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Engineering Structures 33 (2011) 24852494

Contents lists available at ScienceDirect

Engineering Structures

journal homepage: www.elsevier.com/locate/engstruct

Control of vibrations induced by people walking on large span compositefloor decks

Wendell D. Varela a,, Ronaldo C. Battista b

a Faculdade de Arquitetura e Urbanismo, Universidade Federal do Rio de Janeiro, Departamento de Estruturas, Av Pedro Calmon, 550, Prdio da Reitoria/FAU, Cidade Universitria,

Rio de Janeiro, RJ, CEP 21941-901, Brazilb Instituto COPPE, Universidade Federal do Rio de Janeiro, Engenharia Civil, C. Postal 68506, CEP: 21945-970, Rio de Janeiro, RJ, Brazil

a r t i c l e i n f o

Article history:

Received 17 March 2010

Received in revised form

13 April 2011

Accepted 15 April 2011

Available online 1 June 2011

Keywords:

Dynamic control

Composite structures

Floor decks

Human loads

Vibration

a b s t r a c t

The low damping properties of lightweight large span floor decks composed of a reinforced concrete slabon top of a steel space frame structure may lead to undesirable dynamic responses, even to ordinaryhuman actions such as walking.

This problem was investigated through laboratory tests performed on a 1:1 scale prototype of acomposite floor deck structure. Experimental measurements were taken for the structure subjected toseveral dynamic human loads, especially those produced by the random walking of people.

To compensate for the lack of damping, a passive control system was designed and installed in thecomposite structure prototype.

The performance of the mechanical control devices was evaluated by means of straight comparisonsbetween the experimental acceleration amplitudesobtained for the controlledand uncontrolled structuresubjected to similar dynamic forces produced by one or more persons walking. The most relevantresults for both time and frequency responses are presented and used to argue that small and low costpassive control devices can already be included in the design stage of a smart structure as effective

accessories to substantiallyreduce vibrations induced by peoplein low damped large spancomposite floordecks.

2011 Elsevier Ltd. All rights reserved.

1. Introduction

Many excitation sources may generate excessive vibrationsin low damped lightweight large span floor decks, which maycause discomfort to the users of residential, commercial, orpublic buildings. Typical examples of these vibration sources aretraffic of heavy vehicles on neighboring roads, large machinery inneighboring constructions sites, equipment installed in buildings,

and human activities on floor decks, such as walking, running,and jumping. Among these vibration sources, those produced byhuman activities are the most common, and walking is a dailyactivity everywhere.

The number of cases of floor deck structures that presenthuman-induced vibration problems has grown with the increasingnumber of building constructions with composite floordecks spansthat are larger and more slender. Vibration problems induced byhuman walking have been observed for almost two centuries; in

Corresponding author. Tel.: +55 21 25981682; fax: +55 21 2598 1890.

E-mail addresses: [email protected] (W.D. Varela), [email protected]

(R.C. Battista).

1828, Tredgold [1] apud [2] suggested that longer girders shouldbe built with a greater cross-section height to avoid everythingshaking in a room when someone walks on the floor. In thissame direction, structural stiffening has been largely favored byengineers as a practical design solution and as a remedial measureto reduce vibrations in existing structures; however, in certaincases [3], this may lead to non-practical dimensions of structuralcomponents or to a cost-benefit trap.

In the problem addressed in this study, people are simultane-ously vibration sources and displeased users, and sometimes theymay act as energy dissipation devices [4,5]. Although it is possibleto lessen the intensity of the human vibration source by coveringthe floor with layers of fabric and rubber-like materials, more effi-cient and lasting solutions are achieved by increasing the dampingproperties of the structure, by installing dynamic control devices,or, if there is a cost benefit, by stiffening the structure as in com-mon practice.

Whenever allowed by the inner architecture layout, a cheapsolution may be achieved by installing partition walls along withstruts topped with rubber pads compressed against two floorslabs, combining the required increase in structural stiffness anddamping [2,6].

