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Biodynamic response of the human body in the sitting position when subjected to vertical vibration
Journal of Sound and Vibration (1983) 90(3), 423-442
BIODYNAMIC SITTING
RESPONSE
POSITION
OF THE HUMAN
WHEN
SUBJECTED
BODY
IN THE
TO VERTICAL
VIBRATION? P. M. DONATI Laboratoire d’Energetique
AND C. BONTHOUX
et de Mkchanique Thkorique Appliquke, Institut National Polytechnique de Lorraine, 54000 Nancy, France
(Received 2 June 1982, and in revised form 8 January
19831
Previous studies of the location of those areas in which the sensation of vibration is perceived under whole body vertical vibration have underlined the predominance of the relative movement between thorax and pelvis. Experiments were designed to explore systematically the transmissibility between the pelvis and thorax. These were supplemented by measurements of mechanical impedance of the body and absorbed power. To determine the body impedance, a procedure was developed to remove the effect of the load platform itself. Fifteen subjects were presented first with a swept sinusoidal vibration, and then with a broad band random vibration, to see how the wave form of the motion might affect the mechanical response of the body. The results obtained for the seat to thorax transmissibility suggest that within the range of vertical vibration investigated (l-10 Hz, 1.6 m/s’ r.m.s.) the human body in the sitting position can be modelled by a linear system with one or two degrees of freedom according to the subject. Data from the impedance function, which is a more complete description of the response of the body as a mechanical system, lead to systems with one further degree of freedom.
1. INTRODUCTION Sensation perceived by the human body in the sitting position when subjected to vertical vibration is due partly to the important deformation and relative movement of organs and body segments. This observation led the International Standard committee (IS0 5982-1981/E) [l] to write “When considering the effects of shock and vibration on people, it is valuable to have an understanding of the mechanical characteristics of the body”. Indeed, visual observation shows that the human body does not vibrate like a pure mass. Different body parts can be animated with relative movement whose advent is a function of frequency, magnitude and axis of vibration. In particular, the analysis of the relative motion between thorax and pelvis illustrates clearly this observation (see Figure 1). Studies by Coermann [2], and by Wisner et al. [3] have shown that the human body when subjected to whole body vibration can be approximated by rigid masses (head, thorax, pelvis) joined together by systems like springs and dampers (ligaments, muscles, intervetebral discs) whose movements may be assessed with adequate instrument. This scientific approach is principally of interest for analyzing the motion of the body and deducing information on the way the transmission of vibration is effected between two “mechanically discrete” sub-groups. Thus Wisner et al. [3] and then Rowlands [4], with FThis study was conducted in the service “Acoustique, Vibration, Biodynamique” Rowe of the “Institut National I1.N.R.S.). 54500, Vandoeuvre
de Recherche et de S6curiti” les Nancy, France.
for prevention
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and diseases
423 0022-460X/83/190423
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424
P. M. DONATI
AND
C. BONTHOUX
Acceleration measured Seat
5 m/s2 [
IS
Thorax
Dlfference
Time -+
Figure 1. Section of chart record of the acceleration level measured on a subject’s thorax in the sitting position when subjected to a swept sinusoidal vertical stimulus (frequency band l-10 Hz; sweeping duration 10 s; r.m.s. level of the acceleration 1.6 m/s*).
the intention of studying the complete human system, have measured the acceleration transmitted to head, shoulders and thorax. However difficulties in developing efficient techniques of internal measurements make it a little unrealistic to assess the relative and absolute movement of internal body masses (organs) whose role is predominant in understanding how the human perceives the vibration and reacts to it. This shows the restrictions of this type of approach which, being too schematic, appears pertinent only as a description. Therefore we have not carried out a systematic study of the motion of every main component part of the body. Previous studies of the location of those areas in which the sensation of vibration is perceived under whole-body vibration [5] have underlined the predominance of the relative movement between thorax and pelvis. This led us to design an experiment for studying systematically the transmissibility between the pelvis and thorax. Coermann [2], and then Weis et al. [6] and Pradko et al. [7, 81 were interested in defining the mechanical characteristics of the human body in the form of whole body mechanical input impedance. This is why our transmissibility work has been supplemented by the investigation of mechanical functions such as the dynamic force applied to the subject, mechanical impedance of the whole body, and absorbed power, which describe a more general response to vibration. Most studies reported in the literature have been concerned only with sinusoidal motions which may not be representative of vibration conditions experienced in practice on land vehicles, and in particular on industrial machinery. Therefore we have investigated the effect of the wave form of the vertical vibration (sinusoidal and random) on the biodynamic parameters.
HUMAN
BODY
BIODYNAMIC
RESPONSE
425
Furthermore, techniques and experimental conditions used are often poorly defined in the literature, which has prompted us to emphasize in this article the measurement methods employed, in particular that developed to determine the body impedance. 2. PROCEDURE 2.1.
DEFINITION HUMAN
OF
FUNCTIONS
DESCRIBING
THE
BIODYNAMIC
BEHAVIOUR
OF THE
BODY
This study is based upon the assumption that the human body can be approximated by a linear mechanical system, under conditions close to those in practical situations. Sandover’s results [9] appear to corroborate this hypothesis, as do our measurements. 2.1.1. Seat-to-thorax transfer functions In this paper, transfer functions are expressed as continuous functions, the Fourier transform being used. All signals were processed on a Fourier analyzer which can be programmed to obtain the transfer function H(f) from H(f)
= GxY(f)IGXx(f)v
il)
where Gxu(f) is the cross spectrum of the functions X(f) and Y(f) and Gxx(f) is the auto spectrum of X(f). By this process the transmissibility and the phase difference between output and input motions are obtained. The absolute seat to thorax transfer function is l&(f) = GTs(f)/Gss(f), where 7’(fj and S(f) are the complex values of the accelerations measured on the thorax and at the seat. The relative seat to thorax transfer function is H,(f)= GITpSp(f)/GSS(f), where [T-S](f) is computed from the difference of stimuli T(t) and S(t). 2.1.2. Mechanical impedance of the human body Mechanical impedance is expressed as the complex ratio of force transmitted to the body F(f) to velocity V(f) taken at the same point. Referring to formula (l), one has Z(f) = GFv(f)IGvv(f). 2.1.3. Absorbed power In the time domain, absorbed power can be written for an infinite averaging time [8] as T Pm
=limL
ToI
F(t) V(t) dt
It can also be described in the frequency
P,=2 where
I0
when T + 43.
domain as
+m~(f)Gvv(f) ~0sL@(f)1df,
2?(f)cos[Q(f)] is the real part of Z(f).
2.2. APPARATUS AND METHOD The vibrations were produced by an electrohydraulic simulator with a maximum travel of 250 mm in the vertical direction, and a dynamic force capability of 15 kN. The force and acceleration at the subject-seat interface were obtained by seating the subject on a load bearing platform made of duralumin and constructed by the I.N.R.S.
426
P. M. DONATI
AND
C. BONTHOUX
Vertical vibration was measured by using an inductive accelerometer attached to the platform, which allowed the velocity transmitted to the subject to be deduced by analog integration. Vertical motion of the thorax was measured by using a very light piezoresistive accelerometer mounted on a resin block with an adjustable bearing surface of the accelerometer enabling the sensitive axis to be aligned vertically. This block was intimately attached to the xiphoidian point by a harness designed to cause the minimum of discomfort (see Figure 2).
