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The influence of involute contact ratio on the torsional vibration behavior of a spur gear pair is investigated experimentally by measuring the dynamic transmission error of several gear pairs using a specially designed gear test rig. Measured forced response curves are presented, and harmonic amplitudes of dynamic transmission error are compared above and below gear mesh resonances for both unmodified and modified gears having various involute contact ratio values. The influence of involute contact ratio on dynamic transmission error is quantified and a set of generalized, experimentally validated design guidelines for the proper selection of involute contact ratio to achieve quite gear systems is presented. A simplified analytical model is also proposed which accurately describes the effects of involute contact ratio on dynamic transmission error.

A study was conducted to analyze the suppression of bending-torsion flutter through displacement-dependent dry friction damping. A linear, state-space, time-domain framework was utilized to carry out the analysis under a compressible flow environment. Results indicated the possibility of designing the geometry and location of frictional interfaces on airfoils supporting improved damping and better-controlled flutter.

Pull-in study of an electrostatic microactuator is essential for making the electrostatic actuation more effective. In this paper, pull-in analysis is presented for an electrostatic torsion microactuator. The torsion microactuator can be used as a microtorsion mirror. A polynomial algebraic equation for the pull-in voltage and pull-in angle of a torsion microactuator is derived. Two types of microactuators fabricated using bulk micromachining are presented. Measurements done on the fabricated microactuators are reported, showing deviations within 1% error from the calculations. [325] Index Terms - Electrostatic, microactuator, micromirror, pull-in, torsion.

A large-wave generator can be used to test the results of the design philosophy when compared with measurements made with a completed torsional wave machine. The experiment involves clamping one end of the machine to a desk and pulling the other end with three spring balances. The key characteristic of the waves created with the machine is the motion of the rods.

The dynamic response of a massless rigid hemispherical foundation embedded in a uniform homogeneous elastic half-space is considered in this study. The foundation is subjected to external forces, moments, plane harmonic P and SH waves, respectively. The series solutions are constructed by three sequences of Lamb's singular solutions which satisfy the traction-free conditions on ground surface and radiation conditions at infinity, automatically, and their coefficients are determined by the boundary conditions along the soil-foundation interface in the least square sense. The fictitious eigen-frequencies, which arise in integral equation method, will not appear in the numerical calculation by the proposed method. The impedance functions which characterize the response of the foundation to external harmonic forces and moments at low and intermediate frequencies are calculated and the translational and rocking responses of the foundation when subjected to plane P and SH waves are also presented and discussed in detail

Research was conducted to examine a theoretical study of the internal rotation of HSOH. Ab initio calculations at the HF//6-311G level reveal that HSOH is a gauche molecule presenting a double-barrier torsional potential. Good estimations of barrier heights and properties associated with the stable isomer have been obtained. An important result is that the principle of maximum hardness is verified even though the electronic chemical potential varies along the reaction coordinate.

A study was conducted to examine the frequencies of large amplitude modes of dimethylamine. A three-dimensional framework was utilized to carry out the analysis of the modes. The potential energy function was obtained from the electronic energies of selected nuclear conformations. The kinetic parameters for the Hamiltonian were then determined using a numerical differentiation method. Results indicated that fundamental gaps correlated with the torsional interaction terms of the potential.

The seismic performance of liquid-storage steel tanks can be improved by anchoring them to their foundations with energy-dissipating devices rather than with conventional anchors. Case studies of two tanks are presented - one broad and one slender tank, both anchored with torsional-beam steel dampers, which dissipate seismic energy by inelastic deformations induced by uplifting of the tank wall. Numerical results show that tanks anchored with steel dampers experience significantly less foundation overturning moment than similar fully anchored tanks. Relative to unanchored tanks, the tanks anchored with steel dampers experience small values of base uplift, plastic rotation at the plate boundary, hoop stress in the wall, and radial separation between the plate and foundation. In general, tanks anchored with dampers exhibit performance superior to that of similar unanchored or fully anchored tanks. Due to savings in the material of tank wall, foundation, and full base anchorage, the use of energy dissipating anchors is likely to be cost-effective.

This paper presents a new speed control method for a two-mass system coupled by a flexible shaft. Two control loops are proposed; the outer angular speed control loop calculates the reference signal for the inner loop, where the torsion of the shaft is handled as a variable under control. In this paper, the observer-based discrete-time sliding-mode (ODSM) control implementation and experimental verification of direct torsion control is presented. The experimental system consists of a conventional dc servo gear motor with encoder feedback and inertia load coupled by a flexible shaft. The controller was implemented using a transputer as the computation engine. Index Terms - Discrete-time system, flexible structures, observers, variable structure systems, velocity control.

