1st International Conference on Advancements of Medicine and Health Care through Technology, MediTech2007,
27-29th September, 2007, Cluj-Napoca, ROMANIA
Proposal Model for Human Body Behaviour in a
Medium Polluted by Vertical Vibrations
Barbu D. Daniela Mariana
Abstract — This paper shows the modelling of the standing human body for the assessment of the vibration risk. The modal
parameters of this type of subject are extracted in order to understand the dominant natural modes. A simplified model having seven
DOFs is constructed. The transient response analysis is illustrated when a sine input is applied. The relative displacements of human
parts are evaluated, which can be a basis for the assessment of vibration risk. It is suggested that the multi-body dynamic proposal
model is used to evaluate the vibration effect to the standing subjects.
Keywords: Vibrations; Shocks; Human Body; Protection.
1. INTRODUCTION1
Knowledge about comfort and fatigue-decreased
proficiency is based on statistical data collected under
practical and experimental conditions. Because
experiments with human beings are difficult, time
consuming and in extreme cases aesthetical, much of the
knowledge about damaging effects has been obtained
from experiments on animals. It is, of course, not always
possible to "scale" results obtained from animal
experiments to reactions expected from man, but nevertheless such experiments often result in valuable
information.
This paper presents a multi-body modelling of standing
human body. In the model the vertebrae are represented
by rigid bodies and they are connected by revolute joints.
The intervertebral disks are regarded as rotational springs
and rotational dampers. The vibration experiment is
conducted to measure the transmissibility from the seat
surface to the measurement points. The model is
constructed so as to express the experimental
transmissibility. It is suggested that the multi-body
dynamic model can be used to evaluate the vibration
effect to the spinal column of the seated subject. The
synthetic vibration model could facilitate comfort design
in the field of industrial design in general and the
automotive industry in particular. Using the vibration
model in industrial fields will enable us to efficiently
develop various products, whose design will take into
consideration of human comfort.
In constructing the vibration model, we would predict the
characteristics of the physical reactions. In this paper the
vibration model was constructed in accordance with the
results of our research into the characteristics of the
human exposed to a vertical sinusoidal wave force.
Vibrations can be defined as oscillations of mass about a
fixed point. When the body comes in contact with a
mechanical source of vibration the tissues of the body
become displaced from their resting position. In the work
setting there are basically three types of vibration that are
significant to the worker. These include whole body
vibration, segmental vibration and resonance.
The most common form of whole body vibration is
vehicular vibration. In this case vibration enters the body
through the buttocks and the feet and to a lesser extent the
hands. Segmental vibration is the result of mechanical
vibration that comes in contact with body parts and the
effect becomes localized. This form of vibration is
transferred into the hands and arms when we use power
tools.
All physical systems have their own natural frequency.
When tissues of the body are exposed to sources of
vibration corresponding to their natural frequency these
tissues go into resonance. That is, the strength or
amplitude of the vibrations exceeds that of the source.
When the body comes is contact with mechanical
vibration there is a direct adverse physiological effect on
the body. The effect interferes with work efficiency and
in some situations can put the worker at risk for injury.
Any factor that has the potential to impair the worker’s
function is a significant issue in ergonomics and therefore
must be eliminated or reduced to the greatest extent
possible.
The human body is made up of organ systems composed
of different tissues.
When it comes in contact with
a source of vibration it reacts as a set of linked masses.
Each tissue mass has its own natural frequency. Smaller
structures tend to resonate at higher frequencies and
larger masses tend to resonate at lower frequencies.
Biologically the situation is by no means simpler,
especially when psychological effects are included. In
considering the response of man to vibrations and shocks
it is necessary, however, to take into account both
mechanical and psychological effects.
2. PROPOSAL MODEL
2.1. Assumption to simplify the human body
In this paper we assumed that parts of the human body
would only swing back and forth as well as move up and
down. Because it was apparent that the human body
would remain physically symmetry during exposure to
vibration in a vertical direction.
Thus, in the physical vibration model, the transverse
shaking of the human body is ignored. Therefore, we can
D.M. Barbu is with the Transilvania University of Brasov, Romania,
phone: +40-268-413-000; e-mail: [email protected].
445
1st International Conference on Advancements of Medicine and Health Care through Technology, MediTech2007,
27-29th September, 2007, Cluj-Napoca, ROMANIA
⎧m1 &y&1 + c1 y& 1 − c1 y& 1 + k 1 y1 − k 1 y 3 = 0
⎪ &&
&
&
⎪m 2 y 2 + c 2 y 2 − c 2 y 3 + 2 k 2 y 2 − 2 k 2 y 3 = 0
⎪m3 &y&3 + (c 5 + c 2 + c1 + c3 ) y& 3 − c 5 y& 6 − c 2 y& 2 − c1 y& 1 − c 3 y& 4 +
⎪
⎪+ (k 5 + 2 k 2 + k 1 + k 3 ) y 3 − k 5 y6 − 2 k 2 y 2 − k 1 y1 − k 3 y 4 = 0
⎨ &&
⎪m 4 y 4 + (c3 + c 4 ) y& 4 − c 3 y& 3 − c4 y& 5 +
⎪+ (k 3 + k 4 ) y 4 − k 3 y 3 − k 4 y 5 = 0
⎪
⎪m5 &y&5 + c 4 y& 5 − c 4 y& 4 + k 4 y 5 − k 4 y 4 = 0
⎪m &y& + (c + c ) y& − c y& + (k + k ) y − k y = − F
6
5
6
5 3
6
5
6
5 3
p
⎩ 6 6
assume that a two-dimensional model projected on the
central plane, which is a midsagittal plane, of the human
body would simulate the realistic vibration behaviour of
the human body.
