Effects of Inter-Subject Variability and Vibration Magnitude on Vibration Transmission to Head...

Effects of Inter-Subject Variability and VibrationMagnitude on Vibration Transmission to Headduring Exposure to Whole-Body Vertical VibrationMilk Desta, V. Huzur Saran and Suraj P. HarshaVehicle Dynamics Lab., Mechanical and Industrial Engineering DepartmentIndian Institute of Technology Roorkee, India

In this paper, the effect of inter-subject and intra-subject variabilities on transmission of vibration through seatedhuman subjects is discussed using experimental results. The experimental study targeted three representative pos-tures (backrest, erect, and forward lean on table) while performing sedentary activities and under three magnitudes(0.4, 0.8, 1.2 m/s2 rms) of vertical vibration. The frequency range considered is 1 Hz–20 Hz as representative ofthose likely prevailing in wide range of vehicles. The data sets are investigated in terms of STH (seat-to-head) andBTH (back support-to-head) transmissibilities and phase differences, and respective coherences under the magni-tudes and postures undertaken. In addition to determining the effect of different frequencies, subjective readingswere collected at vertical backrest support postures at representative frequencies using the Borg CR 10 comfortscale. The responses show significant variations in transmissibility and phase among all of the subjects. In all pos-tures, the mean STH transmissibility increases with increasing vibration magnitude at body resonance frequency,which lies approximately between 4.5 Hz and 6 Hz. Resonance in STH transmissibility of erect and forward leanon table posture visibly tends to shift to a lower frequency with increasing vibration magnitude. The subjectivereading obtained, in terms of discomfort level, match with experimental data sets and provides evidence that humanbody resonance frequency or discomfort zone is around 5 Hz. Therefore, it might be concluded that the inclusionof vibration magnitude, posture, and inter-subject variabilities in the prediction of seat biodynamic response is es-sential. The development of biodynamic models and design of seat should include the variation of STH and BTHtransmissibility and phase in different possible postures under different vibration magnitude.

1. INTRODUCTION

The study of human response to vibration in a sitting pos-ture is very important to reduce the effects of vibration to hu-man health, activity, and performance. Research on the vibra-tion effects of seated subjects has indicated that the side effectscould be very harmful and in some cases lead to permanent in-juries.1 Some results have suggested that lower back pain is aresult of continuous exposure to vibration,2 and occurs morefrequently among vehicle drivers than in representative controlgroups.3 As traveling increases, the driver is more exposedto vibration that originates primarily from the interaction be-tween the road profile and the vehicle. Therefore, in recentyears people have become more concerned with vibration andare seeking a more comfortable environment. Indeed, a seatwith optimum dynamic properties is one that minimizes theunwanted vibration responses of humans in the relevant vibra-tion environment. The three important factors which determinethe seat dynamic efficiency are vibration environment, seat dy-namic response, and response of the human body. To achievebetter and comfortable vibration condition, that is, to reducevibration to massage movement, there is a pressing need tostudy and identify whole-body vibration discomfort zone invehicle seats. By doing so, criteria for better ride comfort canbe determined so that seat and vehicle systems are designedoptimally.

The study of human response to vibration has been the topicof interest over the years and a number experimental and ana-

lytical studies were established in different vibration environ-ments. The transmissibility of the human body reflects the var-ious biodynamic responses of the body, particularly those be-tween the point at which the vibration enters the body (e.g., ona seat) and the point at which the vibration is measured on thebody (e.g., on the head). The transmissibility, therefore, givessome information on the biodynamic system. It has sometimesbeen assumed that the resonances reflected in, for example,the STH transmissibility indicate frequencies at which injury,discomfort, or interference with activities are most likely tohappen.

The effect of a sitting posture on the apparent mass of a sub-ject (i.e., the ratio of the force to the acceleration as a func-tion of vibration frequency) has previously been reported.4–6

Although Miwa4 has stated that “no clear difference was reck-oned to exist” between sitting relaxed or erect, his data showa small effect that is consistent with results from Fairley andGriffin.5 Kitazaki and Griffin6 suggest that the resonance fre-quency of the human body is higher in a more erect sitting pos-ture. Fairley and Griffin5 have investigated eight subjects whosat in four postures (normal, erect, backrest contact, and tense)and generally exhibited higher resonance frequencies for theerect and tense postures compared to the normal posture. Ki-tazaki and Griffin6 have shown an increase in the mean reso-nance frequency from 4.4 Hz to 5.2 Hz when eight subjects satin slouched and erect postures. The change can be describedas a stiffening effect with erect postures.