A method is proposed to detect shaft torsional vibrations in AC motors and generators from their stator currents. This is achieved by extracting current components at specific frequencies which are the modulation products of the power system frequency and the vibrating frequency. A general closed form proof of this principle is given for both induction and synchronous machines, and the principle is verified quantitatively by digital simulation and experimental results. The effect of the machine operating point is also investigated. The method is applicable to torsional vibrations induced by different causes. When the oscillating torque is developing and the measured stator current is nonstationary, the Wavelet Transform can be used to extend the application of the proposed method to transient conditions.

Comparative investigations of mandibular function among primates have relied upon elementary structural models to estimate states of masticatory stress and strain. In these studies, mandibular corpus morphology is idealized as a homogeneous, isotropic symmetrical body of invariant geometry, and this morphological ion is used to infer relative levels of stress and strain in the jaw. In reality, none of the limiting conditions assumed by these models is satisfied; consequently, it is prudent to ask whether this 'textbook' engineering approach is valid for the inference of biomechanical behavior. In this study, the predictions of various geometric representations of the mandibular corpus are evaluated against strains recorded in a sample of human jaws loaded in torsion. Symmetrical geometrical models (including various 'robusticity' shape indices), although convenient, are probably not consistently reliable for predicting the distribution of strains in the corpus. The experimental data suggest that variations in cortical thickness within sections play a significant role in determining the profile of relative strains. For comparative applications, characterization of the corpus as an asymmetrical hollow ellipse (i.e., with differing thickness of medial and lateral cortical plates) may provide a reasonable portrayal of relative strains. KEY WORDS: stress; strain; mandibular function

A finite element that is capable of modeling the kinematic boundary collisions associated with mixed torsion was developed. The model was intended to capture spanwise torsion-related warping strain effects in open-section composite beams. It features twist and twist rate degrees of freedom which allows the direct implementation of the kinetic boundary conditions associated with torsion-related warping restraints.

In this study, we reconsider the torsion of nonlinear viscous shafts. Attention is paid to the analytical solution of the nonlinear partial differential equation arising in the problem's formulation, and it is concluded that the stresses [[Tau].sub.xy], [[Tau].sub.xz], and the torque T(t) can be found in terms of the partial derivatives of the warping function [Phi]. Theoretical results are given for circular cross sections, and it is shown that the present method gives the same results as those for elastic (m = 0) and perfectly plastic torsion (m [approaches] [infinity]). It is further proved that it is not possible to give analytical solutions for nonregular boundaries, such as rectangular and triangular cross sections.

Recent studies have proved that the operation of three phase synchronous motors from a single phase supply is possible. This adds more flexibility to the operation of these motors and extends their field of application. However, previous work carried out in this respect neglected the effect of the torsional dynamics of the motor-load-shaft assembly, that exist particularly with motors driving a reciprocating type multi-compressor loads. Such an effect may have damaging consequences when one or more of the natural frequencies of the mechanical system coincides with one or more of the natural frequencies of the electromagnetic torque components. This phenomenon is called electro-mechanical resonance. The main objective of this paper is to take the effect of this phenomenon into consideration through the development of a rigorous mathematical model coupled with a sound digital simulation. Keywords: Synchronous motor, torsional dynamics, torsional torque

This paper presents a probabilistic approach to the evaluation of the maximum torsional torques induced in turbine-generator shafts during high-speed reclosing of system faults. In this context, investigations have been conducted on a large turbine-generator model taking into consideration the uncertainty of several factors associated with the practical operation of a power system. The results of these investigations are presented in the form of discrete probability distributions of the maximum torsional torques induced in the turbine-generator shaft sections.

A study investigated, using the finite element analysis, the relationship between torque and angle of twist for two elastic bodies under no previous stress and residual stress. The result of changing material and geometric parameters and the relationships between torque generation and angle relevant to these nondimensionalized parameters are presented. These relationships are significant in examining the mechanics of nonlinear torque in applications such as ball bearings.

