Transverse Oscillation Frequency Research Articles

Natural oscillation frequencies of a Rayleigh sphere levitated in standing acoustic waves.

Acoustic levitation is an important method of container-free processing, which counteracts gravity through exerting the acoustic radiation force on levitated objects. The Gorkov potential function is used to simplify the calculation of the acoustic radiation force acting on a Rayleigh sphere whose radius is much smaller than the wave length. For the case of a plane standing wave levitation system, a systematic analysis of the sphere dynamics is provided in the axial direction, assuming a small perturbation around the stable equilibrium locations. A generalized extension to an arbitrary standing wave field is provided, which gives formal expressions of the axial and transverse natural oscillation frequencies for the sphere. Particular emphasis is put on the natural oscillation frequencies with and without taking gravity into consideration. The computational results for Gauss and Bessel standing waves are provided as two special cases, which show that the transverse natural oscillation frequency will be overestimated when neglecting gravity, especially for a sphere with a relatively large density. Corresponding experiments are conducted to verify the dependence of the transverse natural oscillation frequency on the sphere density. The results obtained in this work are expected to provide a theoretical guide for enhancing the levitation stability and inversing the physical parameters from the sphere dynamics.

Three-dimensionality in the flow of an elastically mounted circular cylinder with two-degree-of-freedom vortex-induced-vibrations

The study numerically investigates the three-dimensionality in the flow and two-degree-of-freedom (2DOF) vortex-induced-vibrations (VIV) characteristics of an elastically mounted circular cylinder. The cylinder is allowed to vibrate in both streamwise and transverse directions. A low value of mass-ratio (m*=2.546) with the zero-damping coefficient (ζ=0) is taken for the simulations. The primary aim is to understand the vortex shedding behind the cylinder and the transition characteristics of the wake-flow from two-dimensional (2D) to three-dimensional (3D). The Reynolds number (Re) is varied from 150 (fully 2D flow) to 1000 (fully 3D flow), which lies inside the laminar range. The reduced velocity (Ur) is varied 2≤Ur≤17, which covers all three major VIV branches [initial branch (IB), upper branch (UB), and the lower branch (LB)]. The oscillating cylinder sweeps the figure-eight trajectory. Two branches (IB, LB) and three branches (IB, UB, LB) amplitude responses are obtained for the low and high Re values, respectively. The wake behind the cylinder with 2DOF VIV undergoes the mode-C transition of 2D to 3D flow as opposed to the direct mode-B transition observed for transverse only VIV in the literature. The critical Re range of the 2D to 3D transition for the 2DOF VIV cylinder at a reduced velocity of 6 is around 250, less than the 1DOF VIV. Also, this range varies with the variation in m* and the streamwise to transverse oscillation frequency ratio (f*). A λz−Re map (where λz represents the spanwise wavelength of the streamwise vortices) is proposed for the 2DOF VIV, highlighting different modes of transition obtained for combinations of f* and Re.

DETERMINATION OF TENSIONS OF SUSPENDED ROPES OF THE BRIDGE BY FREQUENCY OF NATURAL OSCILLATIONS

The article deals with the issues of development and use of equipment for digital measurements of rope tension based on the frequency of free transverse oscillations. accurate measurement of rope tension is of practical importance. The relevance of this task for the national economy of Ukraine lies in the need to develop a simple and reliable method and equipment for quick and convenient measurement by construction engineers and operating engineers of rope tension in the construction industry. The practical significance of the work lies in the need to timely bring the span structure of the Arch Bridge of the Podilsky bridge crossing over the Dnipro River in Kyiv to the design position after the installation of metal structures with the transfer of the weight of the bridge truss to four main supports and 64 suspension cables with full unloading of four mounting supports for further arrangement of the bridge deck and completion of construction works. The object of the research is the process of measuring the tension of suspension ropes from the own weight of the metal part of the bridge during bringing the truss of the Arch Bridge to the design position of the metal structural elements of the bridge. The subject of the study is the determination of the impact of the combined movement of the upper attachment points (threaded cylindrical couplings) of 64 suspended ropes on the redistribution of the frequencies of natural oscillations and tensions in their contours.