Figure 2. Measurement
of the vertical
motion
of the thorax.
The subjects sat directly on the load platform, but to ensure relevance to real work situations (see Figure 3) the vibrations were applied to the entire body of the subject including the feet and hands, which were supported by a footrest and steering wheel, respectively, which had the same motion as the platform. Before starting each run, subjects were asked to adopt a posture which was erect but not stiff.
Figure
3. Biodynamic
measurement
session.
HUMAN
Figure 4. Load bearing
BODY
platform
BIODYNAMIC
used to measure
427
RESPONSE
the force transmitted
to the subjects.
The load detecting element in the platform (see Figure 4 and the Appendix) is a strain gauge bridge cell connected by a linkage arranged so that the platform is not sensitive to the location of the applied load. The absolute average accuracy is of 5 daN. In actual fact, the cell does not measure only the force transmitted to the subject but also the force applied to the platform loaded by the subject’s body. An experimental technique was therefore developed to remove the effect due to the mechanical charactersistics of the platform itself. An impedance study showed that it does not vibrate like a pure mass in the frequency range of l-10 Hz. Hence the traditional use of the mass cancellation technique was rejected in favour of a four-pole method in which the platform was considered as a linear system whose internal mechanic characteristics were ignored. If F0 and F, and i0 and z are the complex values of the forces and velocities taken, respectively, at the interfaces “simulator-platform” and “platform-subject”, one can write
io B(f) Fo = A(f) [I [ I[ 1 Z
C(f)
-o(f)
F
’
This formula gives immediately i = C(f)F,-D(f)F.
(2)
The computation of the body impedance function is a three stage operation, as follows: (a) experimental determination of C(f): since in the case of an unloaded platform F = 0, i can be expressed as i = C(f)F,+ C(f) = i/F,; (b) experimental determination of D(f): when the platform is loaded with a pure mass A4, F = jkh, and then D(f) = of the body impedance: (IljMw) W(f)(Foli)I); (c 1 ex P erimental determination with the platform loaded by the subject, then, from the impedance measured (Z, = F,/z) and expression (2) one has, completing the body impedance computation, Z = {I/D(fW(f)Zo1). From these computations, which were programmed on a Fourier analyzer, one can also deduce the force really transmitted to the subject (see formula (3)) and the power absorbed (see section 2.1.3): F = {C(f)lD(f)}F,-i/D(f).
(3)
Note that this method has the advantage of enabling one to investigate how any type of suspension system put between the subject and the load platform could affect the mechanical response to the human body.
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2.3. EXPERIMENTALDESIGN Subjects were presented first with a swept sinusoidal vertical vibration and then with a broad band random vibration of Gaussian distribution. For both of the vibration stimuli the frequency band was restricted to the l-10 Hz range and the r.m.s. level of the acceleration was 1.6 m/s*. The exposure to each type of signal was of sufficient length (at least 5 min) to allow 110 (n) statistical degrees of freedom in the power spectral density and cross spectral density analysis for 256 frequency points and a sampling rate of 25.6 Hz. This gave a resolution of 0.2 Hz (B). Chebyshev anti-aliasing filters were used with a rejection of 72 dB/octave and an undulation of less than *l dB. From this information the statistical precision of the power spectral density data has been computed; the normalized standard error, given by the formula E = l/dBT where T is the real time duration of the data analyzed (T = 275 s in this study) [lo], is 0.135. Thus at the 95% confidence level, the statistical precision of the magnitude values of the power spectral density estimate is *27%. Fifteen male subjects took part in the experiments. The age, stature and weight of the subject sample are shown in Table 1. Each subject received a medical examination before being allowed to participate in these experiments [ 111. TABLE 1 Main characteristics of the subjects
Mean Standard deviation Maximum Minimum
Age (years)
Stature (m)
Body weight (kg)
Body weight in the seating positiont (kg)
21 2.1 25 18
1.75 0.06 1.84 1.65
62.9 7.4 74 49
45.7 5.6 56 33
t The difference between the overall weight (body weight) and the apparent weight (body weight in the seated position) corresponds roughly to the weight of the limbs.
3. RESULTS
The analysis of the results is a two stage operation: (a) a processing of the analog data on a Fourier analyzer, by the method previously described, which enables the curves of the biodynamic functions to be obtained for every subject; (b) a statistical treatment of these results to see how the wave form of the vibration stimuli (sinusoidal or random) and the subject characteristics can affect the biomechanical responses. Statistical analyses were carried out for each separate frequency point to take into account any effect related to the vibration frequency. Non-parametric statistical tests were used for reasons of homogeneity and comparison. As a matter of fact this research was part of a more extensive study in which subjective methods were involved [5]. 3.1. SEAT TO THORAX TRANSFER FUNCTION Curves showing the modulus and phase of the seat to thorax transfer function have been drawn for each subject for every type of excitation studied (see Figure 5). In the range 3.5-5.5 Hz, depending on the subject, an important resonant response is exhibited
HUMAN
BODY
BIODYNAMIC‘
43 1
RESPONSE
with a peak amplification of 1.5-3.5. Above 4 Hz, a phase difference is observed, proving the existence of relative movements between the thorax and the pelvis, which involve stretching and compression of abdominal masses and musculature. The amplitude of the slope of the phase displacement appears to be correlated with higher frequency resonances. At frequencies below about 2 Hz the thorax moves as a single mass. “There is no simple anatomical explanation for the principal response of man to z axis vibration in the region of 4 to 5 Hz. This response is dictated by the dynamics of at least two resonant systems which may be fairly closely coupled, namely, the thoraco-abdominal system and the pectoral girdle” [12]. The differences between the two types of stimulus were compared using the Wilcoxon matched pair signed rank test. This indicated that the responses to the stimuli did not differ significantly, and did so as well for the absolute transmissibility as for the relative transmissibility, except at frequencies above 8 Hz (p c: 0.05) (see Figure 6). These experiments allow us to deduce that within the range of i’ axis vibration investigated, the part of the body involved in these measurements can be approximated by a linear system.
:v5
2
2.5
3
4
5
6
8
IO
.5
2
25
3
4
5
I:
,
Figure 6. Comparison between the mean values of the seat to thorax absolute (Lf,) and relative (H,) transfer functions of subjects in the sitting position. -, Swept sinusoidal stimulus; - - - , broad band random stimulus (z axis; 1.6 m/s* r.m.s.; l-10 Hz). ....., Response of a “mass-spring-damper” model (f<, = 4 Hz; F = 0.241.
There is evidence of significant correlations between some anthropometric characteristics of the subjects and the modulus of the transfer function at some frequencies (see Table 2). For example, the taller subjects showed higher transmissibilities at 2, 3 and particularly 4 Hz @ < 0.05). At the higher frequencies (8 Hz for t?a and 10 Hz for Ifr), significant negative correlations were found between the transmissibilities and the body weight as well as with some thorax dimensions. These correlations partly explain the reasons for intra-subject variability as shown in Figure 7. Table 3 shows, for the experimental group of subjects, the means and variabilities of their transmissibilities for different frequencies. 3.2.