Traditionally, the analysis of stability in drillstrings is based on longitudinal vibrations only. However, field experience indicates the presence of torsional effects in the form of modulations in longitudinal vibrations. Moreover, torsional dynamic forces are significant and lead to joint problems during drilling. In this paper, we discuss the effect of torsional vibrations on the stability and both longitudinal and torsional forces in drillstrings. Using a model of a typical drillstring that incorporates both longitudinal and torsional multi-degree of freedom, we develop the equations governing displacements and forces at any joint. Using time simulation techniques, we obtain the stability diagram and calculate the dynamic forces at any joint as a function of time. We finally show the effect of torsion on the nature of vibrations through frequency analysis, a technique that is useful in the interpretation of field measurements under various drilling conditions.

Composite pipes have been utilized in the petrochemical industries where corrosion resistance and light weight are important. There is a need to calculate the buckling load for the pipe under torsion which develops from the structural loadings. An analytical model of composite pipe in torsion is developed during this study. Laminated anisotropic plate theory is utilized to derive the kinematics and constitutive relations of the pipe wall laminates. Solutions are obtained by using the Ritz method with suitable boundary conditions. Good agreement is found when comparing the present results with the analytical and experimental results from previous research.

A simplified displacement form for equations of motion of nonlinearly elastic shells of revolution undergoing torsionless axisymmetric motion is integrated with static equations with combined bending and torsion of arbitrary magnitude. Six extensional and bending strains in earlier research are reduced to five effective systems that can be defined as linear and quadratic functions of translational displacements and rotation.

Thin-walled beam behavior is evaluated in terms of a one-dimensional structured continuum. The analysis considers two bifurcation cases. The first case showed that buckling behavior in nonsymmetric cross sections produced imperfection sensitivity. Slighter but similar results are obtained for an axially loaded beam with interaction between flexural and torsional buckling.

An unconventional driven torsion pendulum influenced by gravity has been studied for chaos. Through the use of a symmetric differential capacitive sensor and a galvanometer, phase-space trajectories were generated with an x-y recorder. These were then later compared against output from a computer model of the system which has been further used to generate Poincare sections, Fourier transforms, and time records. Sensitive dependence on initial conditions as a function of frequency and drive amplitude was demonstrated.

When the ratio of the minor axis flexural stiffness to the major axis flexural stiffness is not small, classical analysis may lead to an inaccurate prediction of the flexural-torsional buckling loads of an arch, because prebuckling in-plane deformations change the curvature of the arch. A systematic treatment of the effects of prebuckling in-plane deformations on the elastic buckling of monosymmetric arches is presented in this paper. Nonlinear relationships between the displacements and the strains are obtained using position vectors. Energy equations are formulated for the elastic flexural-torsional buckling of monosymmetric arches, which include the effects of prebuckling in-plane deformations, and closed-form solutions are obtained for arches in uniform bending. The effect of the arch slenderness on flexural-torsional buckling is investigated. Comparisons with the existing theoretical solutions are made.

Fourteen prestressed high-strength concrete beams were tested to study their torsional behavior. The major variables were the concrete compressive strength, the aspect ratio of the beam cross section, the prestressing level, and the amount of torsional reinforcement. Keeping the area constant, three different cross-sectional dimensions, 240 x 240 mm, 170 x 340 mm, and 140 x 420 mm, were used to give aspect ratios of 1, 2, and 3, respectively. The concrete compressive strengths were 70 and 90 MPa (10,000 and 13,000 psi), and the beams were subjected to two levels of prestressing, corresponding to 0.05 [f[prime].sub.c] and 0.10 [f[prime].sub.c]. Test results showed that the torque-twist relations for the tested beams were approximately linear up to cracking, and thereafter they were nonlinear. The aspect ratio and the concrete compressive strength influence both the torsional strength and the torsional stiffnesses at all stages of loading. Several theoretical methods available in the literature and developed for normal-strength concrete were used to predict the torsional behavior of the test beams. The space truss theory with softening of concrete gave the best prediction of the torsional strength of the test beams.

Systems for torsional stiffening, including longitudinal plate, transverse plate, box, and cross stiffeners of I-beams are reviewed. Different configurations for cross stiffeners are presented, including crosses fully formed on both sides of the beam, formed on one side only, or split with half of the cross on one side of the web and the other half of the cross on the other side of the web. The split-cross configuration is particularly desirable, being easy to fabricate but almost as effective as the full-cross configuration. Multiple butting and multiple overlapping cross stiffeners allow torsional stiffening along the entire length of a beam. Relationships for the mechanics of single butting, multiple butting, and multiple overlapping cross stiffeners are developed, and equivalent St. Venant's torsion constant are derived. Design parameters for cross stiffeners are reviewed and a stiffener slope of 45 [degrees] is recommended. The effect of cross stiffeners on lateral torsional flexural buckling of I-beams is shown to significantly increase the beam capacity.

