully laminar. The frequency and amplitude of cylinder oscillation and the vortex-shedding frequency were measured in and around the lock-in region. Fluid velocities in the cylinder wake and cylinder response were recorded simultaneously at Re = 115 in the lock-in region, and traces of cylinder motion were taken in and around resonant conditions. The maximum oscillation amplitude occurs near the lower limit of the lock-in region, while no substantial differences in final response are detectable between the cylinder amplitude developing from rest and the free stream velocity being varied with the cylinder already oscillating. The cylinder oscillation frequency was found to be slightly higher than its natural frequency in air, in the greatest part of the lock-in region.

Experiments on flow-induced vibration of a square-section cylinder

A long elastic body of aerodynamically bluff cross-section, capable of exhibiting either galloping or vortex-induced transverse vibrations in a flow normal to its length, can, if lightly damped, also exhibit large-amplitude vibrations related to the two above forms, but not predictable from information available for either form considered separately. Before a rational explanation of this behaviour can be given it is necessary to have some detailed experimental evidence of the exciting forces on the body during these vibrations. To this end the authors have made wind tunnel measurements on a freely-oscillating cylinder of square section under closely two-dimensional conditions in both smooth and turbulent flow. The test cylinder was constrained to one degree of freedom by air bearings in an elastic system mounted on a rigid external frame independent of the wind tunnel structure. Linear springs and variable magnetic system damping were used. The aerodynamic excitation was measured using a pressure manifold connected to pressure taps along a streamwise line on one face of the test model at mid-span, and reporting to a transducer. Two key theoretical parameters are dimensionless wind speeds, Urfor system resonance with the wake vortex street, and U0for the initiation of galloping. With the highest damping U0was well above Ur and for all turbulence levels the measurements of both excitation and response supported the predictions of galloping theory. With the lowest system damping U0 was less than r for all turbulence levels, and in these cases oscillation always began at Urand cylinder amplitude increased monotonically with U, while the fluctuating pressure excitation was dominated by the component synchronized with the body motion, except near U=3Ur where a peak of the same order occurred in the component at three times body frequency, with corresponding kinks in the body amplitude curves. Generally, the spectrum of the excitation was found to depend strongly on the ratio U0/Ur. All of the parameters appearing in theoretical models of vortex-induced and galloping oscillations were measured in the experiments, and the observed phenomena are analysed in the light of existing knowledge of the two basic forms of oscillation and of existing and possible theoretical models.

Proximity-induced galloping of two interfering circular cylinders

Experiments were conducted to investigate the response of a rigid two-dimensional elastically mounted smooth circular cylinder, with oscillations restricted to a plane normal to the incident flow, as influenced by the vicinity of an identical fixed body placed inside the wake. The static lift and drag coefficients, as well as the vibration amplitude and frequency of the upstream cylinder as functions of relative position of the pair of cylinders are given. Most measurements were carried out under two conditions of free-stream turbulence. Whilst turbulence decreased the magnitude of drag coefficients, it had no appreciable effect on lift coefficients. The forces on the upstream body were found to be influenced by the proximity to the downstream one in a significant way only when the streamwise spacing is less than two diameters.In the dynamic tests, two kinds of instability, namely a vortex-resonance and galloping, were observed, with the latter only occurring when the downstream cylinder was well submerged in the near wake of the upstream one. The vortex-shedding frequency was always found to lock to oscillation frequency. Whereas the vibration characteristics remained essentially unaffected with changing turbulence intensity, the galloping amplitudes were observed to be sensitive to cylinders’ aspect ratio. A quasi-steady theory was developed to predict the galloping behaviour.

Higher Rank Cylinder Amplitude

The dual topological unitarization is investigated for the case of any number of planar SU(N) singlet reggeons. In particular, the detailed structure of the cylinder amplitude is fully investigated. The planar bootstrap constraints are derived for the reggeon propagator and the triple reggeon vertex. The cylinder unitarization of planar poles is performed by means of the planar sewing method. The cylinder equation is described in terms of the factorizable kernel of finite rank. We are then led to the following typical properties of the cylinder. First, the cylinder partial wave amplitude is meromorphic in the J-plane. Secondly, extinction of the input SU(N) singlets is guaranteed. Thirdly, the cylinder residue is factorizable at all t. Fourthly, the cylindrical mixing is inevitable for the higher rank kernel. Moreover, the mixing phenomena are examined for the special case of the single daughter contribution. The repulsive [attractive] mixing pattern is expected to be observed between the even [odd] charge conjugation components of the cylindrically renormalized trajectories in the weak cylindrical mixing limit.