MECHANICAL THE
IMPEDANCE
SUBJECT-ABSORBED
OF THE
WHOLE
BODY-DYNAMIC
FORCE
APPLIED
TO
POWER
In Figures 8 and 9 are plotted individual curves of modulus and phase of the impedance of the human body as well as the power spectral density of the force applied to the subject and frequency distribution of the absorbed power in the frequency range l-10 Hz. Important differences are observed between subjects. While for some (subjects 39 and 42) the resonant response in the region of 4 Hz is well marked, for others (subjects 44
O-46* o-57* 0.59*
Coherence
1.5 2.5
1
o*so*
0.83** 0.56* O-52* O-69** -0.56*
;:;$I
0.46* O-48* 0.63*
0*51*
0.90** 0*93** o-90** 0.62* o-55* 0.80** -O-63*
-o-49*
0*47*
5
(cm)) quantifies the subject’s morphology.
-0.64*
0.82** 0*88** o-91** 0.47* o-50* 0.72** -0.47*
0.62*
realtive transmissibility
Phase of the body impedance
0.81** O-87** O-84** O-48* 0.46* 0*57* -o-45*
4
absolute transmissibility
3
Modulus of the body impedance
0*49* 0.48* 0*51*
Seat-to-thorax
Modulus of the seat-to-thorax
2
Frequency (Hz)
-0.67**
0*45*
0*53*
6
behaviour of the subject’s body according to the frequency characteristics
* p < 0.05, ** p < 0.01 levels of significance. The Pignet coefficient (=height (cm)-weight (kg)-chest circumference
Body weight Height Pignet coefficient
Body weight Weight in seating position Height Trunk height Trunk and head height Chest circumference Pignet coefficient
Body weight Weight in seating position Height Trunk and head height Chest circumference Pignet coefficient
Body weight Weight in seating position Height
Anthropometric
r
Significant correlations found between the mechanical
TABLE 2
-O-46* -0.56*
-0*57*
0*50*
8
,
-O-46*
-o-53*
O-65**
-0.63* O-64*
-0*50* -O-48*
Coherence
10
and their anthropometric
5 N
HUMAN
BODY
01 I.5
I 2
BIODYNAMIC
I 456
I
I
953
433
RESPONSE
1
1
1
6
Frequency(Hz) Figure 7. Modulus of the seat to thorax absolute transfer function. The figure gives the mean values and 100% of the range of experimental values related to 15 male subjects in the sitting position exposed to a broad band random stimulus and a swept sinusoidal stimulus in the frequency range l-10 Hz.
TABLE
3
Means (m) and variabilities (u/m) of the seat-to-thorax transmissibility in the frequency range between 1.5 and 10 Hz related to 15 male subjects Frequency
I
H,a r,mmc%, *’
(Hz)
1.5
2
2.5
3
4
5
6
8
10
1.15 4
1.31 5 0.29 26
1.51 8 0.52 30
1.74 12 O-82 31
2.32 19 1.78 41
1.98 16 2.16 17
1.48 25 2.07 14
0.95 27 1.89 16
1.63 13
~/~(%)
TABLE
4
Means (m) and variabilities (o/m) of the modulus and phase of the impedance of the human body in the frequency range between 1.5 and 10 Hz related to 15 male subjects Frequency
(Hz)
i.5
2
2.5
3
4
5
6
8
10
Swept Sine
m dm
539 16
734 15
964 15
1358 18
1975 17
1622 20
1778 20
1735 20
18
Random
$rn
501 12
756 14
908 15
1152 19
1800 21
1673 22
1775 23
1897 20
1771 16
z
P. M. DONATI
434
AND
C. BONTHOUX
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-200
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iz As,
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. Swept sinusoidal
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Frequency 1.6 m/s’r.m.s.;
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AND C. BONTHOUX
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Frequency (Hz)
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Figure 9. Individual contours of the PSD of the force applied to the subjects and frequency distribution of the power absorbed (z axis; 16 m/s* r.m.s.; l-10 Hz). Swept sinusoidal motion; -, broad band random motion. Scales: for force 10M3N*/Hz, for power W/Hz.
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Frequency
(Hz)
Figure 10. Comparison between the mean values of the body impedance (modulus and phase) of subjects in the sitting position. -, Swept sinusoidal motion; - - -, broad band random motion; (z axis; 1.6 m/s’ r.m.s.; l-10 Hz); ....., response of a single degree of freedom model; + + f, response of a two degree of freedom model.
and 45) the predominance of the damping force precludes this phenomenon. This intra-subject variability correlates with the one observed for the seat to thorax transfer function. Again the Wilcoxon matched pair signed rank test shows that the stimuli did not differ significantly for the modulus and phase of the body impedance, except at the resonant frequency (modulus) (see Figure 10). Significant positive correlations (see Table 2) were found between the impedance modulus and the body weight in the frequency range of 1.5-4 Hz (p < 0.05). This may be explained by the fact the body vibrates like a pure mass below 2 Hz. At higher frequencies (6-10 Hz) the subject morphology and trunk characteristics would appear to be the predominant factors related to the impedance modulus. On the other hand, the correlations observed between the phase and the anthropometric characteristics were less noticeable. However, the taller subjects showed the smaller displacement of phase at 5 and 8 Hz (p < 0.05). Table 3 shows the means and standard deviations of the modulus of the body impedance in the frequency range between 1.5 and 10 Hz for the two types of signals. 4. DISCUSSION 4.1. MODEL A study of the individual response curves shows that the human body in the sitting (erect) position can be modelled by a simplified mass-spring-damper system. Their statistical analysis indicated a negative correlation between transmissibilities at the lower frequencies (below 4 Hz) and transmissibilities above the resonant frequency region (mainly at 6 Hz). This finding would be expected if, for example, the subjects’ response is approximated by a single degree of freedom system with a resonant peak in the region of 4 Hz. Subjects with the higher resonant peak amplitude would correspond to the lower damping factor and consequently to the lower transmissibility above the resonant frequency. The mean values of the absolute seat to thorax transmissibility are compared in Figure 6 with those obtained from the response of a single degree of freedom mass-springdamper system whose resonant frequency was set to 4 Hz and damping coefficient to
HUMAN
BODY
BIODYNAMIC
439
RESPONSE
O-24. Up to 4 Hz, the curves are in broad agreement. Beyond, the slope of the model is more marked. As a matter of fact a study of Figure 5 shows that some of the individual transmissibility curves (subjects 36,42,43 and 5 1) are similar to the response of a system with two degrees of freedom. An analogous observation can also be made for the impedance curves (see Figure 8). However, for this latter function, which is a more complete description of the response of the body as a mechanical system, the contours need to be modelled by systems with one further degree of freedom. Figure 10 shows that the mean curves of the modulus and phase of the body impedance obtained by arithmetic summation of the individual responses are well fitted by a system with two degrees of freedom, except for the phase in the frequency range between 5 and 8 Hz. The values of the parameters proposed for this model would be ml = 40 kg, k, = 26 x 10’ N/m, cl = 780 N s/m, and m2 = 8 kg, kZ = 21 x lo9 N/m, c2 = 250 N s/m. This gives values of fl = 4 Hz, El = 0.39, and f:! = 8 Hz, E2 = 0.38, where E, = ci/2~ik,mi is the reduced damping coefficient and fi is the resonant frequency. It should be noted that a better approach might have been to be more concerned with individual “personalized” models. Also, the models proposed above were proven only within the vibration conditions investigated: frequency range of l-10 Hz and r.m.s. acceleration amplitude of 1.6 m/s’. 4.2. COMPARISON WITH RESULTS OBTAINED BY OTHER LABORATORIES Seat-to-head and seat-to-thorax transmissibility curves obtained from investigations in different laboratories are presented in Figure 11. As shown in this figure seat to thorax transmissibility exceeds seat to head transmissibility in seated men.
