DAMPING SYSTEMS

CONSULTING ENGINEERS & SCIENTISTS

There has been a recent trend towardsutilizing damping systems to reduce buildingaccelerations, motion, or deflections.Traditionally, structural engineers anddesigners concentrated their design effortson the more tangible properties of stiffnessand mass. The balancing of these propertiesusually produced an efficient design, capableof allowing the architect the freedom toachieve a desired aesthetic and the structuralengineer could limit deflections and stressesfor a safe structure.

Given the desire to build higher buildings,longer bridges and more daring structures,the envelope of what is possible withinconventional structural design imposeslimitations. Advances in materials, such as high strength steels and efficiencies in structural design through theuse of advanced 3-D modelling software, produce designs which may have unexpected deficiencies. Taller,longer, and lighter structures tend to be more sensitive to wind-induced vibrations or vibrations due topedestrians, traffic, etc. This has led engineers and architects to turn to the damping of a structure as a means of limiting excessive motions/deflections.

Traditionally, there have only been a few methods of increasing the damping of a structure. Visco-elasticmaterials have been used in some applications, while in others, the Tuned Mass Damper (TMD) has been usedsuccessfully. The direct application of viscous dampers in a structural system or between two separatecomponents has been used. Since the deflections involved are usually small it can be a challenge to design theseviscous damping systems to work effectively.

Research in vibration suppression has led to a large number of different types of damping systems, eachemploying different technological advances. Some of the more common systems are briefly described below:

Tuned Mass Damper (TMD): A TMD is a passive damping system which utilizes a secondary mass attached to avibrating structure. The secondary mass is given dynamic characteristics that relate closely to that of the primarystructure. By varying the mass ratio of the secondary mass to the primary body, the frequency ratio between thetwo masses and the damping ratio of the secondary mass, a certain amount of damping can be produced.Essentially, the TMD can be viewed as an energy sink, where excess energy that is built up in the building orbridge is transferred to a secondary mass. The energy is then dissipated by some form of viscous damping devicethat is connected between the building and the TMD mass itself.

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ISSUE NO. 10

Figure 1: A 3-D rendering of acompound pendulum type TMD.

Figure 1 illustrates a compoundpendulum design produced byRWDI for a TMD in a tall towerin New York. A large mass (600tonnes) hanging on a system ofcables acts as the secondarymass, while viscous dampersprovide the energy absorption.

Tuned Liquid ColumnDamper (TLCD): This passivedamping system is a variationof the TMD. Whereas a springand a viscous damper arecombined with a mass block(usually concrete or steel) inthe TMD, water or other liquidis used in a TLCD, combiningthe functions of the mass,spring and viscous dampingelements. The geometry of thetank that holds the water isdetermined by theory to givethe desired natural frequencyof water motion. A sluice gate(or other similar device) is usedto dissipate the energy in the moving water. Figure 2illustrates scale model tests of a TLCD in RWDI’slaboratories.

The benefits of using a TLCD to reduce motions of abuilding can be threefold. In addition to reducing buildingaccelerations, the water in the tank can also be used forfirefighting purposes and in some instances can be used forchilled water storage as well.

Tuned Sloshing Water Damper (TSWD): The TSWD is yetanother variation of the TMD. In the case of the TSWD, arectangular tank is designed with the correct length andwater depth to initiate wave motion in the tank. Thismoving wave then represents a moving mass that behavessimilarly to the moving mass of a TMD. Energy is dissipatedby using a damping screen or mesh to create turbulence inthe water. Other variations of the TSWD include circularcontainers or a bi-directional tank where the wave movesin two directions. It is also possible to use a different fluidthan water, such as oil, in more hybrid types ofapplications.

A TSWD is an excellent choice of a damping system forretrofit applications. The wide variety of shapes that canbe configured as a TSWD help this type of system fit intoexisting spaces within a structure.