The literature shows that some variables can have large ef-

88 (pp. 88–97) International Journal of Acoustics and Vibration, Vol. 16, No. 2, 2011

M. Desta, et al.: EFFECTS OF INTER-SUBJECT VARIABILITY AND VIBRATION MAGNITUDE ON VIBRATION TRANSMISSION. . .

fects on STH transmissibility; two such examples include sit-ting posture7 and contact with the seat backrest.8, 9 Both bodyposture and muscle tension are reported to affect human trans-missibility.7, 10, 11 Some studies have shown that vibration atone frequency on the seat can result in motion at other fre-quencies at the head.12, 13 In some studies the multiple axishead motion that occurs as a result of single axis seat vibra-tion has also been measured.8, 9, 14–16 Studies of the effects ofposture on body transmissibility have mostly been restrictedto the effects of using a backrest and have not considered vi-bration magnitude as a variable.17 Paddan and Griffin,18 havereviewed 14 studies with lateral vibration, 10 studies with foreand aft seat vibration and 46 studies with vertical seat vibra-tion and different vibration magnitude and frequency. The re-view has considered different sitting postures, various type ofsubjects, and various locations for measuring vibration on thehead, and it has concluded that the variability obtained withinstudies (e.g., due to inter-subject variability and intra-subjectvariability) and the variability between studies (e.g., due to dif-ferent experimental condition or measurement locations) sug-gest that factors other than the vibration frequency have largeeffects on STH transmissibility. The study insists that the ef-fect of vibration frequency is only one of the several factorswhich influence the transmissibility of vibration to the head.Mansfield and Griffin19 have studied the effect of variationsin posture and vibration magnitude on apparent mass and seat-to-pelvis pitch transmissibility under vertical random vibrationover the frequency range 1.0 Hz–20 Hz and have found that theresonance frequencies in the apparent mass and transmissibil-ity decreased with increased vibration magnitude. Panjabi etal.20 have studied the vibration study of the spinal column vi-brations.

In any case, the human sensitivity to vibration depends onvarious extrinsic variables, which are variables that express thestate of the dynamic system or the evolution of phenomenon,like vibration magnitude and frequency, direction of the move-ment, exposure time, etc. It also depends on intrinsic variables,which refer to the human subject (e.g., age, gender, physicalcharacteristics, health conditions, posture of the body, etc.).So, the study of human response to vibration implies identify-ing the direct or indirect effect of the above parameters. There-fore, in any research work related to human vibration the abovepoints are the main foundations and targets.

As discussed above, although a number of experimentalstudies have been investigated to characterize the effect ofinter-subject and intra-subject variabilities on transmission ofvibration through seated human subjects, none of the studieshave attempted to consider the most widely used postures invehicles while performing sedentary activities. This study tar-geted three representative postures (backrest, erect, and for-ward lean on table) under three magnitudes of vibration (0.4,0.8, 1.2 m/s2 rms). The experiments are taken for frequencyrange of 1 Hz–20 Hz, which is considered as representative ofthose likely prevailing in wide range of vehicles. Using an ex-perimental setup, STH and BTH transmissibilities and phasedifference, as well as respective coherence were collected un-der the magnitudes and postures discussed above. In addi-tion, to determining the effect of frequency, subjective read-ings were collected at backrest support with representative si-

Figure 1. Schematic diagram of vibration simulator and accessories.

nusoidal vibration frequencies. With these response functions,the effects of representative variables are investigated.

2. EXPERIMENTAL STUDY

In this study, experimental works were performed to providesupporting information concerning the effect of inter-subjectvariabilities, vibration magnitudes, vibration frequencies, andpostures on dynamic response (transmissibility and phase) ofthe human body under sinusoidal, vertical whole-body vibra-tion. In addition, it was conducted to provide experimentaldata sets to validate the models. Besides dynamic responses,subjective study was conducted to investigate the effect of fre-quencies on comfort.