01 I
I
1
I.5
2
3
4
5
Frequency
6
8
IO
20
(Hz1
Figure 11. Comparison of seat to thorax and seat to head transmissibilities obtained in different laboratories in the case of z sinusoidal vibration transmitted to subjects in the sitting position. Seat to thorax: 1, [3]; 2, results reported in this paper. Seat to head: 3, [7]; 4, [12], 5, [9]. Seat-to-thorax: 1, Wisner, Donnadieu and Berthoz [3]; 2, this paper, seat-to-head: 3, Pradko et al. [7]; 4, Guignard and King [ 111; 5, Sandover [S],
In Figure 12 the results reported here are compared with the impedance curves of the human body presented in the IS0 Standard 5982 [l]. A noticeable difference in the amplitudes of the modulus may be observed. This is explained easily by different experimental conditions. In our study, the feet were supported by a footrest and the hands by a steering wheel, both moving with the seat, so that subjects’ apparent weight
I
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8
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4
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2
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20
Frequency
31.5
1 (Hz)
-40
-20
0
20
40
I
2
I
4
I
0
I
IO
I
20
1 31.5
Figure 12. Comparison of the ranges of modulus and phase values of body impedance in the sitting position (z direction) obtained by the I.N.R.S. (ZZiZ) or given by the International Standard (IS0 5982) (m) [ 11.
200
200
5 8
&
zI
60
80
HUMAN
BODY BIODYNAMIC
RESPONSE
441
(46 kg mean, as measured by the platform located under the subjects’ buttocks) is clearly smaller than their overall weight (63 kg mean, which is rather small) (see Table l), and also the mechanical characteristics of the limbs were partly not taken into account. Amongst the studies referred to in the Standard, only 10 subjects out of 39 were seated under conditions similar to ours. The observations named above restrict our results to relatively young, tall and light subjects (see Table 1). They also underline the necessity to repeat a similar experiment with the same subjects to see how the limbs may affect the body impedance response.
5. CONCLUSIONS The experimental techniques developed appear to be quite acceptable for investigation of the variables affecting human response. It was found that the biodynamic parameters studied were little affected by the wave form of vertical vibration (sinusoidal or random) transmitted to the whole body of seated subjects. Therefore the authors believe that within the range of conditions investigated, the human body can be approximated by a linear system. The results obtained for the seat to thorax transfer function compared with those for the body impedance have shown that model characteristics depend on the type of approach. As a matter of fact, the former function provides information only on one part of the body although this part plays a predominant role, and “forgets” the movements of the other corporeal masses (in particular the viscera). A single degree of freedom system is often sufficient to describe the behaviour of this body part. However for the impedance function, which is a more complete description of the response of the body, the contour needs to be modelled by more complex systems. The main resonant frequency stays the same (4 Hz for both cases), which substantiates the predominant role of the thorax motions. On the other hand, it is found that the pelvis-thorax system is more damped (E = O-24), as compared with the value computed from the impedance response (El = 0.39). REFERENCES 1. INTERNATIONAL ORGANIZATION 2. 3. 4. 5. 6.
7. 8. 9. 10.
FOR STANDARDIZATION 1981 IS0.5982. Vibration and shock-mechanical driving point impedance of the human body. R. R. COERMANN 1961 Wright-Patterson Air Force Base. ASD-TR 61-492. The mechanical impedance of the human body in sitting and standing position at low frequencies. A. WISNER, A. DONNADIEU and A. BERTHOZ 1965 Le trauaif humain Nos 1 and 2, Etude biomecanique de I’homme soumis a des vibrations de basse frequence. G. F.ROWLANDS 1977 Royal Aircraft Establishment Report No. 77068 The transmission of vertical vibration to the heads and shoulders of seated men. P. DONATI 1980 These de Docteur Zngenieur. Effets a court terme sur I’homme assis des vibrations transmises a I’ensemble du corps (approches biomecanique et subjective). E. B. WEIS, M. P.CLARKE,J. W. BRINKLEY and P.J.MARTIN 1964 AerospaceMedicine 35, 945-950. Mechanical impedance as a tool in research on human response to acceleration. F. PRADKO, R. A. LEE and J.D. GREENE 1965 Winter Annual Meeting. Chicago. Human vibration response theory. R. A. LEE andJ.PRADKO 1968 Society ofAutomotive EngineersPaperNo. 680091. Analytical analysis of human vibration. J. SANDOVER 1978 Aviation, Space and Environmental Medicine 49, 335-339. Modelling human response to vibration. J. S. BENDAT andA. G. PIERSOL 1971Random Data : Analysis andMeasurement Procedures. New York, Wiley.
P. M. DONATI
442
AND C. BONTHOUX
INSTITUTION 1973 BSZDD 23. Draft for development: Guide to the safety aspects of human vibration experiments. 12. J. C. GUIGNARD and P. F. KING 1972 AGARD AG. 151. Aeromedical aspects of vibration and noise.
11. BRITISH STANDARDS
APPENDIX:
PRINCIPLE
OF THE PLATFORM
A sketch of the platform is shown in Figure Al. The load cell measures only the vertical reaction. It acts as a vertical support only and is mounted on rollers in order to remove any lateral forces which would damage the cell and also to accommodate the displacement resulting from the use of radial links A-B, C-D.
_--, __-Fi a’
a
A
_--,
D
I
Cl
C
__---
‘I
O’L--------_---------_ ‘&ii
Load cell
Figure Al. Sketch of platform. m , Platform support frame fixed to vibration table; -, the platform as indicated by broken lines (B + B’); A, B, C, D, linkage articulation.
moving part of
Figure A2. Platform dynamics.
Figure A2 illustrates the platform dynamics. R’ is the vertical reaction measured by the load cell. fi is the applied load. fiB and fit are forces exerted, respectively, by the links AB and DC on the vertical part of the platform. These forces are orientated along the axes of the links AB and DC since these are articulated at both of their ends. One can then write the balance of the moving part as R = F, Hs = Hc, and Hshb - Hchc = FI. From this one finds R=F,
Hs=Hc=Fl/(hB--hc).
The formula (Al) shows that the load cell measures a force equivalent load independent of the location of the load on the platform.