0141-0296/$ see front matter 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2011.04.021
http://dx.doi.org/10.1016/j.engstruct.2011.04.021http://www.elsevier.com/locate/engstructhttp://www.elsevier.com/locate/engstructmailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.engstruct.2011.04.021http://dx.doi.org/10.1016/j.engstruct.2011.04.021mailto:[email protected]:[email protected]://www.elsevier.com/locate/engstructhttp://www.elsevier.com/locate/engstructhttp://dx.doi.org/10.1016/j.engstruct.2011.04.021


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2486 W.D. Varela, R.C. Battista / Engineering Structures 33 (2011) 24852494

Fig. 1. Application of multiple TMDs on prefabricated slabs [4]. (a) Full view. (b) Detailed view of a TMD.

Smart concretes with special damping components [7,8] ora sandwich reinforced concrete slab with a thin inner layer ofviscoelastic material [9,10] can be possible solutions.

A substantial reduction of vibrationsinduced by humanwalkingon floor slabs may otherwise be achieved by properly designingand installing tuned mass dampers (TMDs), which are efficient,

low cost, and low maintenance mechanical devices that can beinstalled without interrupting operational or human activitiesin the building. Another advantage that TMDs have over otheralternative solutions is their versatility; they can be designed inmany different shapes and sizes as needed, and as required toaccommodate the architectural aspects and space limitations.

A more advanced control solution can be sought by usingactive mass dampers (AMDs), which in general lead to greaterreductions in vibration amplitudes in relation to those achievedwith TMDs [11] because of the faster response of an active controlsystem and because of the capacity of such a system to operate ina band of frequencies, which is a clear advantage considering therandom characteristics of human walking. However, they presentsome practical drawbacks: a source of electric energy is needed for

operation;special maintenance is required, and they are somewhatmore expensive than their passive counterparts because they arecomposed of several electric and electronic components as well assmaller mechanical devices.

In the present work, it is shown that the problem of excessivevibration amplitudes produced by the random walking of one ormore persons on a composite floor deck structure may be properlysolved by using TMD-like passive control devices.

2. Mechanical devices to attenuate vibrations induced by

people on structures

Subsidiary dynamic devices to reduce the amplitudes of motionin mechanical systems were first conceived by the German

engineer Frahm [12] in 1911, and later applied by German navalarchitects to control the rolling motion of ships. Ormondroyd andDen Hartog, in 1928 [13,14], derived the mathematical equationsfor a two-degree-of-freedom controlled mechanical system, inwhich the controlling device was called a dynamic absorber.

In civil engineering applications, one of the first studies wasconducted by Lenzen [3], who very briefly indicated the possibilityof adopting control devices to damp vibration induced by peopleon floor decks; these devices were then calledtunedmass dampers(TMDs).

Many other studies on the practical application of dynamicattenuators in large civil engineering structures have beenconducted by researchers in various countries. It has beendemonstrated theoretically and experimentally [1526] that the

TMD efficiency depends on the ratios between its frequencyand damping to the fundamental frequency and modal damping

Fig. 2. Large span composite floor deck structure used for human walking tests.

of the structure, respectively. Multiple synchronized dynamicattenuators, MSDAs, can significantly reduce floor slab vibrationamplitudes in one or multiple closed spaced modes of vibration.Battista and Varela [2729] designed an MSDA system tuned to

four different frequencies to reduce vibrations induced by humanswalking on a continuous four-panel composite floor deck (Fig. 1(a)and (b)). The conceptual design of these attenuators followedthat of a simple cantilevered beam with a lump of mass at itstip. For any of the attenuators, frequency tuning was done bysliding the lumped mass along the beams length. The mechanicaldamping inherent to the bolted pieces of the attenuators sufficesfor their good performances. The attenuators were located atpoints of maximum amplitudes of the dominant vibration modeshapes. Over 80% reduction of vibration amplitudes was achieved,contradicting current expectations and past concepts [15].

3. Experimental program

The vibration problem of interest was investigated [4,28]through laboratory tests performed on a 1:1 scale prototype of a9.2 9.2 m square composite floor deck (Fig. 2). The prototypestructure is composed of a reinforced concrete slab with 13 cmthickness on top of a steel space truss formed by pyramidalmodules with a 1.15 1.15 m square base (Fig. 3). The floor deckis a reinforced concrete slab on a corrugated metal sheet with0.65 mm thickness. The concrete has elastic modulus 30.5 GPa andspecific weight 24.5 kN/m3. The connections of the steel shapesare all bolted. The total mass of the structure is 35 t. This largespan structure was conceived by Souza and Battista [30,31] to beemployed as floor decks in shopping center buildings.