2.1. Experimental SetupThe study was conducted on the vibration simulator in nat-

ural laboratory environment, developed as a mockup of a rail-way vehicle, in Vehicle Dynamics Laboratory, IIT Roorkee,India. It consisted of a platform of 2 m � 2 m size made upof stainless steel corrugated sheets, on which a table and tworigid chairs have been securely fixed (see, Fig. 1). The backrestof the chair was rigid, flat, and vertical. Neither the seat, thebackrest, nor the table had any resonances within the frequencyrange studied (up to 20 Hz) in any of the three axes. Threeelectro-dynamic vibration shakers were used to provide vibra-tion stimuli simultaneously to the platform in three axes; lon-gitudinal (x-axis), lateral (y-axis) and vertical (z-axis). Eachvibration exciter had a force capacity of 1,000 N with a strokelength of 25 mm (peak-to-peak). For simplicity and safetyreasons the internal positioning accelerometers of the shak-ers were continuously used for motion feedback. In this studythe subjects were exposed to sinusoidal vertical whole-bodyvibration by vertical electro-dynamics exciter. The tri-axialaccelerometers (KISTLER 8393B10) were placed at seat-lap,

International Journal of Acoustics and Vibration, Vol. 16, No. 2, 2011 89


a. Erect b. Vertical backrest c. Forward lean on table

Figure 2. The three sitting postures considered in this study.

back, and head positions to measure the acceleration at the re-spective points. The vibration signals from the accelerometerswere amplified using three ICP R Sensor Signal Conditioner(480B21) three channels, amplifiers. The amplified signalswere conveyed to the LabVIEW Signal Express software via adata acquisition card (NI 6218). The test subjects were seatedon the chairs rigidly mounted on the platform of Vibration Sim-ulator such that these are excited with the same frequency asthe platform, up to 100 Hz.

2.2. Experimental DesignThe experiments were performed to measure vertical vibra-

tion transmitted to the occupants head in three representativepostures under three magnitudes of vibration in vertical di-rection. Twelve healthy male subjects with an average age of24 years, average weight of 72 kg and average height of 1.72 mtook part in experiment. The subjects had no prior known his-tory of musculo-skeletal system disorders. The physical char-acteristics of the test subjects are summarized in Table 1. Priorto the tests, each subject was informed of the purpose of thestudy, the experimental set-up, and the effect of inconsistencyin desired posture and orientation. Each subject was asked towear a lightweight helmet band and adjust its tension to en-sure a tight but comfortable fit. The experimenter made thenecessary adjustments to ensure appropriate orientation of thehead accelerometer. Each subject was asked to sit comfortablywith average thigh contact with upper legs comfortably sup-ported on the seat pan and lower legs oriented vertically withfeet on the vibrating platform, assuming the desired posture.Each subject was further asked to maintain a steady head posi-tion while the data were being collected. Meanwhile, the sub-ject’s posture during each trial and each specific posture wasvisually checked by the experimenter to ensure consistency.

Each subject was exposed to three sinusoidal vibration mag-nitudes over the frequency range 1 Hz to 20 Hz for 14 repre-sentative frequencies (Table 1) in three different postures. Thethree postures considered in this study were intended to repre-sent the postures of seated human body performing sedentaryactivities while traveling (as shown in Fig. 2):

a. Vertical backrest posture with hands placed on lap,

b. Sitting erect with hands placed on lap,

c. Sitting forward lean on table.

Table 1. Anthropometric data of test subjects.

Test Subjects Total weight (kg) Total height (cm) AgeS1 57 169 20S2 62 160 20S3 68 172 19S4 81 179 24S5 72 175 28S6 67 165 26S7 68 166 21S8 78 176 26S9 73 174 20S10 67 180 20S11 93 182 37S12 72 170 26Average 72 172 24

In each sitting posture, the 12 subjects were exposed to threevibration magnitudes (0.4, 0.8, and 1.2 m/s2 rms). The presen-tation of the three postures and the three vibration magnitudeswas balanced across subjects. The duration of each exposurelasted 60 s.

2.3. Data AcquisitionData acquisition involves gathering signals from measure-

ment sources and digitizing the signal for storage, analysis,and presentation on a computer. For this study, tri-axial ac-celerometers (KISTLER 8393B10) were mounted at the seat,backrest support, and head to measure accelerations in the ver-tical (z) direction. The seat pad tri-axial accelerometers weresecurely attached to the seat and back support at the properplaces to measure the seat and back support acceleration, re-spectively. The accelerometer used to measure head accel-eration was securely attached at the top of very light plastichelmet. Signals from the accelerometers were amplified us-ing three (fore head, back support, and the head) three-channellightweight ICP R sensor signal conditioner (480B21) with thegain of x100 for each channel. Then the signals were conveyedto the LabVIEW Signal Express software via a data acquisitioncard (NI USB-6218) with a capacity of 250 kS/s single-channelsampling rate.