Computational Study of Three-Dimensional Flow Past an Oscillating Cylinder Following a Figure Eight Trajectory

The paper presents a computational study of three-dimensional flow past a cylinder forced to oscillate in a uniform stream, following a figure-eight trajectory. Flow simulations were performed for Re = 400, for different cases, defined in terms of the oscillation mode (‘counter-clockwise’ or ‘clockwise’), for values of the ratio, F, of the transverse oscillation frequency to the Strouhal frequency close to 1.0. The results demonstrate that, for F ≤ 1.0, counter-clockwise cylinder motion is associated with positive power transfer from the flow to the cylinder, corresponding to excitation; for the clockwise motion, power transfer is negative at intermediate to high amplitudes, corresponding to damping. For the clockwise mode, in the range F = 0.9–1.1, a transition to two-dimensional vortex street is identified for transverse oscillation amplitude exceeding a critical value. This results from the induced suction of vortices, which moves vortex formation and shedding closer to the cylinder surface, thus resulting in a narrower wake, characterized by an effective lower Reynolds number. Both oscillation modes are characterized by higher harmonics in the lift force spectrum, with the third harmonic being very pronounced, while even harmonics are present for the case of clockwise mode, resulting from a wake transition to a “S + P” mode.

On the problem of maintaining the transverse oscillation frequencies of the beam lying on the elastic base

On the problem of maintaining the transverse oscillation frequencies of the beam lying on the elastic base

A comprehensive study of heat transfer characteristic and two-dimensional FIV for heated square-section cylinder with different damping ratios

The present study explores the effect of damping ratio and Reynolds number on the flow-induced vibration and heat transfer behavior of a heated square-section cylinder. To this end, fluid-structure interaction simulations based on the finite-volume method are conducted for five different damping ratios of ζ = 0, 0.01, 0.05, 0.1, 0.25 and 0.5 at four representative Reynolds numbers of Re = 80, 90, 220 and 250. By considering the square-section cylinder as a mass-spring-damper system, one can model its free vibration along transverse and streamwise directions due to lift and drag forces exerted from the fluid, in which the dynamic mesh technique is employed to couple the cylinder motion with the flow field. Owing to its sharp corners, the square-section cylinder first experiences the lock-in condition in which the vortex shedding frequency approaches the oscillator natural frequency. After surpassing the critical flow velocity, the square-section cylinder undergoes high-magnitude and low-frequency oscillations known as galloping. For a more comprehensive evaluation, the designated Reynolds numbers encompass all vibration regions of the square-section cylinder: out of lock-in and galloping (Re = 80), middle-point of lock-in region (Re = 90), middle-point of galloping (Re = 220) and the peak of galloping zone (Re = 250). The results show that at Re = 90, as the damping ratio increases from ζ = 0.01 to ζ = 0.05, the amplitude of cylinder oscillations significantly drops due to the de-synchronization type action. A notable reduction in the oscillation amplitude at Re = 220 and 250 occurs with increasing damping ratio from ζ = 0.1 to ζ = 0.25, attributed to the hidden frequency emersion phenomenon in which the fundamental frequency of cylinder transverse oscillations shifts to a secondary value. It is also shown that the heat transfer rate of the square cylinder with free vibration is more than that of a stationary cylinder. With increasing damping ratio, the heat transfer rate of the cylinder decreases compared to the undamped conditions.

Determination of the transition mass ratio for onset of galloping of a square cylinder at the least permissible Reynolds number of 150

The Den Hartog stability criterion tests for galloping of an oscillator. A square cylinder satisfies this and is susceptible to galloping. This criterion being necessary for occurrence of galloping appears insufficient as certain parameters, i.e., angle of incidence, α; mass ratio, m*; damping ratio, ζ; reduced speed, U*; and Reynolds number, Re; also assume key roles in determining if the oscillator motion is vortex-induced vibrations (VIV) or galloping. At Re ≈ 150 and U* ≈ 10 or smaller, a square cylinder does not gallop despite satisfying the Den Hartog criterion. By coupling U* and Re, K. Sourav and S. Sen [“Transition of VIV-only motion of a square cylinder to combined VIV and galloping at low Reynolds numbers,” Ocean Eng. 187, 106208-1–106208-19 (2019)] two-degrees-of-freedom motion over Re ≤ 250, the minimum m* or mtr* as 3.4 below which galloping cannot develop. For transverse-only motion, X. Li et al. [“Mode competition in galloping of a square cylinder at low Reynolds number,” J. Fluid Mech. 867, 516–555 (2019)] considered U* = 40 only and determined mtr*≈4 at the least permissible Re of 150. For α = 0° and ζ = 0, we determine the mtr* numerically at Re = 150. By analyzing the transverse response and oscillation frequency over an extended U* range of 10–60, a novel “VIV-galloping transition map” is generated in the m*–U* plane. From this map, the value of mtr* converges to 3.4. The mtr* decays as U*−2.36. The conditions leading to “VIV forever” of a square cylinder are also identified.