The experimental program was divided into two phases. In thefirst phase, free vibration tests were carried out to obtain some of

the dynamic characteristics of the structure, such as the first threenatural frequencies as well as the corresponding mode shapes and


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W.D. Varela, R.C. Battista / Engineering Structures 33 (2011) 24852494 2487

Fig. 3. Cross-section of the large span composite floor deck structure.

modal damping ratios. These tests additionally servedas a basis fordesigning the TMD-like mechanical control devices. In the secondphase, human walking tests were performed on the uncontrolledstructure and on the controlled structure to evaluate the efficiencyof the control devices in reducing the vibration amplitudes.

4. Free vibration tests of the structure

Free vibration tests were performed by applying heel impactson the deck structure. Accelerometers were installed at charac-

teristic points (Fig. 4) to pick up the first three mode shapes ofthe structure (Fig. 5(a)(c)). Table 1 presents the experimental fre-quencies and damping ratios associated with the first three vibra-tion mode shapes. The mode shapes depicted in this table and theirrelated modal masses were obtained with an experimentally cali-brated refined finite element numerical model. The finite element

Fig. 5. The first three experimental vibration mode shapes drawn with the

instantaneous acceleration amplitudes measured at the points indicated in Fig. 4.

model (FEM) using the actual dimensions and mechanical proper-

ties of the materials led to a good match between the experimentaland numerical results, i.e. no special adjustment of the numericalmodel was needed.

The values of the natural vibration frequencies of the structurewere obtained by applying a fast Fourier transform (FFT) onthe acceleration versus time responses. The modal damping

Fig. 4. Instrumentation plan for tests indicating locations of the accelerometers and points of heel impacts.


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Table 1

Dynamic characteristics of the tested floor deck structure prototype.

Mode number 1 2 3

Frequency (Hz) 7.57 (0.03) 12.21 (0.03) 12.42 (0.03)

Damping ratio 0.25% 0.64% 0.66%Modal mass 20 t 10 t 10 t

Vibration mode shape

Fig. 6. TMDs used in the tests. (a) Schematic of the TMDs installed in the floor deck structure. (b) Pieces used in the fabrication of one of the TMDs.

ratios were obtained by the log decrement method applied tothe frequency band filtered acceleration versus time responses.As the damping ratios were of quite low values, a differentestimation method was used. The results obtained with Ibrahimsmethod [32] confirmedthe valuesobtainedwith thelog decrementmethod.

The amplitudes of the first vibration mode of the structure(7.57 Hz) can be greatly amplified by resonance with the fourth

harmonics (6.49.6 Hz) of human walking excitation forces whosefundamental frequencies fall in the range 1.62.4 Hz.Furthermore,the very low damping ratio (0.25%) of the first vibration modecontributes substantially to the amplification of the responseamplitudes, which may cause discomfort to the users of buildingsconstructed with composite floor decks.

5. Mechanical devices for dynamic control

The preliminary human walking tests on the floor deck struc-ture showed the need for attenuating the vibration amplitudes ofthe dynamic responses to improve human comfort.

To compensate for the lack of damping of the composite floordeck, a passive control system was designed and installed under

the reinforced concrete slab at the center of the prototype struc-ture. The design of the TMD-like mechanical control devices wasbased on the experimental results obtained for the uncontrolledstructure and parametric studies following the authors previousexperience in design works [2729,33].

Fig. 6(a) shows a schematic of the TMDs installed in thestructure. The mobilemass of theTMD is composed by four circularsteel plates sitting on three compressed helicoidal springs. Fig. 6(b)shows the many pieces used in the fabrication of one of thesecontrol devices. Fig. 7(a) shows the two TMDs installed under theslab, and Fig. 7(b) shows a detailed view of one of the TMDs. TwoTMDs were chosen, to make them lighter, and to make them easierto install. For larger mass ratios (i.e. the ratio between the totalmass of the TMDs and the modal mass of the structure related

to its fundamental vibration mode), a larger number of TMDs ora system of multiple synchronized dynamic attenuators [33] is

recommended. An added advantage of multiple TMDs is related tothe operational efficiency: although very robust, if eventually onebreaks the others will continue to perform their work with a smallloss of efficiency. The two TMDs were tuned to frequencies fTMDclose to the first natural frequencyf1, resulting in a frequency ratio

fTMD/f1 0.97. A frequency ratio 0.950.97 allows for changesin modal mass or stiffness (due to added dead loads or structuralalterations), which may occur in the service life of the structure.