2.4. Data AnalysisThe data acquired were reconditioned in time domain and

transformed to frequency domain. The transformed data in-cluded a complex function, the real part, that is, the magnitude(transmissibility), and the imaginary part (phase angle) and aremeasured for each subject who undertook the experiment. Thevertical STH transmissibility was evaluated as the complex ra-tio between the seat acceleration and the vertical head accelera-tion. Likewise, the BTH transmissibility (for backrest postureonly) was evaluated as a complex ratio between the verticalback support acceleration and the vertical head acceleration,such that

TSTH(f) =ahead(f)

aseat(f)TBTH(f) =

ahead(f)

aback(f); (1)

where TSTH(f) is STH transmissibility, ahead(f) is head ac-celeration, aseat(f), and aback(f) is seat and back support ac-celeration, respectively.

The STH, BTH transmissibilities, STH, BTH phase anglesand respective coherence were recorded for each frequency

90 International Journal of Acoustics and Vibration, Vol. 16, No. 2, 2011


Figure 3. Seat-to-head vertical transmissibility, phase for 12 subjects exposedto vertical vibration at 1.2 m/s2 rms in erect posture.

and magnitude undertaken in the experiment. The measureddata of each subjects were collected in Microsoft Excel to cal-culate the lower limit, mean (target values), and upper limit oftransmissibilities, phases, and coherences.

2.5. ResultsThe main factors that determine the vibration discomfort

of the subject exposed to whole-body vibration are vibrationmagnitude, frequency, direction, input position, duration, someintra-subject variability (changes in a person over time), andinter-subject variability (differences between people). The re-sults of the experimental study regarding the above factors willbe discussed as follows.

2.5.1. Effect of Inter-Subject Variability on STHTransmissibility

One of the very important considerations in human responseto vibration is the large differences that occur between sub-jects, or inter-subject variability. In this study, transmissibilityand phase of twelve male subjects maintaining three differentpostures under 1.2 m/s2 rms sinusoidal excitation are presentedin the frequency range of 1 Hz–20 Hz. The analysis is limitedto 1 Hz–20 Hz frequency range since vehicle vibration exci-tation is predominant within this particular range for severalcategories of heavy vehicles, and the main body resonance isknown to occur in this range.

Although the mean subject mass is evaluated as 72 kg, thetest subjects’ characteristics that appear in Table 1 indicateconsiderable variations in the subjects mass and stature. Thetotal body mass ranges from 57 kg for subject S1 to 93 kg forsubject S11; effective mass of the subjects probably has somerelation with the stature of the individuals. In all postures, thepeak transmissibility magnitude occurs between 4.5 and 6 Hzfrequency ranges for all the subjects. The results reveal a cer-tain dependency of the whole-body resonance frequency on thesubject mass and stature (see, Figs. 3, 4, 5).

Figure 4. Seat-to-head vertical transmissibility, phase for 12 subjects exposedto vertical vibration at 1.2 m/s2 rms in backrest posture.

In erect posture the peak transmissibility magnitude occursat about same frequency (5 Hz) for all subjects, and the tallestand heaviest subject of the group shows maximum value ofSTH transmissibility. In this posture the individual variationin both transmissibility and phase difference increase beyondresonance frequency, (see Fig. 4).

In vertical backrest posture, though, there are clear varia-tions between subjects, there are no clear indications of a sub-ject’s variability in the resonance frequency zone. In this pos-ture, lightweight subjects such as S1 (57 kg) show a distinctlyhigher transmissibility magnitude than heavier subjects suchas S11 (93 kg) and S4 (81 kg), for which the transmissibil-ity magnitude is considerably lesser, particularly at about 8 Hzfrequency (see, Fig. 5).

In the forward lean on table posture, lightweight subjects(defined as having a below-average weight) have resonancefrequency at about 5 Hz. Subjects with weights that are aboveaverage have resonance frequencies at about 5.5 Hz (see Fig.5). Subject S11, the tallest and heaviest subject of the group,however, presents an exception with regard to transmissibilityand phase behavior in the frequency range of 6 Hz–12.5 Hz.There are indications that subjects with heavy weights andlarge statures have more transmissibility magnitude and lessphase difference in this frequency range.

The results from all postures show that the transmissibilitymagnitude increases with increasing frequency up to the mainbody resonance frequency, near about 5 Hz. The magnitudeof transmissibility tends to decrease at frequencies higher thanthe resonance frequency. For most subjects, phase response in-creases for lower frequencies, though there is a slight decreaseat the resonance frequency, followed by a high slope increaseup to 10 Hz, beyond which it tends to stabilize. Significantvariations in transmissibility and phase are observed amongthe subjects. High relative variation in STH transmissibilityis observed at a main body resonance frequency for forwardlean on table posture at approximately 0.8. In erect and ver-



Figure 5. Seat-to-head vertical transmissibility, phase for 12 subjects exposedto vertical vibration at 1.2 m/s2 rms in forward lean on table posture.

tical backrest postures, the difference between maximum andminimum STH transmissibility magnitudes at resonance fre-quencies reaches about 0.65 and 0.55, respectively.