(Al)
to the applied
BIODYNAMIC SITTING
RESPONSE
POSITION
OF THE HUMAN
WHEN
SUBJECTED
BODY
IN THE
TO VERTICAL
VIBRATION? P. M. DONATI Laboratoire d’Energetique
AND C. BONTHOUX
et de Mkchanique Thkorique Appliquke, Institut National Polytechnique de Lorraine, 54000 Nancy, France
(Received 2 June 1982, and in revised form 8 January
19831
Previous studies of the location of those areas in which the sensation of vibration is perceived under whole body vertical vibration have underlined the predominance of the relative movement between thorax and pelvis. Experiments were designed to explore systematically the transmissibility between the pelvis and thorax. These were supplemented by measurements of mechanical impedance of the body and absorbed power. To determine the body impedance, a procedure was developed to remove the effect of the load platform itself. Fifteen subjects were presented first with a swept sinusoidal vibration, and then with a broad band random vibration, to see how the wave form of the motion might affect the mechanical response of the body. The results obtained for the seat to thorax transmissibility suggest that within the range of vertical vibration investigated (l-10 Hz, 1.6 m/s’ r.m.s.) the human body in the sitting position can be modelled by a linear system with one or two degrees of freedom according to the subject. Data from the impedance function, which is a more complete description of the response of the body as a mechanical system, lead to systems with one further degree of freedom.
1. INTRODUCTION Sensation perceived by the human body in the sitting position when subjected to vertical vibration is due partly to the important deformation and relative movement of organs and body segments. This observation led the International Standard committee (IS0 5982-1981/E) [l] to write “When considering the effects of shock and vibration on people, it is valuable to have an understanding of the mechanical characteristics of the body”. Indeed, visual observation shows that the human body does not vibrate like a pure mass. Different body parts can be animated with relative movement whose advent is a function of frequency, magnitude and axis of vibration. In particular, the analysis of the relative motion between thorax and pelvis illustrates clearly this observation (see Figure 1). Studies by Coermann [2], and by Wisner et al. [3] have shown that the human body when subjected to whole body vibration can be approximated by rigid masses (head, thorax, pelvis) joined together by systems like springs and dampers (ligaments, muscles, intervetebral discs) whose movements may be assessed with adequate instrument. This scientific approach is principally of interest for analyzing the motion of the body and deducing information on the way the transmission of vibration is effected between two “mechanically discrete” sub-groups. Thus Wisner et al. [3] and then Rowlands [4], with FThis study was conducted in the service “Acoustique, Vibration, Biodynamique” Rowe of the “Institut National I1.N.R.S.). 54500, Vandoeuvre
de Recherche et de S6curiti” les Nancy, France.
for prevention
of industrial
and headed by MI L. injuries
and diseases
423 0022-460X/83/190423
+20 $03.00/O
0198.3
Academic
Press Inc. (London)
Limited
424
P. M. DONATI
AND
C. BONTHOUX
Acceleration measured Seat
5 m/s2 [
IS
Thorax
Dlfference
Time -+
Figure 1. Section of chart record of the acceleration level measured on a subject’s thorax in the sitting position when subjected to a swept sinusoidal vertical stimulus (frequency band l-10 Hz; sweeping duration 10 s; r.m.s. level of the acceleration 1.6 m/s*).
the intention of studying the complete human system, have measured the acceleration transmitted to head, shoulders and thorax. However difficulties in developing efficient techniques of internal measurements make it a little unrealistic to assess the relative and absolute movement of internal body masses (organs) whose role is predominant in understanding how the human perceives the vibration and reacts to it. This shows the restrictions of this type of approach which, being too schematic, appears pertinent only as a description. Therefore we have not carried out a systematic study of the motion of every main component part of the body. Previous studies of the location of those areas in which the sensation of vibration is perceived under whole-body vibration [5] have underlined the predominance of the relative movement between thorax and pelvis. This led us to design an experiment for studying systematically the transmissibility between the pelvis and thorax. Coermann [2], and then Weis et al. [6] and Pradko et al. [7, 81 were interested in defining the mechanical characteristics of the human body in the form of whole body mechanical input impedance. This is why our transmissibility work has been supplemented by the investigation of mechanical functions such as the dynamic force applied to the subject, mechanical impedance of the whole body, and absorbed power, which describe a more general response to vibration. Most studies reported in the literature have been concerned only with sinusoidal motions which may not be representative of vibration conditions experienced in practice on land vehicles, and in particular on industrial machinery. Therefore we have investigated the effect of the wave form of the vertical vibration (sinusoidal and random) on the biodynamic parameters.
HUMAN
BODY
BIODYNAMIC
RESPONSE
425
Furthermore, techniques and experimental conditions used are often poorly defined in the literature, which has prompted us to emphasize in this article the measurement methods employed, in particular that developed to determine the body impedance. 2. PROCEDURE 2.1.
DEFINITION HUMAN
OF
FUNCTIONS
DESCRIBING
THE
BIODYNAMIC
BEHAVIOUR
OF THE
BODY
This study is based upon the assumption that the human body can be approximated by a linear mechanical system, under conditions close to those in practical situations. Sandover’s results [9] appear to corroborate this hypothesis, as do our measurements. 2.1.1. Seat-to-thorax transfer functions In this paper, transfer functions are expressed as continuous functions, the Fourier transform being used. All signals were processed on a Fourier analyzer which can be programmed to obtain the transfer function H(f) from H(f)
= GxY(f)IGXx(f)v
il)
where Gxu(f) is the cross spectrum of the functions X(f) and Y(f) and Gxx(f) is the auto spectrum of X(f). By this process the transmissibility and the phase difference between output and input motions are obtained. The absolute seat to thorax transfer function is l&(f) = GTs(f)/Gss(f), where 7’(fj and S(f) are the complex values of the accelerations measured on the thorax and at the seat. The relative seat to thorax transfer function is H,(f)= GITpSp(f)/GSS(f), where [T-S](f) is computed from the difference of stimuli T(t) and S(t). 2.1.2. Mechanical impedance of the human body Mechanical impedance is expressed as the complex ratio of force transmitted to the body F(f) to velocity V(f) taken at the same point. Referring to formula (l), one has Z(f) = GFv(f)IGvv(f). 2.1.3. Absorbed power In the time domain, absorbed power can be written for an infinite averaging time [8] as T Pm
=limL
ToI
F(t) V(t) dt
It can also be described in the frequency
P,=2 where
I0
when T + 43.
domain as
+m~(f)Gvv(f) ~0sL@(f)1df,
2?(f)cos[Q(f)] is the real part of Z(f).
2.2. APPARATUS AND METHOD The vibrations were produced by an electrohydraulic simulator with a maximum travel of 250 mm in the vertical direction, and a dynamic force capability of 15 kN. The force and acceleration at the subject-seat interface were obtained by seating the subject on a load bearing platform made of duralumin and constructed by the I.N.R.S.
426
P. M. DONATI
AND
C. BONTHOUX
Vertical vibration was measured by using an inductive accelerometer attached to the platform, which allowed the velocity transmitted to the subject to be deduced by analog integration. Vertical motion of the thorax was measured by using a very light piezoresistive accelerometer mounted on a resin block with an adjustable bearing surface of the accelerometer enabling the sensitive axis to be aligned vertically. This block was intimately attached to the xiphoidian point by a harness designed to cause the minimum of discomfort (see Figure 2).
Figure 2. Measurement
of the vertical
motion
of the thorax.