The torsional straining of commercially pure titanium induces flow instability during adiabatic heating, which is determined by an empirical criterion obtained by integrating an uncoupled constitutive equation over the strain increment accepted by the material and modifying the thermal softening equation. During a rise in temperature and a lowering in the strain rate, the instability shear strain increases. A comparative study of the experimental and asserting measurements reveal the flow instability at strains approximately equal to the thermo-plastic instability strains for 150 degree centigrade.

The laminar fully developed flow problem in a helical square duct with a finite pitch is solved numerically using the finite-volume method with the SIMPLEC algorithm. [h.sup.2]-extrapolation is used to locate the limit points of the stable solution branches. Results for the friction factor are presented. For helical ducts of small pitch, or torsion, it is verified that all investigated flow properties are very similar to those for a toroidal duct with the same dimensionless curvature. A new correlation is proposed for the friction factor ratio.

A procedure is developed for including the effects of accidental torsion in seismic design of buildings. It has four steps. First, the ratio between the fundamental frequencies of uncoupled torsional and lateral motions of the building is computed. This ratio and plan dimensions are then used to estimate the increase in displacements at the edge of the building resulting from all sources of accidental torsion. Third, from these edge displacements the increase in displacements at the location of interior resisting planes are estimated. Finally, the design forces in structural members are computed by amplifying the forces ignoring accidental torsion by the increase in building displacements determined previously. This procedure has several advantages over the code-specified static and dynamic analysis procedures to include accidental torsion, such as: (1) The elimination of cumbersome static or three-dimensional dynamic analyses to account for accidental torsion effects in building design; and (2) the inclusion of the effects of all sources of accidental torsion. Two building examples are presented to illustrate these advantages as well as the computational steps required to implement the new procedure.

The primary objective of code torsional provisions is to limit to acceptable levels the element ductility demands and deformations in plan-eccentric structural systems. Such levels are determined from well-established seismic design criteria applied to the appropriately defined reference systems. Information is available from comprehensive recent studies focusing on the effectiveness of code torsional provisions in meeting that objective. The major controlling factors have been identified as the total design strength incorporated in plan-eccentric structures and its code-dependent distribution among the lateral load-resisting elements. The results and conclusions of these related studies have been based on a comparison of the response of elements in plan-eccentric systems with that of the corresponding element in the selected reference system. This paper demonstrates that when a reference model is adopted that adheres rigorously to the design regulations of codes, including provisions for so-called accidental torsional effects, significant period dependency of inelastic seismic torsional response behavior is revealed. To demonstrate this, a reevaluation of the equivalent static torsional design procedures of codes is presented.

The inelastic combined bending and torsion of I-section beams is investigated in this paper using the finite-element method. The elastic-plastic load-deformation relationships of beams under combined bending and torsion are determined by taking into account the effects of large deformations, material inelasticity, and initial conditions of residual stresses and geometric imperfections. The interactions between in-plane bending, flexural-torsional buckling, and torsion are studied. The effects of secondary bending actions about the minor axis caused by torsional rotations are important for the interaction between bending (with flexural-torsional buckling) and destabilizing torsion. Interaction equations for the design of I-section beams against combined bending and free torsion, and against combined flexural-torsional buckling and destabilizing torsion, are proposed. It is found that a commonly quoted circular interaction equation for combined bending and torsion does not always provide a true lower bound for I-section beams.

The effects of the nonlinear shear modulus of panels functioning under an incomplete diagonal shear stress explain the similarities between theoretical and experimental analysis of advanced composite wing boxes under pure torsion. Postbuckling fields can accommodate working composite panels, but the buckling of panels causes a major decrease in the efficient torsional stiffness of the whole structure. Following this, the static and dynamic behavior of an entire wing can be altered to change flight performance.

This paper presents the adaptive reclosing technique as a new concept to reduce the high torsional torques to which the turbine-generator shafts might be subjected during high-speed reclosing of multi-phase system faults. In this context, investigations have been conducted on a large turbine-generator model for various multi-phase faults. In this paper, the principle of such an adaptive reclosing technique is explained and its effectiveness is demonstrated in the case of three-phase faults. The paper presents also the idea of applying the principle of adaptive reclosing to single-pole reclosing.