2.5.2. Effect of Vibration Magnitude on STHTransmissibility

Figures 6, 7, and 8 compare mean vertical STH transmis-sibility responses for twelve subjects while exposed to threeexcitation levels (0.4, 0.8, 1.2 m/s2 rms) under three postures(erect, vertical backrest, forward lean on table), respectively.The results distinctly reveal that resonance in STH transmissi-bility of erect and forward lean on table postures visibly tendsto shift to a lower frequency with increasing vibration mag-nitude. This suggests that in erect and forward lean on tablepostures, the upper body part exhibits more of a softening ten-dency than when it is under higher magnitudes of vertical vi-bration.

The STH transmissibility magnitude results suggest that themean body resonance for the erect and forward lean on tablepostures decrease by approximately 0.5 Hz (from 5.5 Hz to5 Hz) and 0.4 Hz (from 5.65 Hz to 5.25 Hz), respectively,when vertical excitation magnitude is increased from 0.4 to1.2 m/s2 rms, as shown in Figs. 6 and 8. Similarly, the meanSTH transmissibility shows that body resonance frequency ofvertical backrest posture also shifts, but only by a very smallamount (see Fig. 7).

In all postures, mean STH transmissibility increases withincreasing vibration magnitude at body resonance frequenciesand lie between approximately 4.5 Hz and 6 Hz. For the fre-quency range above the body resonance zone, the erect posturemean STH transmissibility increases with increasing vibrationmagnitude (see Fig. 6). For vertical backrest posture, the meanSTH transmissibility is higher for lower magnitudes of vibra-tion in the frequency range of 6 Hz to 12 Hz; on the other handthe vertical backrest posture exhibits higher STH transmissi-bility for a higher magnitude, above a frequency 12 Hz (see,

Figure 6. Mean STH transmissibility for 12 subjects exposed to vertical sinu-soidal vibration at 0.4, 0.8 and 1.2 m/s2 rms in erect sitting posture.

Figure 7. Mean STH transmissibility for 12 subjects exposed to vertical sinu-soidal vibration at 0.4, 0.8 and 1.2 m/s2 rms in vertical backrest posture.

Figure 8. Mean STH transmissibility for 12 subjects exposed to vertical sinu-soidal vibration at 0.4, 0.8 and 1.2 m/s2 rms in forward lean on table sittingposture.

Fig. 7). For the forward lean on table posture, the mean STHtransmissibility in the frequency range of 6 Hz to 9 Hz is higherfor a lower magnitude of vibration and the vibration magnitudehas a very small effect above 9 Hz (see Fig. 8). In general, theeffect of vibration magnitude on the mean STH transmissibil-ity in erect posture is higher than the other postures at the bodyresonance frequencies. The result in the vertical backrest pos-ture reveals that the mean STH transmissibility variation due tovibration magnitude shows a maximum in the frequency rangeof 6 Hz to 10 Hz.

2.5.3. Effect of Vibration Magnitude on BTHTransmissibility

When a subject is in a backrest sitting posture, the lower partof the body is supported by the seat and the upper part of bodyis leaning on a back support. The backrest support contributesto a decrease in muscle tension and maintains a relatively re-



Figure 9. Mean BTH transmissibility for 12 subjects exposed to vertical sinu-soidal vibration at 0.4, 0.8 and 1.2 m/s2 rms in backrest sitting posture.

laxed sitting posture. There is also a significant amount of vi-bration input through the backrest. Thus, it is naturally rea-sonable to include the effect of this source of vibration to thebody. To investigate this effect, BTH transmissibility was de-termined for twelve subjects. The mean BTH transmissibilityreveals that the peak value frequency decreases as magnitudeincreases. The peak value frequency under vibration magni-tude of 0.4 m/s2 rms laid at 5 Hz and of 0.8, 1.2 m/s2 rms at4.5, 4 Hz respectively (see, Fig. 9).