The total mass of each TMD (mobile mass plus the other parts)is approximately 55 kg. The effective total mass of the two TMDsis approximately 94 kg (each with a mobile mass of 47 kg), whichcorresponds to 0.47% of the modal mass (20 t) related to the firstvibration mode or 0.27% of the total mass (35 t) of the wholecomposite structure. A mass ratio of 0.21%is, in general, adequatefor obtaining substantial reductions of vibration amplitudes.

After the fabrication, the TMDs were bench tested to checktheir mechanical behavior and to verify if the required dynamiccharacteristics were fully attained. The bench tests of the TMDswere performed by exciting the mobile mass manually; thiswas instrumented with a micro-accelerometer. The dampingcoefficient was then estimated by the logarithm decrementtechnique applied to the free vibration response signal. The

hysteretic damping of the TMDs was inherent to their ownmechanism and some friction between their moving masses andguiding axles. The values of the damping ratios obtained in thebench tests fell in the range 11.5%. Despite this low damping,the motion amplitude of the mobile mass is very small in theworking frequency of the TMDs. The springs shortening equals thisamplitude, which yields an even smaller variation in the pitch ofthe coils. This range of damping allowed for a good performanceof the TMDs. It is worthwhile noting that a too large dampingcoefficient may lock the TMDs mobile mass in the structure.

6. Human walking tests

A series of tests was performed on the controlled and uncon-

trolled floor slab prototype model under excitation produced byone and several persons walking (see Fig. 8(a)(c)).


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Fig. 7. TMDs installed on the floor deck structure for controlled tests. (a) Full view. (b) Detailed view of a TMD instrumented with an accelerometer.

Fig. 8. Walking tests performed on the prototype composite floor deck structure.

(a) Test A: one person walking. (b) Test B: six persons walking side by side. (c) Test

C: six persons walking randomly.

Several tests were performed, and the most relevant resultsof the experimental measurements are summarized herein forthe three most representative tests on the structure. (i) Test A:one person (0.73 kN weight) walking in a predefined trajectorywith an approximately constant step frequency in quasi-resonancewith a subharmonic of the fundamental frequency of the structure(Fig. 8(a)); (ii) Test B: six persons walking (average weight 0.77 kN)side by side with closely synchronized steps (Fig. 8(b)); and

(iii) Test C: six persons walking (average weight0.77 kN) randomlyon the slab and at random step frequencies (Fig. 8(c)). It should

be observed that the frequencies and lengths of the volunteerssteps were spontaneous, i.e., without the aid of any visual or audiostimulations. Tests A and C lasted 180 s and Test B lasted 60 s.The duration of each test represents a significant sample of therandomness of the human walking characteristics.

The statistical parameters for walking extracted from anextensive editing work of video records and careful frame-to-

frame visual observation (30 frames per second resolution) forboth uncontrolled and controlled tests (Table 2) were shown tobe similar. Furthermore, it can be noted in Figs. 9(a)(c), and10(a) and (b) that the walking trajectory prints and frequencyhistograms are also similar for related controlled and uncontrolledtests. These trajectory prints and histograms were constructedas follows: for each person, and for each test, the points wherepeople touched the floor with the heel were marked on gridsof orthogonal lines, and the corresponding elapsed time of thetest were registered. Then, these marked grids were scanned andpassed through image recognition software. The coordinates of thewalking path were obtained by taking the known coordinates ofthe floor deck boundaries. The walking frequencies could also beobtained from the registered time intervals between the markedpoints.

7. Experimental results

The performance of the control systemwas evaluatedby meansof straightforward comparisons of the measured accelerationamplitudes in both controlled and uncontrolled structures undersimilar dynamic forces. In other words, each test was performedtwice: first for the uncontrolled structure in which the TMDswere locked, and next for the controlled structure, both subjectedto dynamic forces produced by the same people walking withalmost the same trajectories and step frequencies. The similaritybetween the tests performed sequentially on controlled anduncontrolled structures was proven by comparative analysis ofthe resulting human walking statistical parameters and trajectory

prints. Comparisons between the controlled and uncontrolleddynamic responses are presented in both the time and frequencydomains.