Experiments show that a.c. potentials can evaluate the extent of multiaxial low-cycle creep fatigue damage in super alloys such as Alloy 738LC better than other methods. Use of a rectangular a.c. wave length with fast Fourier transformation makes it possible to calculate a.c. potentials at many frequencies with one reading. High frequency potentials are more sensitive to small cracks while low frequency potentials detect large cracks better. High frequency potentials are better than low potentials for estimating crack density and the maximum crack length.

Ripple currents on the DC side of both HVDC synchronous and asynchronous Links together with cleared HVDC and AC system disturbances can excite in some circumstances onerous torsional vibrations in large steam generator shafts. The problem has assumed importance in recent months on account of the HVDC Link between Scotland and Northern Ireland going ahead, on account of the proposed Eire/Wales Link, and because AC/DC/AC couplers are to be installed extensively to interconnect the East and West European Grid Systems. This paper discusses and analyses excitation of shaft torsional vibrations in steam turbine-generator-exciter shafts in close proximity to HVDC converter stations by (i) variable-frequency ripple currents superimposed on the DC currents in asynchronous Links, and (ii) disturbances at bi-polar converter stations. In (i) shaft torques in multi-machine networks are evaluated by proportioning HVDC Link disturbance currents to each machine at risk using system network data, generator data, fault analysis data, and load flow data, considering frequency dependence of the system parameters. This scaling factor is calculated for different scenarios of system operation and load. Equivalent circuits for the synchronous generator are employed appropriately to correlate HVDC Link disturbance current impressed on the generator stator with steady-state torque excitation from which magnitude for turbine-generator-exciter shaft torque is deduced. In (ii) shaft torques are evaluated by time domain computation using converter station phase currents and a faithful single machine-infinite busbar equivalent of the multi-machine power system where converter station currents are proportioned to the particular machine which is under investigation. Generator air-gap torque is evaluated by solution of the converter station/synchronous machine/infinite system differential equations. Turbine-generator-exciter torque is computed from transient generator airgap torque either in the time domain using differential equations for the turbine-generator-exciter shaft or in the frequency domain using stiffnesses, inertias and damping of modal vibrations of the shaft. Detailed (2d,3q) and reduced (1d,2q) and (1d,1q) phase-variable models for the synchronous-generator are employed. The time responses and tables show that for the systems studied variable-frequency ripple currents superimposed on the DC current in asynchronous Links can excite shaft torsional vibrations, that very small noncharacteristic currents could result in onerous shaft torques which might damage the machine, and that DC line faults at converter stations in close proximity of steam turbine-generator units can excite onerous turbine-generator shaft torsional response. Detailed simulation of the HVDC converter and generator is necessary for precise assessments of shaft torsional response following HVDC converter station faults. 500MW, 660MW, 1000MW and 1300MW machines are considered in the analyses that are made.

The method of solving the problem of torsion of rectangular bars with multiple cavities requires the Laplace equations in polar coordinates. Each set of cavities are harmonious with the two axes of symmetry of the rectangular section. The torsional rigidity is similar to that of an unreinforced shaft and does not change when reinforcing rods are used.

This paper proposes a fast and robust speed controller for motor drive systems having torsional loads and containing a gear backlash. The controller is designed using the state feedback technique combined with state variable observers and is implemented on a digital signal processor. Analysis, simulation and experimental results of a prototype speed drive system are presented and discussed. It is shown that the proposed speed controller yields a robust system with respect to system uncertainties and modeling errors and is very effective for the suppression of mechanical vibrations.

The behavior of unsymmetric buildings excited by incoherent seismic ground motions is studied, and the assessments and information reported make it possible to gain valuable insight into the resulting dynamic response. The effects of the ground motion incoherence and of the structural eccentricity are first considered independently of one another, and attempts are made to identify their relative importance. The torsional effects induced by the incoherence actions are interpreted in terms of normalized accidental eccentricities; and comparisons are made of these eccentricities with the value of 0.05 specified by design codes. Such comparisons form a frame of reference for the assessment of the importance of the torsional effects resulting from the ground motion incoherence. The coupled effects of incoherence and eccentricity are then considered, and it is reported that they can be approximately represented by proper combinations of the corresponding independent effects, under conditions that are of practical importance. This approximation leads to the definition of effective modified eccentricities, which can be useful for the appreciation of the torsional effects induced in building structures by earthquakes.

