Keywords: human comfort, random acceleration process, linear discomfort accumulation criteria.

This paper presents a technique to obtain the probabilistic structure of the stochastic process of occupant discomfort in terms of the probabilistic structure of the narrow band random acceleration process. The linear discomfort accumulation criteria and vibration limits given by the International Standard ISO 2631 (1978) for human exposure are taken into account. Closed expressions for the expected and the standard deviation of damage are derived for the stationary narrow-band acceleration random process.

Human sensitivity to vibration has been studied in the last decades by Irwin [1], Coermann et al. [2], Kitazani and Griffin [3]. The dynamic mechanical response of the human body is a very complex problem Coermann et al. [2]]. To study the human body reactions to vibration, it is necessary to consider not only the pathological and physiological effects, but also the psychological effects. Furthermore, factors such as body position, direction of vibration, duration of vibration, body type and environment also affect human reactions.

The first important factor affecting human comfort is the vibration amplitude. Some investigators have stated that above a certain frequency, only amplitude affects human discomfort. Human beings are not directly sensitive to velocity. They are sometimes indirectly sensitive, as when high velocity produces high wind pressure upon part of the body. When carried inside a completely closed box moving without vibration, a human being could not tell whether the box was standing or being moved at low or extremely high velocity. The root mean square (rms) of acceleration has been considered the most appropriated factor to describe the human reaction to vibration as prescribed by international code [4].

The International Standard ISO 2631 [4] has set limits of exposure to vibrations in both vertical (foot to head direction) and horizontal directions, and deals with random and shock vibrations as well as harmonic vibration. The covered frequency range is from 1Hz to 80Hz, while the criteria are expressed in terms of measured effective root mean square of the acceleration (rms). Thus, human comfort phenomenon is considered frequency dependent problem. In this International Standard three different levels of human discomfort are distinguished. The first one is the reduced comfort boundary, which applies to the threshold at which activities such as eating, reading or writing are disturbed. The second one is the fatigue-decreased proficiency boundary, which applies to the level at which recurrent vibrations cause fatigue to personnel work with consequent reduction efficiency. This occurs at about three times the reduced comfort boundary. The third one corresponds to the exposure limit, which defines the maximum tolerable vibration with respect to health and safety, and is set at about six times the reduced comfort boundary. Usually the criteria are given by graphical representation for both longitudinal and transverse vibrations.

The attention is devoted to a narrow band acceleration random process. Narrow band means that the spectral density occupies only a narrow frequency band. As the structures oscillate predominantly in their natural frequencies, the narrow band model is indicated to study the structures dynamic response. In practice, good results can be obtained just considering the first mode of vibration. Accurate results are obtained considering the first two or three modes [5].

When it is assumed that the ergodic acceleration random process and its derivative are Gaussian processes, the distribution of peaks for narrow band acceleration random process is given by the classic Rayleigh distribution [5]. But, in a number of applications of the theory, the Gaussian assumption may not be valid. A more general Wiebull distribution is then used.

A closed expression for the mean square value of the cumulative discomfort damage is developed for a single narrow-band acceleration process. The convolution theorem permits to formulate the probabilistic model of the human response to random vibration for the cases involving two or more independent narrow band acceleration processes. Using first order Newton's quadrature formula numerical versions for convolution integrals are presented.

1

A.W. Irwin, "Motion in Tall Buildings", Second Century of Skyscraper, Council on Tall Buil, 759-778, Van Nostrand Reinhold Company, 1987.

2

R.R. Coermann, G.H. Ziegenruecker, A.L. Wittwer and H.E. Von Gierke, "The Passive Dynamic Mechanical Properpties of the human Thorax-Abdomen System and of the Whole Body System", Aerospace Medicine, 443-455, 1960.

3

S. Kitazaki and M.J. Griffin, "A modal analysis of whole-body vertical vibration, using a finite element model of the human body", Journal of Sound and Vibration, 83-103, 1997. doi:10.1006/jsvi.1996.0674

4

ISO-2631, "Guide to the Evaluation of Human Exposure to Whole-Body Vibration", 1978.

5

D.E. Newland, "An Introduction to Random Vibrations, Spectral & Wavelet Analysis", Logman, 1993.

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