As is noticed in figure 1, the structure is formed from the
follow components: head; internal viscera; thorax;
scapular belt; superior member; pelvis.
The dampers and the springs represent joints, tendons and
another ale bindery organs modelling.
Is considered that the subject is submissive of a formal
disturbances F p = F0 sin ωt and is followed the analysis
in which: mi - masses; ci - amortizations; ki - rigidities;
yi - displacements; y& i - velocities, &y&i - accelerations and
F is a sinusoidal force.
behaviour of human organism (the precise maul of the
seven parts of human organism) to this type of vertical
vibrations.
Additionally, to simplify the model of the human body
further, the following conditions were assumed:
1. It was assumed that the human body consists of
head, internal viscera, thorax, scapular girdle,
superior member and pelvis. Each part of the
human body has a mass and a rotating inertia at
the centre of gravity (Fig. 1).
2. The lower leg could be connected to the thigh
and the thigh to the abdomen by a joint with an
axis of rotation and generating a viscosity
resistance moment. The resistance moment
represents the passive resistance element of
ligaments. The abdomen and chest are connected
by a viscoelasticity element that consists of a
spring and a damper and the thorax and head are
connected in the same way.
3. Only portions of the back of head, the back and
the lower pelvis are exposed to the external
force of the vibration.
4. So that the head, trunk (chest, abdomen) and
pelvis would never slip on the surface of the
chair, there is sufficient frictional force at each
point of contact.
Finally, we simplified the human body to a twodimensional vibration model consisting of masses, rigid
links, springs and dampers with nine degrees of freedom
(Fig. 1).
HAND
m5
c4
k4
HEAD
SCAPULAR
GIRDLE
m4
m1
k1
c1
m3
k2
c3
k3
m2
k2
c2
k5
c5
VISCERA
2.2. Formulation of the equation of motion for the
simplified human vibration model
In order to simplify the formulation of the equation of
motion for the two-dimensional vibration model, we
further assumed the following:
(1) Each part of the vibration model slightly vibrates
around each static force equalizing position.
(2) The righting moment of springs and the attenuating
force of dampers are in proportion to the displacement
and the velocity, respectively.
(3) The saturation viscosity resistance moment is applied
to the resistance moments between the lower leg and the
thigh and between the thigh and the abdomen.
Finally, the equation of motion consists of the coefficient
matrices illustrating the effects of the masses, rigid links,
springs and dampers. The equation also has nine degrees
of freedom, which were 3 rotations and 6 translations,
which did not perpendicularly intersect each other.
THORAX
PELVIS
m6
c6
k6
Fp
Figure 1. Proposal Model
3. RESULTS
3.1. The Own Vibrational Modes
The own pulsations and the forms of own modes (fig. 2)
are obtained through the solution of the system of
homogeneous equations for the free vibrations
unamortized with next form: [M ]{&y&} + [K ]{y} = {0} .
446
1st International Conference on Advancements of Medicine and Health Care through Technology, MediTech2007,
27-29th September, 2007, Cluj-Napoca, ROMANIA
THE HEAD
w = 7.5713 rad/s
1,5
1
0,5
0
-0,5
VP
THE INTERNAL VISCERA
w = 6.7979 rad/s
1
0,5
0
1
2
3
1
-0,16
-0
4
5
0,01 -0,01
6
7
8
0
-0
0
-0,5
1
2
3
4
5
6
7
8
VP 0,29 0,05 -0,05 -0,19 0,83 -0,42 0,09 -0,01
THE SCAPULAR GRIDLE
w = 1.1579 rad/s
THE THORAX
w = 5.3263 rad/s
1
0,5
0,5
0
-0,5
1
2
3
4
5
6
7
0
8
VP 0,47 0,23 0,19 -0,42 -0,2 0,24 0,62 -0,17
1
2
3
4
5
6
7
8
VP 0,38 0,38 0,39 0,33 0,43 0,47 0,21 0,12
THE HAND
w = 2.5329 rad/s
THE PELVIS
w = 3.7840 rad/s
1
1
0,5
0
-1
0
1
2
3
4
5
6
7
-0,5
8
VP 0,42 0,38 0,53 0,14 -0,29 -0,5 0,12 0,17
1
2
3
4
5
6
7
8
VP 0,56 0,41 0,26 -0,19 0,01 0,14 -0,44 0,45
Figure 2. The own modes of vibration
F0 = 4 L60 and ω = 6 L 50 rad / s , we obtained the
movements represented the charts in the following
figures:
3.2. The graphic representation of the system solutions
Each solution of the system can be writhed in the likeness
of:
M r &ξ&r + Cr ξ& r + K r ξ r = f r
which describes the modulo of motion, characterized by
the variation of main coordinate ξ r .