The efficiency of the mechanical control devices in reducingthe amplitudes of vibrations induced by human walking in eachtype of test was evaluated according to three different criteria:(i) direct comparison of the percentage of reduction in vibrationamplitudes; (ii) volunteers perception to vibrations; and (iii) thehuman perception criterion as recommended by ISO 2631-2 [34],and the acceptance criteria for human comfort recommended bySCI [35] and AISC [2].

Fig. 11(a) and (b) show the dynamic responses in terms ofthe vertical acceleration at the center of the composite deckfor the uncontrolled and controlled structures, respectively, in

Test A. These figures also show the TMD responses in twodistinct conditions: (a) locked, andturned into small added masses


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Fig. 9. Trajectory prints of people walking during tests. (a) Test A: one person walking. (b) Test B: six persons walking side by side. (c) Test C: six persons walking randomly

(trajectory shown for just one person).

Table 2

Statistical parameters obtained from the human walking tests.

Test Walking frequency (Hz) Step length (m) Velocity (m/s)

Average Standard deviation Average Standard deviation Average Standard deviation

A Uncontrolled 1.87 0.07 0.79 0.07 1.48 0.14Controlled 1.85 0.07 0.79 0.07 1.47 0.13

BUncontrolled 1.77 0.06

Controlled 1.74 0.06

CUncontrolled 1.74 0.08 0.72 0.07 1.24 0.14Controlled 1.71 0.08 0.70 0.07 1.20 0.13

Fig. 10. Walking frequency histograms. (a) Test A: one person walking. (b) Test C:

six persons walking randomly.

clamped to the structure (the TMDs and the structure presentthe same acceleration amplitudes at the same location); (b) free,and operating as proper dynamic control devices (the TMDs andthe structure present different acceleration amplitudes at the

same location). The maximum relative displacement amplitudeof TMD mass with respect to the structure (estimated by double

integration of the acceleration signals) was attained for Test A, andreached0.73 mm.

A great reduction in the vibration amplitudes of the structurewas achieved with the two TMDs, as can be observed in Fig. 11(a)and (b), through direct comparison between the controlled (b)and uncontrolled (a) responses of the structure. This reductionof vibration amplitudes is explained by the TMD operation asfollows: theTMD frequency, which wastunednear thefirst natural

frequencyof the structure, and their appropriate location on it (at apoint of greatest amplitudein thefirstvibration mode shape)causetheaccelerationof thesteel mobile masses of theTMDs, generatinginertia forces that are in opposition to the inertia forces producedby the external action on the structure.

Figs. 1217 show comparisons between the measured uncon-trolled and controlled dynamic responses (in both the time andfrequency domains) of the structure for Test A to Test C given interms of the vertical accelerations at the deck center.

It can be noticed in the experimental frequency responses(Figs. 1517) that the acceleration amplitudes of the first vibrationmode (7.57 Hz) show large reductions (4784%) in the controlledstructure compared to the amplitudes of the uncontrolledstructure.

In Figs. 1517, the synchronized control devices (TMDs)

introduced an additional degree of freedom into the structuralsystemthat resulted in twonew eigenfrequencies of the controlledsystem around the first vibration frequency (7.57 Hz) of theuncontrolled structure: one slightly smaller (fTMD = 7.32 Hz) andone slightly higher (f1 = 7.81 Hz).

The greatest reductions in vibration amplitudes were found inTest A for only one person walking, which can be explained bythe quasi-resonance phenomena produced by a component of theexcitation force (the fourth harmonic of the walking load; 4 1.87Hz = 7.48 Hz) on the first vibration mode of the uncontrolledstructure (7.51 Hz for the locked TMDs), as shown in Figs. 12 and15(a). These results demonstrate that the efficiency of the passivecontrol system is greater when one harmonic component of thewalking loading has a frequency close to the frequency of one of

thestructural vibrationmodesto which theTMDs aretuned, whichdominates the dynamic response of the structure.


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Fig. 11. Structure and TMD time responses for Test A. (a) TMDs locked. (b) TMDs unlocked.

Fig. 12. Uncontrolled and controlled time responses of the structure for Test A. (a) Structure responses. (b) Enlargement of the time response: resonance of the fourth

harmonic of the walking force with first vibration mode frequency.