The subjects sat directly on the load platform, but to ensure relevance to real work situations (see Figure 3) the vibrations were applied to the entire body of the subject including the feet and hands, which were supported by a footrest and steering wheel, respectively, which had the same motion as the platform. Before starting each run, subjects were asked to adopt a posture which was erect but not stiff.
Figure
3. Biodynamic
measurement
session.
HUMAN
Figure 4. Load bearing
BODY
platform
BIODYNAMIC
used to measure
427
RESPONSE
the force transmitted
to the subjects.
The load detecting element in the platform (see Figure 4 and the Appendix) is a strain gauge bridge cell connected by a linkage arranged so that the platform is not sensitive to the location of the applied load. The absolute average accuracy is of 5 daN. In actual fact, the cell does not measure only the force transmitted to the subject but also the force applied to the platform loaded by the subject’s body. An experimental technique was therefore developed to remove the effect due to the mechanical charactersistics of the platform itself. An impedance study showed that it does not vibrate like a pure mass in the frequency range of l-10 Hz. Hence the traditional use of the mass cancellation technique was rejected in favour of a four-pole method in which the platform was considered as a linear system whose internal mechanic characteristics were ignored. If F0 and F, and i0 and z are the complex values of the forces and velocities taken, respectively, at the interfaces “simulator-platform” and “platform-subject”, one can write
io B(f) Fo = A(f) [I [ I[ 1 Z
C(f)
-o(f)
F
’
This formula gives immediately i = C(f)F,-D(f)F.
(2)
The computation of the body impedance function is a three stage operation, as follows: (a) experimental determination of C(f): since in the case of an unloaded platform F = 0, i can be expressed as i = C(f)F,+ C(f) = i/F,; (b) experimental determination of D(f): when the platform is loaded with a pure mass A4, F = jkh, and then D(f) = of the body impedance: (IljMw) W(f)(Foli)I); (c 1 ex P erimental determination with the platform loaded by the subject, then, from the impedance measured (Z, = F,/z) and expression (2) one has, completing the body impedance computation, Z = {I/D(fW(f)Zo1). From these computations, which were programmed on a Fourier analyzer, one can also deduce the force really transmitted to the subject (see formula (3)) and the power absorbed (see section 2.1.3): F = {C(f)lD(f)}F,-i/D(f).
(3)
Note that this method has the advantage of enabling one to investigate how any type of suspension system put between the subject and the load platform could affect the mechanical response to the human body.
4
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P. M. DONATI AND C. BONTHOUX
430
2.3. EXPERIMENTALDESIGN Subjects were presented first with a swept sinusoidal vertical vibration and then with a broad band random vibration of Gaussian distribution. For both of the vibration stimuli the frequency band was restricted to the l-10 Hz range and the r.m.s. level of the acceleration was 1.6 m/s*. The exposure to each type of signal was of sufficient length (at least 5 min) to allow 110 (n) statistical degrees of freedom in the power spectral density and cross spectral density analysis for 256 frequency points and a sampling rate of 25.6 Hz. This gave a resolution of 0.2 Hz (B). Chebyshev anti-aliasing filters were used with a rejection of 72 dB/octave and an undulation of less than *l dB. From this information the statistical precision of the power spectral density data has been computed; the normalized standard error, given by the formula E = l/dBT where T is the real time duration of the data analyzed (T = 275 s in this study) [lo], is 0.135. Thus at the 95% confidence level, the statistical precision of the magnitude values of the power spectral density estimate is *27%. Fifteen male subjects took part in the experiments. The age, stature and weight of the subject sample are shown in Table 1. Each subject received a medical examination before being allowed to participate in these experiments [ 111. TABLE 1 Main characteristics of the subjects
Mean Standard deviation Maximum Minimum
Age (years)
Stature (m)
Body weight (kg)
Body weight in the seating positiont (kg)
21 2.1 25 18
1.75 0.06 1.84 1.65
62.9 7.4 74 49
45.7 5.6 56 33
t The difference between the overall weight (body weight) and the apparent weight (body weight in the seated position) corresponds roughly to the weight of the limbs.
3. RESULTS
The analysis of the results is a two stage operation: (a) a processing of the analog data on a Fourier analyzer, by the method previously described, which enables the curves of the biodynamic functions to be obtained for every subject; (b) a statistical treatment of these results to see how the wave form of the vibration stimuli (sinusoidal or random) and the subject characteristics can affect the biomechanical responses. Statistical analyses were carried out for each separate frequency point to take into account any effect related to the vibration frequency. Non-parametric statistical tests were used for reasons of homogeneity and comparison. As a matter of fact this research was part of a more extensive study in which subjective methods were involved [5]. 3.1. SEAT TO THORAX TRANSFER FUNCTION Curves showing the modulus and phase of the seat to thorax transfer function have been drawn for each subject for every type of excitation studied (see Figure 5). In the range 3.5-5.5 Hz, depending on the subject, an important resonant response is exhibited
HUMAN
BODY
BIODYNAMIC‘
43 1
RESPONSE
with a peak amplification of 1.5-3.5. Above 4 Hz, a phase difference is observed, proving the existence of relative movements between the thorax and the pelvis, which involve stretching and compression of abdominal masses and musculature. The amplitude of the slope of the phase displacement appears to be correlated with higher frequency resonances. At frequencies below about 2 Hz the thorax moves as a single mass. “There is no simple anatomical explanation for the principal response of man to z axis vibration in the region of 4 to 5 Hz. This response is dictated by the dynamics of at least two resonant systems which may be fairly closely coupled, namely, the thoraco-abdominal system and the pectoral girdle” [12]. The differences between the two types of stimulus were compared using the Wilcoxon matched pair signed rank test. This indicated that the responses to the stimuli did not differ significantly, and did so as well for the absolute transmissibility as for the relative transmissibility, except at frequencies above 8 Hz (p c: 0.05) (see Figure 6). These experiments allow us to deduce that within the range of i’ axis vibration investigated, the part of the body involved in these measurements can be approximated by a linear system.
:v5
2
2.5
3
4
5
6
8
IO
.5
2
25
3
4
5
I:
,
Figure 6. Comparison between the mean values of the seat to thorax absolute (Lf,) and relative (H,) transfer functions of subjects in the sitting position. -, Swept sinusoidal stimulus; - - - , broad band random stimulus (z axis; 1.6 m/s* r.m.s.; l-10 Hz). ....., Response of a “mass-spring-damper” model (f<, = 4 Hz; F = 0.241.
There is evidence of significant correlations between some anthropometric characteristics of the subjects and the modulus of the transfer function at some frequencies (see Table 2). For example, the taller subjects showed higher transmissibilities at 2, 3 and particularly 4 Hz @ < 0.05). At the higher frequencies (8 Hz for t?a and 10 Hz for Ifr), significant negative correlations were found between the transmissibilities and the body weight as well as with some thorax dimensions. These correlations partly explain the reasons for intra-subject variability as shown in Figure 7. Table 3 shows, for the experimental group of subjects, the means and variabilities of their transmissibilities for different frequencies. 3.2.