Vortex shedding frequency in open-channel lateral cavity

This article aims at predicting the oscillation frequency of open-channel lateral cavities, which are common sheltered zones of riverine environments, and have important ecological impact. Using a theoretical analysis based on an existing model for acoustic cavities and a free-surface lateral cavity experiment, we show that the vortex shedding in the mixing layer between the cavity and the open channel is always constrained by gravity waves even for low Froude numbers ( $F<0.6$ ). This expands previous results from the literature showing the impact of gravity waves on the vortex shedding frequency for high Froude number ( $F>0.6$ ). Measurements of the free-surface oscillation and transverse velocity oscillation frequencies reveal a unique frequency along the mixing layer, equal to the free-surface oscillation frequency anywhere in the cavity. Hence, it is shown that the vortex shedding frequency in an open-channel lateral cavity always equals a match between a natural frequency of the cavity and a solution of the feedback model developed herein for low to moderate Froude numbers.

Special features of the formation of welded joints in vertical laser-arc welding of low-alloy steels

ABSTRACTInvestigations were carried out into the special features of the technology of vertical laser-arc welding of large structures made of high-strength and low-alloy steels with a variable welding gap and a large root face.The parameters of the conditions of vertical laser-arc welding of root passes in the low-alloy steel 30–40 mm thick with a root face of 10 mm (welding speed, the amplitude and frequency of transverse oscillations, the intensity of welding current, arc voltage, laser radiation power) resulting in the formation of high-quality welded joints are determined. The experimental results show that the laser radiation power, required for producing continuous penetration of the root face, depends on the thickness of the parent metal: for the metal thickness of 14–30 mm the sufficient laser radiation power is 3.8 kW, for a thickness of 40 mm it is no less than 4.6 kW to penetrate a depth of 5 mm.The welded joints have a fine-dispersed acicular structure of the martensitic – bainitic type. The experimental results were used to develop a technology of welding of low-alloy steels of different thickness using robotic equipment.

Interconnection of maximum deflections and frequencies of free vibrations of composite two-layeroval plates on pliable connections

The paper considers the relationship between the maximum deflections and the frequencies of natural oscillations of oval isotropic composite plates, as well as the dependence of the stiffness coefficient of the seam on the stiffness of the shift connections and the frequency of the natural oscillations of the plate. At the first stage, the system of differential equations of transverse bending of a plate under the action of a uniformly distributed load and the differential equation of free transverse oscillations of the plate is solved. The composite plate at this stage is represented in the form of a solid structure with cylindrical stiffness Ds, which is equivalent to the cylindrical rigidity of the composite plate on the pliable connections. After the transformations, the following regularity is obtained, connecting the maximal deflection of the plate with its frequency of transverse oscillations. Oval two-layer composite plates with a ratio of small to major axis from 1.0 to 0.2 with transverse connections and shift connections of variable stiffness were studied over the entire surface of the plate for rigid pinching and pivoting along the contour. The determination of oscillation frequencies and deflections was carried out by a numerical method. As a result of the research it was established that the oval composite plates, regardless of the support scheme and the stiffness of the shift connections, comply with the regularities (1) with an accuracy of 5%. Based on the results of the study, the graphs of the dependence of the maximum deflection and the natural oscillation frequency of the plate on the stiffness of the shift connections at hinged support and pinching along the contour are constructed. On the second stage of the research, based on A.P. Rzhanitsyn’s theory of compound rods, an analytical dependence of the stiffness of the seam on the rigidity of the shift connections was obtained. Based on the results of numerical studies, the dependence of the frequency of natural oscillations on the stiffness coefficient of the seam was obtained. The graphs of the dependence of the frequency of the natural oscillations of the composite plate and the stiffness coefficient of the seam upon the stiffness of the shift connections were constructed.