Fig. 13. Time response for Test B.

In Fig. 15(b), the uncontrolled and the controlled responses inTest A have close peak amplitudes in the first three harmonicsof the walking force in a range of frequencies far from resonanceto the vibrational frequencies of the structure. This closenessdemonstrates that both the uncontrolled and the controlled testswere performed for walking excitations with very similar dynamiccharacteristics, which validates all the correlations made betweenthe controlled and uncontrolled measured responses.

As compared to the results of Test A, those obtained in Tests Band C show, for the controlled structure, smaller but yet importantreductions of the response amplitudes in the first vibration mode.This is explained as follows: the response amplitude of thestructure at any instant of time is composed of the amplitudes

of multiple vibration modes in varied frequencies. On the otherhand, both TMDs were tuned to the first mode frequency. As a

Fig. 14. Time response for Test C.

consequence, no reduction of response amplitudes is expected forother higher frequency vibration modes. In Tests B and C, peoplewalked without synchronismand at walking frequency ratios apartfrom resonance with the fundamental vibration mode as occurredin Test A. That is why the observed reductions are greater in TestA, and that is why the observed reductions of vibration amplitudesin the non-filtered acceleration response signals are very differentfrom the root mean square (rms) filtered acceleration responsesin Tests B and C. It should be emphasized that the evaluation ofthe efficiency of the TMDs was made with the rms values of thesignalfilteredto a short bandwidth aroundthe first vibration modefrequency.

An interesting fact is that the amplitudes of vibrations for one

person walking in Test A reached values close to that of six personswalking side by side in Test B and greater values than for six


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Fig. 15. Frequency response for Test A. (a) Frequency response. (b) Enlargement of the frequency response.

Fig. 16. Frequency response for Test B.

Fig. 17. Frequency response for Test C.

persons walking randomly in Test C. This is because the responseamplitudes depend mainly on the closeness of the excitationfrequency to a natural vibration frequency of the structure, in thiscase associated with its fundamental vibration mode. In Test A, thefourth harmonic of the average walking frequency (4 1.87 Hz =7.48 Hz) is very close to the fundamental frequency (7.51 Hz) ofthe uncontrolled structure; this closeness is not attained in Test B(4 1.77 Hz = 7.08 Hz) and in Test C (4 1.74 Hz = 6.96 Hz).

7.1. Efficiency evaluation of the MSDA system (composed of a pair ofsynchronized TMDs)

Table 3 presents the ratios between the controlled anduncontrolled vertical acceleration amplitudes for both the time

and frequency (rms) responses filtered to the first vibration modeof the composite floor deck structure. It can be observed that

Table 3Reductions in rms vertical acceleration amplitudes (av) in the first vibration mode.

Test (Controlled av)/(Uncontrolled av)

Time re sponse ( %) Fr eq uen cy re spons e (%)

A 81 84

B 58 70

C 32 47

the reductions in vibration amplitudes for the first mode variedfrom 32% to 81% in time responses and 47% to 84% in frequencyresponses.

The reductions in vibration amplitudes due to the installationof the passive control devices were the greatest for Test A (up to

84% in frequency responses), for which only one person walked inquasi-resonance with the first vibration mode of the structure.


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Table 4

Subjective classification of the vibrations given by the volunteers.

Person Classification

Uncontrolled structure Controlled structure

01 Uncomfortable Perceptible

02 Uncomfortable Imperceptible

03 Intolerable Perceptible

04 Intolerable Uncomfortable

05 Intolerable Perceptible06 Uncomfortable Perceptible

In Test B, where six persons walked side by side in quasi-synchronism, the responses were again largely dominated by thefirst mode, but less so than in Test A. Even so, the reductions invibration amplitudes were still very large (up to 70% in frequencyresponses), although smaller than in Test A.

Finally, in Test C, where six persons walked randomly (withoutsynchronismin their steps), the reductions in vibration amplitudeswere still substantial (up to 47% in frequency responses), althoughless than in the previous tests.

7.2. Human perception of the vibrations

The volunteers for the tests were asked how they felt, andthey classified the vibrations in the structure. After test C, onevolunteer remained standing at the center of the slab while theother five volunteers walked around. The response amplitudes inthe perception tests differ slightly from those in Test C for whichall six volunteers walked around. The variation of accelerationamplitudes in these two types of test was found to be only 5%.

