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51 Fig. 8: Number of cycles to failure for an intermediate driver
Fig. 9 : Exposure limit versus acceleration at the seat
The number of cycles before failure of the trabecular bone
N can be expressed as a function of the excitation level of
the rms value of acceleration at the seat A (m/s2):
N= 1012 A-7.98 with R2= 99.7% (8)
Evaluation of human exposure to random vibration
Using the damage model D developed by Pidaparti et al
(2001) [47] and our predictive model for number of cycles
before injury (Eq.8), the rms acceleration limit A (m/s2)
as measured at the driver’s seat can be expressed as a
function of the exposure duration Y (years) and natural
excitation frequency fn (Hz). The exposure duration in year
considers that a driver is exposed to vibration during 1920
h/year, at the rate of 8h/day during 240 days a year.
The damage model D for bone is :
(9)
where n and N are respectively the number of accu-
mulated cycles and the number of cycles before injury
(equ.9) at the excitation level of the rms value of accel -
eration A. The number of accumulated cycles ‘n’ submit-
ted to the lumbar spine is the produce of the excita-
tion frequency ‘fn ’ (Hz) by the duration of exposure ‘t ’
(second). The considered excitation frequency fn varied
from 4 Hz to 6 Hz.
Then if we consider a damage D equal to 1 (D=1), the dura-
tion of exposure t (s) can be expressed by equation 10 :
(10)
The duration Y in years becomes:
(11)
with ƒn is the natural frequency that varied between 4
and 6 Hz.
Figure 9 represents the rms seat acceleration A (m/s2)
versus the duration of exposure Y (years) for frequencies
ranging between 4 to 6 Hz.
The results show that if the excitation frequency was contin-
uously excited the lumbar spine resonance due to random
or transient excitations coming from rough roads, the rms
acceleration level should be lower than values ranging from
2.25 to 2.35 m/s2, whatever the excitation frequency, in
order to limit the probability of low–back disorders before
40 years of working. Furthermore, it is shown that accel-
eration amplitudes greater than 3 m/s2 could, in this case
of excitation, present a high probability level of injury in
a short duration of exposure. These limit levels of accel-
eration should be carefully considered due to the strong
assumption on the excitation frequency. However, if they
were controlled at the seat, it is sure that the drivers
should present a very low probability of injury.
Conclusion
The assumption of this research is that low-back pain
occurs among drivers exposed to whole-body vibrations
and that such vibrations may induce stresses liable to cause
fatigue failure of the bone. The study enables the evalua-
tion of lumbar spine mechanical fatigue when exposed to
the continuous whole-body vibration for the prediction of
the vertebral lifespan when subject to long-term exposure
to low-frequency and low-amplitude dynamic loads. In doing
so, it helps for validating the assumption that whole-body
vibration can induce microfractures in the bony elements of
the spine, which, in turn, can lead to adverse health effects.
A finite element numerical model of the lumbar spine has
been developed using a parametric model. Specifically, the
model representing the L4-L5 motion segments, was gener-
ated to predict the stresses and number of cycles to fail-
ure. The fatigue model is aimed for evaluating the potential
risk of adverse health effects for professional drivers while
in a seated position. Furthermore, the computed stress/
strain distribution has identified the osseous locations most
susceptible for damaging: the trabecular bone and endplate.
The results of this study are confined to the evaluation of a
ride safety level. The proposed method is a general theo-
retical guide in order to estimate the long-term effect of
repeated exposure of a human being subjected to a series
of vibrations. Under the strong assumption that the excita-
tion frequency continuously stimulates the resonance of the
lumbar spine due to random or transient excitations coming
from the road, this study has revealed a quantitative rela-
tionship between the acceleration limit as measured at the
seat accordingly with the exposure duration. It is revealed
that an excitation acceleration of 2.3 ms-2 applied to the