Each such equation can solved asunder, identically with
the equation of constrained vibrations ale of the system
with a degree of freedom and can be writhed in the
likeness of:
1⎛
qω ⎞
q
⎟ sin pt + 2
x = x0 cos pt + ⎜⎜ v0 − 2
sin ωt
2 ⎟
p⎝
p −ω ⎠
p − ω2
where:
4. CONCLUSIONS
In the previously figures we represented in MAPLE the
variations of displacements, velocities and accelerations
of the system for ω = 6..50 rad/s, t = 0..100 s and
F0 = 30 N.
As per graphic the movement of the eye varies between
80 and 80 mm, with speeds contained between 600 and 600 mm/s and accelerations of -4000 to 4000 mm/s2,
what represents the very big values. Thence, such force
solicits much eye and, by default, he steps in operable
see.
Is can noticed from charts that the movements other
systems are very little (don't exceed 2 mm, what means
that applied force don't influences very many state of the
systems. In addition, the values of the speeds and the
found accelerations are very little by-paths.
As a general conclusion, we can say that the human
organism modelled as a system of table, springs and
dampers is behaved like every mechanical systems. Most
affected parts ale the organism are eye, head (the
neurological systems) and the internal viscera. Law for
which first sensations perceived by organisms to
resonance is the sensation of bad (dizziness, sickness), as
well as the disturbance of the sight and, here, he
diminishes the orientation in space. The visual function is
stricken, in fore rank, because the visual analyzer is a
sensory system, but and by reason of this orientation after
a visual axis, carry temporally the vibration is earnest
affected.
p = k m , q = F0 m , Fp = F0 sin ωt
and
x0 , v0 are initial displacements, respectively
velocities.
qω
q
, than x = 2
sin ωt .
p 2 − ω2
p − ω2
For the proposal model, we consider:
If x0 = 0, v0 =
p = k r mr , q = F0 mr , F p = F0 sin ωt
Reduced masses are identically with the masses of the
system’s elements and the reduced rigidities are:
k r = 1 , k r = 2k 2 , k r = k 1 + 2k 2 + k 3 + k 5 ,
1
2
3
k r4 = k 3 + k 4 , k r5 = k 4 , k r6 = k 5 + k 6
y (ω, t ) =
F0
sin ωt
k − ω2 m
This is the expression of the system’s movements. For
or
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2
acceleration [mm/s ]
velocity [mm/s]
displacement [mm]
1st International Conference on Advancements of Medicine and Health Care through Technology, MediTech2007,
27-29th September, 2007, Cluj-Napoca, ROMANIA
2
acceleration [mm/s ]
velocity [mm/s]
displacement [mm]
Figure 3. Displacements, velocities and acceleration representations of the head
velocity [mm/s]
2
acceleration [mm/s ]
displacement [mm]
Figure 4. Displacements, velocities and acceleration representations of the internal viscera
velocity [mm/s]
displacement [mm]
2
acceleration [mm/s ]
Figure 5. Displacements, velocities and acceleration representations of the thorax
2
acceleration [mm/s ]
velocity [mm/s]
displacement [mm]
Figure 6. Displacements, velocities and acceleration representations of the scapular gridle
2
acceleration [mm/s ]
velocity [mm/s]
displacement [mm]
Figure 7. Displacements, velocities and acceleration representation of the hand
Figure 8. Displacements, velocities and acceleration representation of the pelvis
vertical sinusoidal vibration, Japanese Journal of Ergonomics
32 (1), 1996;
[5] Matsumoto, Y., Griffin, M.J. Dynamic response of the
standing human body exposed to vertical vibration, Journal of
Sound and Vibration 212 (1), 1998;
[6] Kuboa and al.. An investigation into a synthetic vibration
model for humans: An investigation into a mechanical vibration
human model constructed according to the relations between
the physical, psychological and physiological reactions of
humans exposed to vibration, International Journal of Industrial
Ergonomics 27, 2001;
[7] Randall, J.M., Mattehews, R.T., Stiles, M.A. “Resonance
frequencies of standing humans”, Ergonomics 40 (9), 1997.
6. REFERENCES
[1] Bogert, A.J. Analysis and simulation of mechanical loads
on the human musculoskeletal system. Exercise and Sport
Sciences Reviews 22, 1994;
[2] ISO 2631-1 Mechanical vibration and shock - Evaluation
of human exposure to whole-body vibr. Part 1: General
requirements, 2nd ed., 1997;
[3] Kitazaki, S., Griffin, M.J. A model analysis of wholebody
vertical vibration, using a finite element model of the human
body. Journal of Sound and Vibration 200 (1), 1997;
[4] Liu, J.Z. and al. The transfer function of human body on
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