The volunteers were not informed when the control systemwas in operation. The options for classification were as follows:(i) imperceptible: the volunteer reported that he could not feelany vibrations; (ii) perceptible: the volunteer reported that hecould feel vibrations, butthey were notdisturbing; (iii) uncomfort-able: the volunteer reported that he could feel vibrations, and theywere annoying; and(iv) intolerable: the volunteer reported that he

could feel vibrations, and they were unbearable.Table 4 summarizes the results. All of the volunteers changed

their opinion positively on the vibration level when the TMDswere in full operation as compared to when the TMDs were locked(i.e., out of operation). When the TMDs were locked, half of thevolunteers felt uncomfortable, andthe other half could nottoleratethe vibrations. When the TMDs were released, four of the sixvolunteers classified the vibrations as only perceptible, one ofthe other two classified them as imperceptible, and only one stillclassifiedthem as uncomfortable.Moreover, better results couldbeachieved with extra units of the same TMD, that is, by increasingthe ratio between the TMD mass and the structural modal mass.

As human perception is the best way to evaluate vibrationattenuation, one can state that the passive control system isan attractive, cost-effective, and successful means to mitigateundesirable vibrations in floor deck structures.

Table 5 presents the application of human perception criteriafrom ISO 2631-2 [34] and acceptance criteria from SCI [35] andAISC [2] to the maximum amplitudes of vertical accelerationsin the controlled and uncontrolled structure. The values ofamplitudes are related to the time response signals obtained fromthe experimental tests and frequency band filtered to the firstvibration mode of the composite floor deck structure. In Table 5,the prescribed ISO 2631-2 [34] limit values for acceleration relatedto continuous vibrations were chosen because people walkedcontinuously during the tests.

Forthe uncontrolledstructure, it canbe noted in Table 5 that themeasured acceleration amplitudes are excessive according to allthe guidelines when applied to people at rest in conference rooms

and offices. For shopping malls, the accelerations measured in TestA are found excessive according to AISC [2].

Table 5

Comparison between rms values of measured accelerations and recommended

acceptance acceleration values.

Measured acceleration (mm/s2) Test

A B C

Uncontrolled structure 161 77 72

Controlled structure 31 32 49

Acceleration valuesSource Destination alimit (mm/s2)

ISO 2631-2 [34] criteriaOffice 20

Conference room 40

SCI [35] criteria

Special office 20

General office 40

Busy office 60

AISC [2] criteriaOffice 35

Shopping mall 106

For the controlledstructure, the measured vibration amplitudes(Table 5), although substantially reduced, do not comply fully withthe acceptance values related to the guidelines. The accelerationamplitudes measured in Tests A and B are lower than theacceptance values forall destinations other than offices andspecialoffices according, respectively, to ISO 2631-2 [34] and SCI [35]criteria. Conversely, the measured amplitudes in Test C are higherthan the acceptance values for all destinations other than busyoffices and shopping malls according, respectively, to SCI [35] andAISC [2] criteria.

8. Conclusions

The problem of excessive vibration amplitudes produced byhumans walking on lightweight large span composite floor deckstructures and the effectiveness of simple mechanical synchro-nized dynamic control devices tuned to a frequency close to thestructures fundamental frequency were investigated through ex-perimental measurements and human perception criteria, and also

in the light of the acceptance criteria given in design guides.The results show that, for any of the applied human loads, thepassive control system provides significant reductions in vibrationamplitudes, considerably improving the dynamic performance ofthe structure and user comfort. It is also worth noting that themechanical control devices had a total mobile mass equal to only0.5% of the modal mass related to the first vibration mode of thestructure. As such, these low cost and low maintenance passivecontrol mechanical devices can be proposed for the rational designof smart structures of low damping lightweight large span floordecks of buildings intended for residential, commercial, or publicuse.

Acknowledgments

We thank the CAPES (The Brazilian Research Council forEnhancement of Faculty Members) and the Instituto COPPE ofthe Universidade Federal do Rio de Janeiro for financial support.Special thanks go to the volunteers for the walking tests and thetechnicians of COPPEs laboratory of structures, whomade thetestspossible.

Appendix. Supplementary data

Supplementary material related to this article can be foundonline at doi:10.1016/j.engstruct.2011.04.021.

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