MECHANICAL THE
IMPEDANCE
SUBJECT-ABSORBED
OF THE
WHOLE
BODY-DYNAMIC
FORCE
APPLIED
TO
POWER
In Figures 8 and 9 are plotted individual curves of modulus and phase of the impedance of the human body as well as the power spectral density of the force applied to the subject and frequency distribution of the absorbed power in the frequency range l-10 Hz. Important differences are observed between subjects. While for some (subjects 39 and 42) the resonant response in the region of 4 Hz is well marked, for others (subjects 44
O-46* o-57* 0.59*
Coherence
1.5 2.5
1
o*so*
0.83** 0.56* O-52* O-69** -0.56*
;:;$I
0.46* O-48* 0.63*
0*51*
0.90** 0*93** o-90** 0.62* o-55* 0.80** -O-63*
-o-49*
0*47*
5
(cm)) quantifies the subject’s morphology.
-0.64*
0.82** 0*88** o-91** 0.47* o-50* 0.72** -0.47*
0.62*
realtive transmissibility
Phase of the body impedance
0.81** O-87** O-84** O-48* 0.46* 0*57* -o-45*
4
absolute transmissibility
3
Modulus of the body impedance
0*49* 0.48* 0*51*
Seat-to-thorax
Modulus of the seat-to-thorax
2
Frequency (Hz)
-0.67**
0*45*
0*53*
6
behaviour of the subject’s body according to the frequency characteristics
* p < 0.05, ** p < 0.01 levels of significance. The Pignet coefficient (=height (cm)-weight (kg)-chest circumference
Body weight Height Pignet coefficient
Body weight Weight in seating position Height Trunk height Trunk and head height Chest circumference Pignet coefficient
Body weight Weight in seating position Height Trunk and head height Chest circumference Pignet coefficient
Body weight Weight in seating position Height
Anthropometric
r
Significant correlations found between the mechanical
TABLE 2
-O-46* -0.56*
-0*57*
0*50*
8
,
-O-46*
-o-53*
O-65**
-0.63* O-64*
-0*50* -O-48*
Coherence
10
and their anthropometric
5 N
HUMAN
BODY
01 I.5
I 2
BIODYNAMIC
I 456
I
I
953
433
RESPONSE
1
1
1
6
Frequency(Hz) Figure 7. Modulus of the seat to thorax absolute transfer function. The figure gives the mean values and 100% of the range of experimental values related to 15 male subjects in the sitting position exposed to a broad band random stimulus and a swept sinusoidal stimulus in the frequency range l-10 Hz.
TABLE
3
Means (m) and variabilities (u/m) of the seat-to-thorax transmissibility in the frequency range between 1.5 and 10 Hz related to 15 male subjects Frequency
I
H,a r,mmc%, *’
(Hz)
1.5
2
2.5
3
4
5
6
8
10
1.15 4
1.31 5 0.29 26
1.51 8 0.52 30
1.74 12 O-82 31
2.32 19 1.78 41
1.98 16 2.16 17
1.48 25 2.07 14
0.95 27 1.89 16
1.63 13
~/~(%)
TABLE
4
Means (m) and variabilities (o/m) of the modulus and phase of the impedance of the human body in the frequency range between 1.5 and 10 Hz related to 15 male subjects Frequency
(Hz)
i.5
2
2.5
3
4
5
6
8
10
Swept Sine
m dm
539 16
734 15
964 15
1358 18
1975 17
1622 20
1778 20
1735 20
18
Random
$rn
501 12
756 14
908 15
1152 19
1800 21
1673 22
1775 23
1897 20
1771 16
z
P. M. DONATI
434
AND
C. BONTHOUX
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Figure 8. individual
-200
contows
!modulus
I
iz As,
i;---;-1
and phase; uf the bodyimpedanir
46
I 10Hz).
54
I
. Swept sinusoidal
(Hz)
Frequency 1.6 m/s’r.m.s.;
E
51
I
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1
I
, broad handrandom
J
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P. M. DONATI
AND C. BONTHOUX
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IO 0
1 2
4
6
6
IO
0
Frequency (Hz)
2
4
6
6
IO
0
I
2
4
6
6
Figure 9. Individual contours of the PSD of the force applied to the subjects and frequency distribution of the power absorbed (z axis; 16 m/s* r.m.s.; l-10 Hz). Swept sinusoidal motion; -, broad band random motion. Scales: for force 10M3N*/Hz, for power W/Hz.
0
1j
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I
I
,
I
/
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3
4
5
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AND C. BONTHOUX
-
I.5
Frequency
(Hz)
Figure 10. Comparison between the mean values of the body impedance (modulus and phase) of subjects in the sitting position. -, Swept sinusoidal motion; - - -, broad band random motion; (z axis; 1.6 m/s’ r.m.s.; l-10 Hz); ....., response of a single degree of freedom model; + + f, response of a two degree of freedom model.
and 45) the predominance of the damping force precludes this phenomenon. This intra-subject variability correlates with the one observed for the seat to thorax transfer function. Again the Wilcoxon matched pair signed rank test shows that the stimuli did not differ significantly for the modulus and phase of the body impedance, except at the resonant frequency (modulus) (see Figure 10). Significant positive correlations (see Table 2) were found between the impedance modulus and the body weight in the frequency range of 1.5-4 Hz (p < 0.05). This may be explained by the fact the body vibrates like a pure mass below 2 Hz. At higher frequencies (6-10 Hz) the subject morphology and trunk characteristics would appear to be the predominant factors related to the impedance modulus. On the other hand, the correlations observed between the phase and the anthropometric characteristics were less noticeable. However, the taller subjects showed the smaller displacement of phase at 5 and 8 Hz (p < 0.05). Table 3 shows the means and standard deviations of the modulus of the body impedance in the frequency range between 1.5 and 10 Hz for the two types of signals. 4. DISCUSSION 4.1. MODEL A study of the individual response curves shows that the human body in the sitting (erect) position can be modelled by a simplified mass-spring-damper system. Their statistical analysis indicated a negative correlation between transmissibilities at the lower frequencies (below 4 Hz) and transmissibilities above the resonant frequency region (mainly at 6 Hz). This finding would be expected if, for example, the subjects’ response is approximated by a single degree of freedom system with a resonant peak in the region of 4 Hz. Subjects with the higher resonant peak amplitude would correspond to the lower damping factor and consequently to the lower transmissibility above the resonant frequency. The mean values of the absolute seat to thorax transmissibility are compared in Figure 6 with those obtained from the response of a single degree of freedom mass-springdamper system whose resonant frequency was set to 4 Hz and damping coefficient to
HUMAN
BODY
BIODYNAMIC
439
RESPONSE
O-24. Up to 4 Hz, the curves are in broad agreement. Beyond, the slope of the model is more marked. As a matter of fact a study of Figure 5 shows that some of the individual transmissibility curves (subjects 36,42,43 and 5 1) are similar to the response of a system with two degrees of freedom. An analogous observation can also be made for the impedance curves (see Figure 8). However, for this latter function, which is a more complete description of the response of the body as a mechanical system, the contours need to be modelled by systems with one further degree of freedom. Figure 10 shows that the mean curves of the modulus and phase of the body impedance obtained by arithmetic summation of the individual responses are well fitted by a system with two degrees of freedom, except for the phase in the frequency range between 5 and 8 Hz. The values of the parameters proposed for this model would be ml = 40 kg, k, = 26 x 10’ N/m, cl = 780 N s/m, and m2 = 8 kg, kZ = 21 x lo9 N/m, c2 = 250 N s/m. This gives values of fl = 4 Hz, El = 0.39, and f:! = 8 Hz, E2 = 0.38, where E, = ci/2~ik,mi is the reduced damping coefficient and fi is the resonant frequency. It should be noted that a better approach might have been to be more concerned with individual “personalized” models. Also, the models proposed above were proven only within the vibration conditions investigated: frequency range of l-10 Hz and r.m.s. acceleration amplitude of 1.6 m/s’. 4.2. COMPARISON WITH RESULTS OBTAINED BY OTHER LABORATORIES Seat-to-head and seat-to-thorax transmissibility curves obtained from investigations in different laboratories are presented in Figure 11. As shown in this figure seat to thorax transmissibility exceeds seat to head transmissibility in seated men.