Specifics of determining the tension forces of the cable-stayed bridge elements

Objective: to improve the method of determining the force in the cable stays by frequencies of natural transverse oscillations. Methods: synthesis and analysis of theoretical and experimental data, experimental methods for studying the structures. Results: in the paper, the problems of determining the tension forces of the cable stays by the frequencies of their natural oscillations are considered taking into account various factors (the design of anchor fastenings, the angle of inclination and sagging of the cable stay, the change of temperature). The estimation of possible errors in calculations is given. The degree of coincidence of the actual and design stress-strain state of the cable stays depends on the correctness of accounting the influence of the factors considered. The effect of the temperature change and the anchor fastening structure on the frequency of the natural oscillations of the cable stays has been experimentally tested. The recommendations on the determination of the forces in the cable stays by dynamic parameters are given. A method for controlling the tension forces of the cable stays and specialized software “Vant” (“Cable”) for automation of the measurement process are developed. The method has been tested on several bridge structures that have cable-stayed elements. Practical significance: the ability to use the developed method for controlling the tension forces of cable-stayed elements during the operation of artificial structures.

Interactions between two in-line drops rising in pure glycerin

The behaviors of time-dependent interaction between two buoyancy-driven in-line deformable drops rising in pure glycerin at Re<1 were studied, where the diameter for the leading drops ranged from 9.51mm to 12.6mm and for trailing drops from 12.7mm to 15.8mm. The situation while a larger drop chasing a smaller one was specifically considered which typically led to the smaller drop “coating” the larger one. Two approaches, the geometric feature approach and the energy change one, were used to judge the starting and ending times of the interaction between two drops. Based on a conical wake model, the drag coefficient of two approaching drops was calculated. Due to the approaching effect of the trailing drop, the leading drop was accelerated and the average drag coefficient was smaller than that for a free rising single drop. The frequency spectrums of the lateral oscillation of two drops during the interaction were obtained by using Fourier analysis. The oscillation frequency of the interactional drops was also different from that for a free rising single drop because of the wake effect produced by the leading drop. Due to a superposition of the drop shape oscillation and the drop internal circulation, the transverse oscillation frequencies of two drops have the same trend during the approaching process.

STUDY OF THE VIBRATIONS OF MODERATELY THICK DOUBLY CURVED SHELLS VIA EFFICIENT 3D ELEMENTS

In this work, we propose a modified version of the classical 20 nodes serendipity element for the dynamic analysis of doubly curved shells. Instead of using the classical strain displacements relations, we propose to formulate the strain displacements relations in a general curvilinear coordinates. The main goal of the work is putting forward a 3D element, valid for general shell structures, which provides some desirable features like avoidance of locking and zero energy modes with decreasing thickness and good behaviour in dynamic analysis. Until now, most works are usually referred to shallow and thin shells. In this work the study of the vibrational frequencies of transverse oscillations of moderately thick shells by 3D elements for non shallow shells has been treated. We expose also different kinds of mass matrices and study a close variant of the classical lumped mass matrix.

Sensitivity of two-dimensional flow past transversely oscillating cylinder to streamwise cylinder oscillations

In this paper we study the sensitivity of flow past a transversely oscillating cylinder to streamwise harmonic perturbations. The value of the Reynolds number is equal to 150, for which the flow is two-dimensional. We start with a transversely oscillating cylinder and then impose a small streamwise (in-line) perturbation with a frequency equal to twice the transverse oscillation frequency. The cylinder is thus following an eight-shaped trajectory, which can be traversed in a counter-clockwise or clockwise direction. For low values of the in-line amplitude, we find for the counter-clockwise mode that the power transfer from the fluid to the structure increases with the amplitude of oscillation in the streamwise direction, even though the magnitude of the fluctuations of the forces is decreased. For the clockwise mode of motion we observe the reverse trend, i.e., the power transfer from the fluid to the structure is decreased, even though the magnitude of the fluctuations of the forces is increased. It is shown that the variation of the power transfer in both types of motion is due primarily to the variation of the phase between the transverse oscillation of the cylinder and the vortex lift force as a result of the in-line oscillation. For higher values of the streamwise amplitude, the contribution of the fluctuating drag to the power transfer also becomes important, especially for the counter-clockwise mode. Both modes of oscillation are characterized by the presence of the third harmonic in the spectrum of the lift force as the in-line oscillation is increased and by the appearance of a combination of single vortices on the one side of the wake, and vortex pairs on the other side.