2.5.4. Effect of Posture on STH Transmissibility

Figures 10, 11, and 12 compare the mean vertical STH trans-missibility magnitude responses of twelve subjects exposed toexcitation level of 0.4, 0.8, 1.2 m/s2 rms, respectively, mea-sured with three different postures (erect, vertical backrest, andforward lean on table). It is clearly noticeable that the differ-ence between the mean STH transmissibility of the three pos-tures decreases and the body resonance frequency also becomecloser to each other as the magnitude of vibration increases.

For all the three postures, the mean STH transmissibility in-creases at resonance frequency with increasing vibration mag-nitude, as is seen in Figs. 10, 11, and 12. It is observed thatthe mean STH transmissibilities of all three postures steadilyincrease up to a certain resonance frequency and generally de-crease for higher frequencies. There is a decrease in the res-onance frequency with an increase in vibration magnitude forerect and leaning on table postures. The lowest transmissibil-ity occurrs with the backrest posture and highest transmissi-bility occurrs in erect posture under all magnitudes of vibra-tion undertaken at resonance frequency. The peak value fre-quency (resonance frequency) for backrest posture is lesserthan the peak value frequency of other postures. The peakvalue frequency for erect and leaning forward on table pos-tures decreases as vibration magnitude increases, while thereis no clear indication for backrest posture. It is also observedthat the lean forward on table posture shows more mean STHtransmissibility in the frequency range of 6 Hz to 9 Hz and thebackrest posture exhibits more STH transmissibility for higherfrequencies.

2.5.5. Coherence

The coherence is the extent of correlation between an inputand an output signal.21 If the vibration at the output is perfectlycorrelated to the vibration at the input, then the coherence hasa value of 1. Any nonlinearities or errors in the signals (e.g.,

Figure 10. Mean STH transmissibility for the three postures exposed to verti-cal sinusoidal vibration of magnitude 0.4 m/s2 rms.



electrical noise in the data acquisition system or interference)will reduce the coherence. In this work, coherence in all pos-tures and magnitudes is recorded for all subjects undertaken inthe experiment. The average coherence of 12 subjects over thefrequency range 1 Hz–20 Hz are drawn for different magni-tudes of vibration (0.4, 0.8, 1.2 m/s2 rms) in different postures(erect, backrest, forward lean on table), as is shown in Figs. 13,14, and 15.

The coherence values in the laboratory measurement shouldbe near perfect for human vibration applications (i.e., > 0:95at all frequencies of interest).2 In an erect posture, the coher-ence values are > 0:95 for the frequency range from 1 Hz–18 Hz, and above that frequency, the values exceed 0.95 forhigh magnitudes of vibration (see, Fig. 13). In the backrestposture, coherence values are > 0:95 for all frequency rangesconsidered. Therefore, the coherence is high in the backrest



Figure 13. Average coherence for erect posture under vertical sinusoidal vi-bration of 0.4, 0.8 and 1.2 m/s2 rms.

Figure 14. Average coherence for backrest posture under vertical sinusoidalvibration of 0.4, 0.8 and 1.2 m/s2 rms.

Figure 15. Average coherence for forward lean on table posture under verticalsinusoidal vibration of 0.4, 0.8 and 1.2 m/s2 rms.

posture. Coherence follows the same pattern beyond 6 Hz; thevalues decrease as the magnitude of vibration increases. Rel-atively low coherence values are observed in the forward leanon table posture. In this posture the coherence values decreaseas the frequency increases.

In general, the coherences reaches reasonable values in thepostures considered. However, in some frequency ranges orvalues the coherence drops. This indicates that the signalsmeasured at the seat and head are less well correlated withinthis range of frequencies. That might often arise from noise,unexpected motion of subjects, and lack of vibration energy atthat frequency.

2.5.6. Head Helmet Relation

There are two popular methods to measure head vibration:bite bar (measured at mouth using accelerometer mountedon bite bar/plate) and helmet (collected from accelerometermounted on helmet). Many studies have been used a bite

Figure 16. Mean head helmet transmissibility and phase difference under1.2 m/s2 rms magnitude of vibration.

bar,22–25 and a helmet has been also used in many studies.26–29

In this study a helmet is used because it is the easiest methodto measure head acceleration.

In order to determine STH and BTH transmissibility func-tions, accelerations were measured at the seat-buttock inter-face, back and back support interface, and on the head. Headvibration was measured using the accelerometer mounted on aplastic helmet. Since there is relative motion between the headand the helmet, it is necessary to analyze the error that wasinduced. It was analyzed by the use of averaged plots of thetransmissibility transfer function of the head helmet system, asshown in Fig. 16. Acceleration data of the head helmet system,also given in Fig. 16, were measured under sinusoidal excita-tion on one subject, repeated five times, and then averaged.The subject is a member of the tested group. It is found thatabove 10 Hz, the errors increase and the maximum errors oc-cur at approximately 20 Hz of resonance frequency because, atthat point, the magnitude of transmissibility are highest. Thisshould be taken into consideration while analyzing the data inthe frequency domain. To be more specific, frequencies above10 Hz will not be desirable to consider for further analyses.