01 I
I
1
I.5
2
3
4
5
Frequency
6
8
IO
20
(Hz1
Figure 11. Comparison of seat to thorax and seat to head transmissibilities obtained in different laboratories in the case of z sinusoidal vibration transmitted to subjects in the sitting position. Seat to thorax: 1, [3]; 2, results reported in this paper. Seat to head: 3, [7]; 4, [12], 5, [9]. Seat-to-thorax: 1, Wisner, Donnadieu and Berthoz [3]; 2, this paper, seat-to-head: 3, Pradko et al. [7]; 4, Guignard and King [ 111; 5, Sandover [S],
In Figure 12 the results reported here are compared with the impedance curves of the human body presented in the IS0 Standard 5982 [l]. A noticeable difference in the amplitudes of the modulus may be observed. This is explained easily by different experimental conditions. In our study, the feet were supported by a footrest and the hands by a steering wheel, both moving with the seat, so that subjects’ apparent weight
I
I
8
I
4
I
2
I
IO
I
20
Frequency
31.5
1 (Hz)
-40
-20
0
20
40
I
2
I
4
I
0
I
IO
I
20
1 31.5
Figure 12. Comparison of the ranges of modulus and phase values of body impedance in the sitting position (z direction) obtained by the I.N.R.S. (ZZiZ) or given by the International Standard (IS0 5982) (m) [ 11.
200
200
5 8
&
zI
60
80
HUMAN
BODY BIODYNAMIC
RESPONSE
441
(46 kg mean, as measured by the platform located under the subjects’ buttocks) is clearly smaller than their overall weight (63 kg mean, which is rather small) (see Table l), and also the mechanical characteristics of the limbs were partly not taken into account. Amongst the studies referred to in the Standard, only 10 subjects out of 39 were seated under conditions similar to ours. The observations named above restrict our results to relatively young, tall and light subjects (see Table 1). They also underline the necessity to repeat a similar experiment with the same subjects to see how the limbs may affect the body impedance response.
5. CONCLUSIONS The experimental techniques developed appear to be quite acceptable for investigation of the variables affecting human response. It was found that the biodynamic parameters studied were little affected by the wave form of vertical vibration (sinusoidal or random) transmitted to the whole body of seated subjects. Therefore the authors believe that within the range of conditions investigated, the human body can be approximated by a linear system. The results obtained for the seat to thorax transfer function compared with those for the body impedance have shown that model characteristics depend on the type of approach. As a matter of fact, the former function provides information only on one part of the body although this part plays a predominant role, and “forgets” the movements of the other corporeal masses (in particular the viscera). A single degree of freedom system is often sufficient to describe the behaviour of this body part. However for the impedance function, which is a more complete description of the response of the body, the contour needs to be modelled by more complex systems. The main resonant frequency stays the same (4 Hz for both cases), which substantiates the predominant role of the thorax motions. On the other hand, it is found that the pelvis-thorax system is more damped (E = O-24), as compared with the value computed from the impedance response (El = 0.39). REFERENCES 1. INTERNATIONAL ORGANIZATION 2. 3. 4. 5. 6.
7. 8. 9. 10.
FOR STANDARDIZATION 1981 IS0.5982. Vibration and shock-mechanical driving point impedance of the human body. R. R. COERMANN 1961 Wright-Patterson Air Force Base. ASD-TR 61-492. The mechanical impedance of the human body in sitting and standing position at low frequencies. A. WISNER, A. DONNADIEU and A. BERTHOZ 1965 Le trauaif humain Nos 1 and 2, Etude biomecanique de I’homme soumis a des vibrations de basse frequence. G. F.ROWLANDS 1977 Royal Aircraft Establishment Report No. 77068 The transmission of vertical vibration to the heads and shoulders of seated men. P. DONATI 1980 These de Docteur Zngenieur. Effets a court terme sur I’homme assis des vibrations transmises a I’ensemble du corps (approches biomecanique et subjective). E. B. WEIS, M. P.CLARKE,J. W. BRINKLEY and P.J.MARTIN 1964 AerospaceMedicine 35, 945-950. Mechanical impedance as a tool in research on human response to acceleration. F. PRADKO, R. A. LEE and J.D. GREENE 1965 Winter Annual Meeting. Chicago. Human vibration response theory. R. A. LEE andJ.PRADKO 1968 Society ofAutomotive EngineersPaperNo. 680091. Analytical analysis of human vibration. J. SANDOVER 1978 Aviation, Space and Environmental Medicine 49, 335-339. Modelling human response to vibration. J. S. BENDAT andA. G. PIERSOL 1971Random Data : Analysis andMeasurement Procedures. New York, Wiley.
P. M. DONATI
442
AND C. BONTHOUX
INSTITUTION 1973 BSZDD 23. Draft for development: Guide to the safety aspects of human vibration experiments. 12. J. C. GUIGNARD and P. F. KING 1972 AGARD AG. 151. Aeromedical aspects of vibration and noise.
11. BRITISH STANDARDS
APPENDIX:
PRINCIPLE
OF THE PLATFORM
A sketch of the platform is shown in Figure Al. The load cell measures only the vertical reaction. It acts as a vertical support only and is mounted on rollers in order to remove any lateral forces which would damage the cell and also to accommodate the displacement resulting from the use of radial links A-B, C-D.
_--, __-Fi a’
a
A
_--,
D
I
Cl
C
__---
‘I
O’L--------_---------_ ‘&ii
Load cell
Figure Al. Sketch of platform. m , Platform support frame fixed to vibration table; -, the platform as indicated by broken lines (B + B’); A, B, C, D, linkage articulation.
moving part of
Figure A2. Platform dynamics.
Figure A2 illustrates the platform dynamics. R’ is the vertical reaction measured by the load cell. fi is the applied load. fiB and fit are forces exerted, respectively, by the links AB and DC on the vertical part of the platform. These forces are orientated along the axes of the links AB and DC since these are articulated at both of their ends. One can then write the balance of the moving part as R = F, Hs = Hc, and Hshb - Hchc = FI. From this one finds R=F,
Hs=Hc=Fl/(hB--hc).
The formula (Al) shows that the load cell measures a force equivalent load independent of the location of the load on the platform.
(Al)
to the applied