Hydrodynamic Forces and Flow Structures in Flow Past a Cylinder Forced to Vibrate Transversely and Inline to a Steady Flow

This paper reports computational results of forces and wake structure in two-dimensional flow past a circular cylinder forced to vibrate both transversely and inline to a uniform stream, following a figure-eight trajectory. For a flow stream from left to right, we distinguish between a counterclockwise mode and a clockwise mode, if the upper part of the trajectory is traversed counterclockwise or clockwise, respectively. The present computations correspond to a range of transverse oscillation frequencies close to the natural frequency of the Kármán vortex street and several oscillation amplitudes, both for counterclockwise motion and clockwise motion. The nondimensional forces and nondimensional power transfer from the fluid to the body are calculated. The results demonstrate a strong dependence of the forces and power transfer on the direction in which the figure-eight is traversed. In general, counterclockwise motion maintains positive power transfer at higher oscillation amplitudes. Flow visualizations show that the wakes are characterized by the presence of two single (2S) vortex shedding mode at low oscillation amplitudes and can attain more complex structures at higher amplitudes.

Effect of static axial compression on the natural frequencies of helical springs

Purpose – The purpose of this paper is to address the practically important problem of the load dependence of transverse vibrations for helical springs. At the beginning, the author develops the equations for transverse vibrations of the axially loaded helical springs. The method is based on the concept of an equivalent column. Second, the author reveals the effect of axial load on the fundamental frequency of transverse vibrations and derive the explicit formulas for this frequency. The fundamental natural frequency of the transverse vibrations of the spring depends on the variable length of the spring. The reduction of frequency with the load is demonstrated. Finally, when the frequency nullifies, the side buckling spring occurs. Design/methodology/approach – Helical springs constitute an integral part of many mechanical systems. A coil spring is a special form of spatially curved column. The center of each cross-section is located on a helix. The helix is a curve that winds around with a constant slope of the surface of a cylinder. An exact stability analysis based on the theory of spatially curved bars is complicated and difficult for further applications. Hence, in most engineering applications a concept of an equivalent column is introduced. The spring is substituted for the simplification of the basic equations by an equivalent column. Such a column must account for compressibility of axis and shear effects. The transverse vibration is represented by a differential equation of fourth order in place and second order in time. The solution of the undamped model equation could be obtained by separation of variables. The fundamental natural frequency of the transverse vibrations depends on the current length of the spring. Natural frequency is the function of the deflection and slenderness ratio. Is the fundamental natural frequency of transverse oscillations nullifies, the lateral buckling of the spring with the natural form occurs. The mode shape corresponds to the buckling of the spring with moment-free, simply supported ends. The mode corresponds to the buckling of the spring with clamped ends. The author finds the critical spring compression. Findings – Buckling refers to the loss of stability up to the sudden and violent failure of seed straight bars or beams under the action of pressure forces, whose line of action is the column axis. The known results for the buckling of axially overloaded coil springs were found using the static stability criterion. The author uses an alternative approach method for studying the stability of the spring. This method is based on dynamic equations. In this paper, the author derives the equations for transverse vibrations of the pressure-loaded coil springs. The fundamental natural frequency of the transverse vibrations of the column is proved to be the certain function of the axial force, as well as the variable length of the spring. Is the fundamental natural frequency of transverse oscillations turns to be to zero, is the lateral buckling of the spring occurs. Research limitations/implications – The spring is substituted for the simplification of the basic equations by an equivalent column. Such a column must account for compressibility of axis and shear effects. The more accurate model is based on the equations of motion of loaded helical Timoshenko beams. The dimensionless for beams of circular cross-section and the number of parameters governing the problem is reduced to four (helix angle, helix index, Poisson coefficient, and axial strain) is to be derived. Unfortunately, that for the spatial beam models only numerical results could be obtained. Practical implications – The closed form analytical formulas for fundamental natural frequency of the transverse vibrations of the column as function of the axial force, as well as the variable length of the spring are derived. The practically important formulas for lateral buckling of the spring are obtained. Originality/value – In this paper, the author derives the new equations for transverse vibrations of the pressure-loaded coil springs. The author demonstrates that the fundamental natural frequency of the transverse vibrations of the column is the function of the axial force. For study of the stability of the spring the author uses an alternative approach method. This method is based on dynamic equations. The new, original expressions for lateral buckling of the spring are also obtained.

