Experimental methods used in analyses of the human behavior in a vibrational medium.

Barbu, Daniela Mariana ; Barbu, Ion

Abstract Vibrations are mechanical oscillations, produced by regular or irregular period movements of a member or body about its rest position. Vibration can be a source problems at an engineering level because they can result in damage to equipment, loss of control of equipment, and reduction in the efficiency of operation of machines. Vibration is most normally a problem experienced in driving vehicles and in operating tools. Vibration can affect visual perception, muscles, concentration, circulation and the respiratory system and at certain levels can even result in physical harm to the body. The effect of vibration on the human body is related to the natural frequency of parts of the human body affected. The human tissue heavily damps frequencies of above 30 Hz. The aim of this paper is to present an experimental method that study human behavior in vibrational medium.

Key words: Human Body, Vibration, Experimental Model.

1. INTRODUCTION

Many people are exposed to whole-body vibration in vehicles: cars, buses, trains, ships and airplanes, on a daily basis. In our previous paper, it was confirmed that whole-body vibration caused a subject discomfort, fatigue and physical pains [Liu et al., 1987]. There are several reports describing how vibration interferes with people's working efficiency, safety and health [Bogert, 1994]. Therefore, many researchers have concentrated their efforts on reducing the amount of vibration from products and vehicles. There are many reports describing the measurement of the transmissibility of the human body under vibration [Griffin, 1975], [Matsumoto & Griffin, 1998 ], [Liu et al., 1996]. It has also measured the transmissibility of the whole body in sitting and lying posture exposed to vertical vibration [Yoshimura et al., 2005]. The results of these reports indicated the resonance of the human body depended on various factors: the posture, the materials of the given seat surface, vibration magnitude and frequency. The measurements of the transmissibility of the body under various vibrations are inefficient, laborious, tedious and expensive. On the other hand, there are a few computer-automated procedures used to predict the human body's responses to vibration [Amirouche, 1987], [Yoshimura et al., 2005], [Kitazaki & Griffin, 1997]. It is difficult to accurately estimate the behavior of the human body under vibration, because it is a complex active dynamic system. Further, it is most important to bear in mind that the complexity is not only due to physical characteristics but also due to psychological and physiological characteristics. However, no vibration model concerning the physiological and the psychological reactions of a person exposed to vibration environments has been found.

In vehicle designs, it is necessary to assess the effect of vibration to the drivers or passengers from the viewpoint of health. Occupational drivers of industrial vehicles such as power shovels, bulldozers or tractors may suffer from chronic lumbago or low back pain after some period of engagement. Therefore, the exposure limit of whole body vibration needs to be made clear. Usually the vibration effect is assessed based on the pressure changes at the lumbar vertebral endplates. It can hardly be measured, though the vibration response of the spinal column can be measured at the surface. Therefore, it is necessary to have the dynamic model of the human body, which can interpret the vertebral behavior. One of the possible ways is to build a dynamic model, which represents the vertebrae's response.

This paper presents a multi-body modeling of seated human body. In the model, rigid bodies represent the vertebrae 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 multibody dynamic model can be used to evaluate the vibration effect to the spinal column of the seated subject.

This paper's aim is to develop and analyze a synthetic vibration model of a seated human body exposed to external vibrations. The synthetic vibration model consisted of a mechanical vibration model simulating the physical behavior of the human body and multiple regression equations describing the above three relations. The mechanical vibration models formalized according to Lagrange's equation of motion were employed. As a result, it was clear that there were resonance points showing remarkable shaking of the head, the chest and the abdomen in the frequency range 2-11 Hz. Moreover, it was indicated that the relations between the physical reactions and the resulting psychological and physiological reactions might be expressed in terms of multiple regression analysis.

2. PROPOSAL MODEL

2.1. Assumption to simplify the human body

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, to predict the physical reaction the transverse shaking of the human body is ignored. Therefore, we can 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 behavior of the human body.

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, chest (from the upper point of the breastbone to the third lumbar vertebra), abdomen (from the third lumbar vertebra to the trochanteric point), thigh, and lower leg. 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 chest and head are connected in the same way. The viscoelasticity element could simulate lumber and cervical vertebrae.

3. The horizontal plane of the experimental chair and the surface of the vibration table could support the weight of the lower legs, so that the weight of the lower legs has no effect on the pelvis.

4. Only portions of the back of head, the back and the lower pelvis are exposed to the external force of the vibration.

5. 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.

6. Finally, we simplified the human body to a two-dimensional vibration model consisting of masses, rigid links, springs and dampers with nine degrees of freedom.

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:

* Each part of the vibration model slightly vibrates around each static force equalizing position.

* The righting moment of springs and the attenuating force of dampers are in proportion to the displacement and the velocity, respectively.

* 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.

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. Therefore, the equations were formulated with generalized coordinates according to the general process of Lagrange's equation of motion. The equation of motion of the human body is

[M]{[d.sup.2]x/[dt.sup.2]}+[C]{dx/dt}+[K]{x}={f}

where {x} is generalized coordinates and {f} is generalized forces.

Each [f.sub.i] corresponds to each generalized coordinate in the equation of motion. Coefficient matrices, [M], [C] and [K], are symmetric positive matrices that have nine degrees of freedom. In this paper, [k.sub.i] was the spring constant and [c.sub.i] was the damping coefficient.

The damping matrix [C] corresponds to velocity and [M] and [K] correspond to acceleration and displacement, respectively, so that the phase differences between the generalized coordinates {x} of each part of the body are induced.

2.3. Perspectives

For the future, we need to develop and to analyze this proposal model. Therefore, we will find and analyze the own pulsations of each parts of the human organism defines in model. In addition, we need to compare the movements, the speeds and the accelerations obtained through the proposal model to the existing models presented hereinbefore.

[FIGURE 1 OMITTED]

3. REFERENCES

Amirouche, F.M.L. "Modeling of human reactions to whole-body vibration", Journal of Biomechanical Engineering 109 (3), 210-217, 1987, ISSN 1528-8951.

Bogert, A.J. "Analysis and simulation of mechanical loads on the human musculoskeletal system". Exercise and Sport Sciences Reviews 22, 23-51, 1994, ISSN 0091-6331.

Griffin, M.J. "Vertical vibration of seated subject, effect of posture, vibration level, and frequency". Aviation Space and Environmental Medicine 46 (3), 269-276, 1975, ISSN 0095-6562;

Kitazaki, S., Griffin, M.J. "A model analysis of whole body vertical vibration, using a finite element model of the human body". Journal of Sound and Vibration 200 (1), 83-103, 1997, ISSN 0022-460X.

Liu, J.Z., Kubo, M., Aoki, H., Liu, N., Kou, P.H., Suzuki, T. "A study on the difference of human sensation evaluation to whole body vibration in sitting and lying postures", Journal of Physiological Anthropology 14 (5), 219-226, 1995, ISSN 13453475;

Liu, J.Z., Kubo, M., Aoki, H., Terauchi, F. "The transfer function of human body on vertical sinusoidal vibration", Japanese Journal of Ergonomics 32 (1), 29-38, 1996, ISSN 0549-4974.

Matsumoto, Y., Griffin, M.J. "Dynamic response of the standing human body exposed to vertical vibration", Journal of Sound and Vibration 212 (1), 85-108, 1998, ISSN 0022-460X;

Yoshimura, T., Nakai, K., Tamaoki, G. "Multi-body Dynamics Modeling of Seated Human Body under Exposure to Whole-Body Vibration", Industrial Health, 43, 441-447, 2005, ISSN 0019-8366.