Viscous Damping System: Installing viscous dampers in astructure has long been recognized as an effective meansof reducing the effects of wind and earthquakes. Thebenefits of a viscous damper are well known in the

automobile industry. Recent technological advances inviscous damper technology and ingenious means ofamplifying small structural motions make this type ofdamping system more viable for suppressing wind-inducedmotions.

Viscoelastic Damping System: In a system similar to aViscous Damping system, the use of viscoelastic dampingmaterial, such as rubber, has been used for someapplications. Shearing action of a rubber compound placedbetween layers of steel dissipates energy. The installationof this system at locations in a structure where relativemotion exists has been effectively used in some tallbuildings to reduce the effects of wind and earthquakes.

Active Mass Damper (AMD): Another method ofreducing vibrations is to try to counter the force that isactually causing the vibration. The Active Mass Damper is asystem that attempts to achieve this. Motion in a structureis sensed by instruments, such as an accelerometer, and acomputer controlled actuator system moves a large mass togenerate a force to counter that which is causing themotion in the first place. The keys to a successful AMD arefast sensing equipment, stable control algorithms andresponsive actuator technology. A benefit of an AMD isthat for a given amount of mass, a larger amount of“damping” can be provided than a passive TMD. However,a typical AMD is generally more expensive than a passiveTMD and has higher maintenance requirements. In someapplications where seismic loads govern, this type ofdamping system can be effective in reducing the impact ofthe seismic event.

Figure 2: A scale model experimental set-up that was used to confirm the theoreticalpredictions for natural frequency and internal damping for a large 600 ton TLCDinstallation for a Vancouver building.

Many engineered structures have cables exposed towind, rain, and ice. Electrical power lines, guyssupporting communication towers, and cablessupporting certain types of roofs are examples. Thisarticle focuses on cable-stayed bridges. Interactionof wind and precipitation with cables can result indamage to or failure of the cable system.Most problems are caused by cable oscillations ratherthan the simple lateral force of the wind (althoughthis can be a factor in severe icing conditions). Manyinstances of cable oscillations have been reportedand a variety of solutions have been tried.

One well-known type of vibration is aeolianvibration or vortex shedding. The wind blowing pasta cable is broken up into a series of vortices that trailoff the downwind side of the cable in a vortex wake.The vortices are shed at a distinct frequency, n,which is given by the formula

(1)

where S is a constant known as the Strouhal number, U isspeed, and D is cable diameter. For most cables, theamplitude of oscillation caused by vortex shedding is smalland not a cause of many problems. On bridge stays, it istypically no more than a few millimetres. It is not uncommonto see higher vibration modes excited on a bridge cable. Theoscillation amplitude of vortex shedding vibrations variesroughly in inverse proportion to the aerodynamic stabilityparameter called the Scruton number. It is defined as

Scruton number, Sc = (2)

where m = mass of cable per unit length, ς = damping ratio,� = air density, and D = cable outside diameter. Since vortexoscillations become smaller as the Scruton number isincreased, the more dense and highly damped the cable, theless it will oscillate.

The vibration that has caused most problems on bridge cablesis called rain-wind vibration. This occurs in wind combinedwith rain and is caused by rivulets of water running down theinclined cables. Two rivulets are formed, one on the top sideof the cable to the windward of the highest point, and oneon the bottom side. The positions of these rivulets on thecable perimeter affect the aerodynamic force in the across-wind direction, but are influenced by the aerodynamic forceson the rivulets themselves and by accelerations due to cablemotions. This gives rise to coupled motions of the rivuletsand cable.

Rain-wind oscillations begin in the wind speed range of 7 m/sto 15 m/s and can reach amplitudes higher than a metre.Below this speed, the top rivulet does not form because thewind force is insufficient to prevent it from runningdownwards around the windward face to the bottom of thecable. Above this range, the wind forces on the rivulets arehigh enough to blow them right off the cable. Like vortexexcitation, a range of vibration modes can be excited by rain-wind oscillations.