2.5.7. Subjective Study

In addition to data acquired from transducers, the subjectswere asked to give subjective readings under different vibra-tion frequencies according to the Borg CR 10 comfort levelscale. The rating is modified, which is shown in Table 2.The subjective reading drawn against the frequency (as seenin Fig. 17) and the average opinion of all the subjects werefound.

In Fig. 17, the star points stand for data points of each sub-ject and the bold line indicates the average value of all thereadings. The average values reveal that the human body feelsmore discomfort in a frequency range from 4 Hz to 5.5 Hz,or according to the Borg CR 10 scale, it is difficult to travel



Table 2. Borg CR 10 scale rating of perceived exertion.

Rating of Perceived Exertion: Borg CR 10 Scale0 Nothing at all Sitting in a chair relaxed0.3 - -0.5 Extremely Weak Just noticeable0.7 - -1 Very weak Slightly discomfort1.5 - -2 Weak Small discomfort2.5 - -3 Moderate Somewhat difficult but not especially hard,

it feels difficult to continue.4 - -5 Strong Very difficult to travel6 - -7 Very Strong Very difficult to travel and high pain

and discomfort8 - -9 Extremely strong Impossible to travel in this condition10 - -

Figure 17. Subjective reading of twelve subjects exposed to vertical sinusoidalwhole body vibration under 1.2 m/s2 rms magnitude in backrest posture. Thebold line is the average value of both subjects.

with this range of frequency under this magnitude (1.2 m/s2

rms) of vibration. Moreover, the subjective reading indicatesmore judgment variations for lower frequencies as comparedto higher.

3. DISCUSSION

Although a number of experimental studies have beeninvestigated to characterize the effect of inter-subject andintra-subject variabilities on transmission of vibration throughseated human subjects, none of the studies have attempted toconsider the most widely used postures in vehicles while per-forming sedentary activities. This study concentrated on threerepresentative postures under three magnitudes of vibration.These postures (backrest, erect, and forward lean on table) andmagnitudes (0.4, 0.8, 1.2 m/s2 rms) under a frequency rangeof 1 Hz–20 Hz are considered as representative of those thatlikely prevail in wide range of vehicles. With experimentalsetup discussed in this study, STH and BTH transmissibilities,phase differences, and respective coherence were collected un-der the magnitudes and postures discussed. In addition, to de-termine the effects of frequency, subjective readings were col-lected at backrest supports with representative frequencies asmentioned. With these response functions the effects of somerepresentative variables are investigated.

Inter-subject variability has found a large effect on both STHand BTH transmissibilities and phases under the prescribed

magnitudes and postures. The individual responses show thattransmissibilities and phases vary rapidly with change in fre-quency and have several peaks. These individual responsesdifference are observed in all postures, though the variationsare quite different in all postures. These individual responsedifferences are attributed to the individual physical and physio-logical difference. It is observed that subjects mass and stature(height) have great influence on transmissibilities and phasesof all postures.

Most experimental conclusion and biodynamic studies havedepended on average transmissibilities and phases that losethe individual differences and show slower changes with fre-quency and have fewer peaks. The process of averaging the in-dividual data to obtain a mean or median transmissibility curvefor one condition loses the individual response and masks thelarge range of inter-subject variability. The process of aver-aging data across studies results in a further loss of the differ-ences obtained with different subject groups or different exper-imental conditions. To some extent, these losses leave the finalaverage transmissibility with few useful applications such asmodeling. Certainly, from a scientific point of view, the formand causes of inter-subject variability are more interesting thanthe final average.

For simplification, the averages of 12 subjects has been de-termined to study the effect of vibration magnitude and postu-ral difference. It is generally observed that as magnitude in-creases, both STH and BTH transmissibilities increase at peakvalue frequency. These strengthen the hypothesis that statesthat as vibration magnitude increases the vibration transmis-sion also tends to increase. In other words, discomfort in-creases.