On the Higher Rank Cylinder Kernel

Finite energy corrections are estimated in the dual topological unitarization by introduc­ tion of a planar nonleading Regge trajectory. The cylinder amplitude is controlled by the factorizable kernel of rank two and guarantees automatically the extinction of the planar leading as well as nonleading SU(N) singlet. The idea of pomeronf identity is modified as a natural consequence of the cylindrical mixing mechanism. §I. Introduction The dual topological unitarization (DTU) has provided us with a persuasive approach to hadronic interactions at high energies. 1> The most emblematic con­ sequence of the DTU framework reads the pomeron:f identity, i.e., the bare pome­ ron is identified with the cylindrically renormalized f trajectory.l)-a> Moreover the cylinder amplitude is free of j-plane cuts so long as the planar amplitude obeys the pole-to-pole bootstrap condition. 4> Both of these results have been established in the standard DTU framework in which a cylinder equation is described by the factorizable kernel of rank one. It has not yet been settled, however, whether these results are commonly inherent in the DTU scheme or particularly characteris­ tic of the simplest Fredholm kernel. It will therefore be of physical importance to examine a typical cylinder equation of the higher rank kernel. This is performed in the present note by considering the possible finite energy effect. In § 2 an integral equation is derived for the cylinder by introducing a planar nonleading reggeon. In § 3 the dynamical equation is solved. Conspicuous features of the cylinder are investigated. Finally § 4 is devoted to clarifying the cylindrical mix­ ing mechanism. For the details of the notation and the definition, we refer to Ref. 4) .*>

Wave Impact Loads on Cylinders

Sarpkaya, Turgut, Naval Postgraduate School, Monterey, Ca. Abstract The evolution of forces acting on horizontal cylinders subjected to impact by a sinusoidally oscillating free surface was investigated both theoretically and experimentally. The experiments were conducted in a large U-shaped tunnel, with cylinders 3 to 8 in. (76 to 203 mm) in diameter. The results are expressed in terms of three force coefficients:the general slamming coefficient that expresses the normalized force acting on the cylinder at any time after the impact.the normalized impact force at the initial instants of slamming, andthe maximum drag coefficient that occurs when the cylinder is immersed in water about 1.8 diameters. The slamming-force coefficient was found to equal 3.2. Also, the force experienced by the cylinder cannot be considered in dependently of the dynamic response of that cylinder. In fact, the slamming-force coefficient may be amplified to a value as high as 6.3 through the dynamic response of the cylinder and its supports. Introduction Information about the forces acting on bluff bodies subjected to wave slamming is of significant importance in ocean engineering and naval architecture. The design of structures that must survive in a wave environment depends on a knowledge of the forces that occur at impact, as well as on the dynamic response of the system. Two typical examples include the structural members of offshore drilling platforms at the splash zone and the often encountered slamming of ships.The general problem of hydrodynamic impact has been studied extensively, motivated in part by its importance in ordnance and missile technology. Extensive mathematical models have been developed for cases of simple geometry, such as spheres and wedges. These models have been well supported by experiment. Unfortunately, the special case of wave impact has not been studied extensively. Kaplan and Silbert developed a solution for the forces acting on a cylinder from the instant of impact to full immersion. Dalton and Nash conducted slamming experiments with a 0.5-in. (12.7-mm) diameter cylinder and small amplitude waves created in a laboratory tank. Their data exhibited large scatter and showed no particular correlation with either the predictions of the hydrodynamic theory or identifiable wave parameters. Miller presented the results of a series of wave-tank experiments to establish the magnitude of the wave-force slamming coefficient for a horizontal circular cylinder. He found an average slamming coefficient of 3.6 for those trials in which slamming was dominant.Evaluating slamming effects with wavy flows is extremely difficult partly because of the limited range of wave amplitudes that can be achieved and partly because of the difficulty of measuring the partly because of the difficulty of measuring the fluid velocities at the instant of impact.Faltinsen et al. investigated the load acting on rigid horizontal circular cylinders (with end plates and length-to-diameter ratios of about 1) that were forced with constant velocity through an initially calm free surface. They found that the slamming coefficient ranged from 4.1 to 6.4. They also conducted experiments with flexible horizontal cylinders and found that the analytically predicted values were always lower (50 to 90%) than those found experimentally.This investigation was undertaken (1) to examine the existing theoretical models for determining wave slam forces on circular cylinders; (2) to furnish data, obtained under controlled laboratory conditions, about forces acting on circular cylinders subjected to impact with a sinusoidally oscillating water surface; (3) to determine the relative importance of the inertia- and drag-dominated forces during fluid impact; and (4) to correlate these data for identifiable wave parameters such as the Froude number (NFr); the Keulegan-Carpenter number (NK); and the Reynolds number (NRe).This investigation does not deal with the relatively more complex impact situations arising from the slamming of random ocean waves on the members of offshore structures. SPEJ p. 29