As with vortex shedding, the Scruton number is an importantparameter. The higher the number the better. The latestdraft of the Handbook on Cable-Stayed Bridges of the Post-Tensioning Institute proposes that to avoid rain-windoscillations the Scruton number should be greater than 10, i.e.

> 10 (3)

This means that methods of augmenting the natural dampingof cables need to be found for many bridges. Hydraulicdampers have been added to the cables of several bridges.Another approach is to attach secondary transverse cables orcross ties to the main cables. These add extra damping andeliminate some of the lower modes of vibration that could beexcited. Some damping does come from neoprene split-ringwashers used at the ends of bridge cables to reduce bendingmoments at the cable anchorages. However, on long cablesthe split-ring washers often do not result in a damping ratioany higher than about ς ≈ 0.003 and in most cases ς needs tobe at least 0.006.

Figures 1 illustrates the measurement of the damping ofcables on an existing bridge by RWDI’s field monitoring team.Accelerometers mounted on the cable enable its damping andnatural frequencies to be measured. These dampingmeasurements can be useful in assessing whether the cable’sinherent damping will be sufficient to avoid problems orwhether special damping systems need to be added. Typically,the longer the cable, the lower its inherent damping. Thus,shorter cable-stayed bridges tend to run into less vibrationproblems than longer ones.

An alternative approach to avoiding rain-wind oscillations is toshape the outer sleeve of the cable so the rivulets of water aredisrupted. For example, both a helical bead wound around thesleeve and dimpled surfaces have been tried. Theireffectiveness is still not really confirmed due to limited use inthe field and because they have usually been tried at the sametime as other measures such as increased damping or cross ties.

Figure 1: RWDI’s field monitoring team undertaking measurements on bridgecables.

WIND-INDUCED CABLE OSCILLATIONSBy Peter Irwin, Principal

Un = S D

mς—�D 2

mς—�D 2

Besides rain-wind oscillations there are a number of lesscommon types of oscillation. These are in need of furtherresearch for bridge cables. Two that are frequently cited are:wind forces acting on the main bridge structure that causeoscillations in a vibration mode primarily consisting of cablemotions; and inclined cable “galloping”. The latter does notrequire rain and typically begins at a higher wind speed thanrain-wind oscillations. It can reach amplitudes of severalmetres and tends to involve only the lowest modes ofvibration. A tentative criterion giving the onset wind speedUCRIT for galloping is

UCRIT = cnD SC (4)

where c = constant. The value of the constant c for this type

of galloping is probably around 40, but needs furtherinvestigation.

Increasing the Scruton number Sc, which can be achieved byadding damping to the cables, makes galloping a less likelyproblem. It increases the wind speed required to initiategalloping and makes it less probable. Equation 4 also showsthat increasing the frequency, n, increases the critical velocity.A cost effective way of increasing the frequency is to installsecondary, small diameter cables as cross-ties between themain cables. This has been implemented and shown to beeffective on a number of bridges as long as the cross-ties areinstalled with adequate pretension.

Rowan Williams Davies & Irwin Inc. (519) 823-1311 www.rwdi.com

RWDI Anemos Ltd.01582 470250 www.rwdi-anemos.com

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Figure 2: Example of an accelerometer oscillation-decay trace used for determining the damping of a cable.

Cable E10SW (Filtered)

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Rowan Williams Davies & Irwin Inc. (RWDI) is a leading wind engineering and microclimateconsulting firm - the result of more than 30 years of growth and development. From offices inCanada, the United States and the United Kingdom, our consultants meet the world’s most complexstructural and architectural challenges with experience, knowledge and superior service. In the earlyplanning stages, careful attention to the effects of wind, snow, ventilation, vibration and relatedmicroclimate environmental issues on buildings and structures will save time, save money and reducerisk. Our capable and qualified staff uses advanced engineering tools and carefully defined consultingprocesses to deliver understandable and useful results.