During travel, people may need to perform some sedentaryactivities in which some postures are usually practiced. In thisstudy, the three representative and general postures have beenconsidered. Upon selection of these postures with represen-tative magnitudes of vibration, STH and BTH transmissibili-ties and phases were considered to analyze the effect of vibra-tion magnitudes and postures. These response functions weremeasured and drawn against frequency and provide the gen-eral effect and resonance frequencies of the human body. TheSTH transmissibility variations observed in the erect posturewith different vibration magnitudes were less, as comparedto other postures over all frequency ranges. However, muchpeak value frequency deviation was observed in erect postures.Much variation was observed in the leaning forward on tableposture in a frequency range from 3 Hz to 8 Hz, and likewisehigh variation was observed in vertical back support posturedue to a magnitude change over the frequency range of 6 Hzto 10 Hz. The STH transmissibility difference between erectand back-on posture was relatively small at all magnitudes ofvibration, except at its highest difference around peak valuefrequency, and the difference with leaning forward on table in-creases with increase in vibration magnitude. The changes ofresonance frequency with magnitude and posture were signifi-cant for all measures of STH transmissibility. The high magni-tude of STH transmissibility lies between 4.5 Hz and 6 Hz, andit continues to decrease beyond 6 Hz. The reduction of STHtransmissibility above 6 Hz may be associated with posteriortilting of the pelvis, flattening of the lumbar curve, and incli-



nation or anterior tilting of the pelvis and forward inclinationof the whole back. In a frequency range of 6 Hz–8.5 Hz, thelean forward on table posture shows more STH transmissibil-ity relative to other postures that might be associated with ei-ther exposure of vibration through other sources, such as handand table interface or anterior tilting of the whole body. At aresonance frequency, STH transmissibility is less on the backposture, which might be linked to either change of the lumbarcurve and back relaxation or energy dissipation between theback and back support.

In all measurements, coherences exhibit reasonable value inthe postures and magnitude of the vibration considered. How-ever, in some frequency ranges or values the coherence drops.This indicates that the signals measured at the seat and headare less well correlated within this range of frequencies. Thatmight often arise from noise, unexpected motion of the subject,or a lack of vibration energy at that frequency.

The subjective reading conducted in this study pointed outthe frequency that makes the human body experience more dis-comfort and the variation between subjects perception. Almostall subjects feel more discomfort in the frequency range of4 Hz–5.5 Hz. In general, more variation in a subject’s per-ception was observed for low frequencies and small variationfor higher frequencies. It is observed that more variations wereobserved for low frequencies due to subject’s expectation.

4. CONCLUSION

It is apparent that vibration affects human health, perfor-mance, activities, and comfort. In biodynamic response stud-ies, experimental and analytical works are conducted to createcomfortable, luxurious, well-performing, and healthy environ-ments, which require a better understanding of human responseto vibration. In this study, three representative postures underthree magnitudes of vibration have been selected, and in totalnine conditions have been considered for experimental study.

All postures considered in this study have a firm relationwith our daily lives while traveling. In the study of the bio-dynamic response of seated human subjects, both posture andvibration magnitude have significant effects.

The study found determined the respective resonance fre-quency of three seated postures under three vibration magni-tudes, and it demonstrated that high-vibration STH transmissi-bility occurred in erect postures at all levels of vibration mag-nitude. It is also found that there was much difference in STHtransmissibility and phases between individuals who partici-pated in experimental work, and the tallest and heaviest subjectof the group was observed to show maximum value of STHtransmissibility in erect posture.

The results from all postures show that the transmissibilitymagnitude increases with increasing frequency up to the mainbody resonance frequency, which is about 5 Hz. The magni-tude of transmissibility tends to decrease at frequencies higherthan the resonance frequency. Resonance in STH transmissi-bility of erect and forward lean on table postures visibly tendsto shift to a lower frequency with increasing vibration mag-nitude. This suggests that in erect and forward lean on tablepostures the upper body part exhibits more of a softening ten-dency than under higher magnitudes of vertical vibration.

In all postures, the mean STH transmissibility increases withincreasing vibration magnitudes at body resonance frequenciesthat lie between approximately 4.5 Hz to 6 Hz. This frequencyzone is the most uncomfortable zone for the human body invehicle seat postures. The subjective reading obtained in termsof discomfort level match with experimental data sets. Bothprovide evidence that human body resonance frequency or dis-comfort zone is around 5 Hz. It might therefore be concludedthat the inclusion of vibration magnitude, posture, and inter-subject variabilities in the prediction of seat biodynamic re-sponse is essential. The development of biodynamic modelsand design of seat should include the variation of STH trans-missibility in different possible postures under different vibra-tion magnitude.

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