The vortex-excited lift and reaction forces on resonantly vibrating cylinders

The purpose of this paper is to present new experimental results pertaining to the vortex-excited oscillations of bluff cylinders. Measurements of the structural damping and the fluid dynamic reaction or damping in phase opposition with the cylinder's velocity were measured for three cylinders in a wind tunnel. The fluid damping measurements spanned a range of incident flow speeds which included the locking-on of the vortex shedding to the resonant cylinder vibrations. A mathematical representation is proposed wherefrom the components of the lift or excitation force transverse to the incident flow can be obtained once the structural damping and fluid reaction forces are known. The lift component in phase with the cylinder velocity, by which energy is transferred to the system, was measured and is in agreement with analogous measurements in water. The non-linear dependence of the lift force on the cylinder amplitude confirms the “wake-oscillator” hypothesis put forward by several previous investigators.

Exchange degeneracy breaking in the scattering and particle regions

We perform the analytic continuation, from the scattering ( t < 0) to the particle ( t > 0) region, of the non-planar diagrams (having torus topology) which generate a splitting between planar trajectories with non-zero iso-spin. Using heavily our previous work on the planar and cylinder amplitudes, we derive “asymptotic planarity” and estimate the rate of approach to it, also for the torus under rather general assumption on the Reggeon-Reggeon amplitude fixed pole residue.

Base Pressure of Oscillating Circular Cylinders

Experiments have been made to investigate the base pressure coefficients of circular cylinders oscillating transversely in a stream for a wide range of cylinder amplitudes and frequencies. This is thought to give a good indication of the variation in drag coefficient. The locking-on of vortex shedding at the cylinder frequency, associated with vortex-induced vibrations, was carefully studied. Locking-on at a third of the cylinder frequency was found to produce especially low base pressures, i.e., high drags.

Vibration of a Cylinder Caused by Wake Force

In this report experimental results on the vibration of a cylinder caused by shedding vortices are presented. The experiments were undertaken at larger Reynolds number than in author's previous report. There are two experiments in this study, one being on an elastically supported cylinder and the other on a crank-excited cylinder. In the former, the exciting force coefficient is determined from a decrement and an amplitude of the cylinder. In the latter, the exciting force coefficient is found by an integration of pressures on the cylinder surface. These two results coincide with each other ; the exciting force suddenly decreases at nearly the critical Reynolds number. Moreover, at sub-critical Reynolds number a self-exciting force is induced just as in authors' previous report, but at super-critical Reynolds number the exciting force decreases with an increasing cylinder amplitude and at too large an amplitude the force is changed to a damping force.

Flow Separation on a Vibrating Circular Cylinder

The location of the boundary-layer separation point on a circular cylinder has been investigated experimentally for a stationary cylinder and for a cylinder which is performing vortex-excited oscillations. The results for the stationary cylinder are in close agreement with published data. For the vibrating cylinder, the range of angular displacement of the separation point was found to depend upon the vibration amplitude and frequency, and the peak displacement occurred at a different frequency from that which gave the peak cylinder amplitude. As the frequency of the wake motion increases beyond that which gives that maximum range in the location of the separation point, the range of the motion of the separation point decreases. For given cylinder and wake frequencies, the higher the cylinder amplitude, the greater the motion of the wake. The phase shift of the actual wake was found to be close to 180 deg behind that of an ideal wake which aligns itself behind the relative velocity vector of the flow. The phase shift was found to be independent of cyclinder amplitude.

On the dynamic motion of a thin flexible cylinder in a viscous stream

The stability and time-dependent deflexions of a thin flexible cylinder with zero bending rigidity set in a viscous stream are examined. The cylinder is fixed at one end and free at the other. Modal shapes are found based on solutions to linearized equations resulting from small deflexion assumptions; the dependence of cylinder motion upon the aerodynamic, elastic and physical size characteristics of the cylinder is exhibited. It is found that the cylinder motion is always unstable and that cylinder amplitude increases without bound as time is increased.

Theory of an Oscillating Coaxial Cylinder Viscometer for Viscoelastic Materials

A theory of an oscillating coaxial cylinder viscometer for viscoelastic materials is presented. The outer cylinder is fixed and the inner cylinder is suspended by a wire, the upper end of which is twisted sinusoidally. A viscoelastic material is placed in the annular space between the two cylinders. The inner cylinder oscillates with the same frequency, but with different phase. There must be relationships between the amplitude and phase lag of the inner cylinder and the dynamic shear modulus and dynamic viscosity of the viscoelastic material. As is well known, the relationships become very simple, if the inertia effect of the viscoelastic material is neglected. The inertia effect upon the relationships is investigated in this paper. It is shown that the exact treatment of the problem requires the use of Bessel functions and the relationships are extremely complicated. Following the method of Markovitz, formulae for the dynamic shear modulus and the dynamic viscosity are obtained to the first approximation. A new method of calculation has been devised to obtain the second approximation without using Bessel functions.