A procedure is presented for evaluating building-code provisions for accidental torsion from analysis of earthquake-induced motions of nominally symmetric-plan buildings. This procedure is used to analyze the motions of three buildings recorded during recent California earthquakes. Two alternative approaches to evaluate the code accidental torsion provisions are developed. The first one considers the response histories of base shear and base torque in the building, and the second, the 'actual' forces in the structural elements during the earthquake. The results show that base rotational motions cause between 25% and 45% of the total accidental torsion in the buildings. They also demonstrate that the accidental torsional moments specified by the Uniform Building Code are sufficient in representing the torsion in the recorded motions of the three buildings. Further, it is shown that accidental torsion need not be considered in the design of two of the three buildings studied. This observation, however, may not necessarily apply to other structures, such as buildings with torsional vibration periods much longer than their lateral vibration periods.

A finite element approach to calculate directly the critical wind velocity for the nonlinear lateral-torsional buckling instability of long-span cable-stayed bridges under the displacement-dependent wind loads is presented. An analytical modeling of wind-induced lateral-torsional buckling is formulated taking into account the three components of displacement-dependent wind loads as well as geometric nonlinearity. A combination of the eigenvalue analysis and the updated bound algorithm for wind velocity is applied to automatically calculate the critical wind velocity. The results show that the incorporation of the three components of displacement-dependent wind loads as well as the geometric nonlinearity in the analytical modeling of the lateral-torsional buckling instability results in significant reduction in the critical wind velocity compared with both the conventional nonlinear torsional divergence and linearized lateral-torsional buckling.

The Fourier coefficients are investigated for such a periodic time function whose magnitude keeps constant during the time of every half-period. In this case the relationship between the mean value and the Fourier coefficients is achieved using appropriate mathematical theory. It was applied successfully to the study of torsional harmonic excitations due to gas pressure in a four-cycle IC engine. A formula relating the truncated Fourier coefficient series to MIP has been established with very little error. The series simulation of Fourier coefficients is utilized in the determination and analysis of excitations.

Torsion in base-isolated structures with inelastic elastomeric isolation systems due to bidirectional lateral ground motion is studied. In a companion paper by the writers, torsional coupling in sliding base-isolated structures was investigated. in this paper, which is the second part of the sequence, torsional coupling in elastomeric base-isolated structures is investigated. Various multistoried structural systems with elastomeric isolation systems are investigated, with the objective of studying the influence of: (1) The flexibility of the superstructure; (2) the ratio of uncoupled torsional to lateral frequencies; (3) stiffness eccentricity in the superstructure; (4) eccentricity in the isolation system; (5) higher mode effects; and (6) number of bearings in the isolation system. Response to different ground motions is also studied. The results are used to explain: 1) The behavior of actual buildings; and (2) some inconsistencies in the conclusions of previous studies. It is shown that, although the total superstructure response is reduced significantly due to the effects of elastomeric base isolation, torsional amplification can be significant depending on the isolation and superstructure eccentricity and the lateral and torsional flexibility.

Test results of 17 axially prestressed concrete beams without stirrups and containing a transverse circular opening are presented. Mainly, beams having two different opening diameters were subjected to various combinations of torsion and bending. Test results show that the bending moment has a beneficial effect and increases the torsional strength for beams with high TIM ratios. For beams with low TIM ratios; however, the torsional strength decreases rapidly with increasing the bending moment. Strength equations to predict the torsional strength at initial cracking are developed. Based upon the initial cracking strength, empirical equations are suggested to predict the ultimate torsional strength for all combinations of torsion and bending. The proposed equations predicted closely the torsional strength of the test beams. Comparison of similar prestressed concrete beams with and without stirrups shows that the introduction of stirrups promotes the development of a consistent failure pattern and increases the ductility and the torsional strength considerably.

The paper presents the results of a study on the utilization of shunt reactors for the damping of common torsional mode interactions of a power system containing series-capacitor compensation. The IEEE Second Benchmark Model, system-2, which has two sets of nonidentical turbine-generators connected to an infinite bus via a common series-capacitor compensated transmission line, is employed to investigate the possible unstable Subsynchronous Resonance (SSR) modal interactions can be suppressed by using reactive power compensation. A set of shunt reactors are proposed and connected to the studied system and a unified approach based on modal control theory is employed to design shunt reactor controllers in order that all SSR modes in the system can be stabilized. For clearly demonstrating the effectiveness of the proposed scheme, SSR mode eigenvalues under different loading conditions and sensitivity analysis of shunt reactor controllers' parameters are performed. Dynamic responses of the nonlinear system simulation under a torque disturbance on generator shaft and a severe three-phase short-circuit fault at infinite bus are also carried out.