Numerical Simulation of Three-Dimensional Flow Past a Cylinder Oscillating at the Strouhal Frequency

The paper presents computational results of 3D flow past a cylinder forced to oscillate: (a) transversely with respect to a uniform stream and (b) both transversely and in-line with respect to a uniform stream, following a figure-eight trajectory. For a flow from left to right the figure-eight is traversed counterclockwise in the upper half-plane. Direct numerical simulation (DNS) of the Navier–Stokes equations for 3D flow is performed using a spectral element code. Computations are carried out for a Reynolds number equal to 400, at a transverse oscillation frequency equal to the natural frequency of the Kármán vortex street. For both oscillation modes, the transverse oscillation amplitude is varied from 0 to 0.60 cylinder diameters. The forces on the cylinder are calculated and related to flow structure in the wake. The results indicate that, in general, the presence of in-line oscillation increases the magnitude of forces acting on the cylinder, as well as the power transfer from the flow to the structure. Flow visualizations indicate that, for the figure-eight mode, low-amplitude forcing tends to reduce the wake three-dimensionality. However, at high oscillation amplitudes, the wake structure is found to become more complex at increasing amplitude.

Vortex dynamics and associated fluid forcing in the near wake of a light and heavy tethered sphere in uniform flow

Time-resolved particle image velocimetry measurements of vortex-induced vibrations of a negatively (“heavy”) and positively (“light”) buoyant tethered sphere in uniform flow, and its wake characteristics were performed in a closed-loop water channel. Experiments for both spheres were performed at similar bulk velocities, ranging between 0.048 < U < 0.32 m/s, corresponding to reduced velocities, 2.2 < U * < 13.5. Initially stationary, with increasing U, the amplitude response displayed periodic oscillations beyond the Hopf bifurcation as a result of “lock-in” between vortex shedding and the natural structural frequency. However, while the heavy sphere’s amplitude decreased beyond U * = 7.0, the light sphere’s amplitude continuously increased. In the periodic oscillation region, flow field characteristics in the wakes of both spheres (at comparable U * ) were similar, characterized by alternately shed hairpin vortices having a horizontal symmetry plane. Primary vortex trajectories in the frame of reference of the sphere collapsed for different U * (but not for different m * ) when scaled by f 2,s/U, where f 2,s is the sphere’s transverse oscillation frequency. This allows determination of vortex positions based on sphere dynamics and bulk flow conditions only. Associated vortex convection velocities as a function of downstream position from the sphere also nearly collapsed when normalized by U. In addition, fluid forcing and energy transfer from fluid to sphere were estimated based on an analogy between aircraft trailing vortices and hairpin vortices. Maximum forcing occurred at vortex pinch-off. For the highest comparable U * , despite different amplitudes, total transferred energy during one oscillation period was similar for both spheres. Changes in sphere dynamics must therefore be related to differences in inertia.

Shaking-induced dynamics of cold atoms in magnetic traps

We describe an experiment in which cold rubidium atoms, confined in an elongated magnetic trap, are excited by transverse oscillation of the trap centre. The temperature after excitation exhibits resonance as a function of the driving frequency. We measure these resonances at several different trap frequencies. In order to interpret the experiments, we develop a simple model that incorporates both collisions between atoms and the anharmonicity of the real three-dimensional trapping potential. As well as providing a precise connection between the transverse harmonic oscillation frequency and the temperature resonance frequency, this model gives insight into the heating and loss mechanisms, and into the dynamics of driven clouds of cold trapped atoms.

Transverse Oscillation of Precise Cable Drive System

Precise cable drive has been developed as an alternative transmission element to gearbox, belt and pulleys, chains and sprocket in Electro-Optical Tracking system. Precise cable drive has several significant advantages including backlash free, high stiffness, high efficiency, no lubrication etc. This paper develops analytical methods to predict the transverse oscillation frequency of precise cable drive to enable designers to better assess dynamic performance in the design study phase. Theoretical formulation of transverse oscillation equation for precise cable drive is carried out based on Hamiltons principle taking into account flexural rigidity of cable. Furthermore, the transverse oscillation frequency is obtained from the transverse oscillation equation assuming small and linear vibration. Parametric studies are conducted to evaluate the relationship between the oscillation properties and cable drive parameters.