Medical and Biological Engineering and Computing

, Volume 36, Issue 6, pp 686–692 | Cite as

Three-dimensional biomechanical model for simulating the response of the human body to vibration stress



Several investigations have revealed that long-term exposure to whole-body vibrations can induce low back pain. In analogy to materials handling, the health risk can be assessed if the forces transmitted in the spine during vibration are known. To estimate the forces a biomechanical model has been developed in which the human trunk, neck, head and arms are represented by 16 rigid bodies. An additional body simulates the vibrating seat. The bodies are connected by visco-elastic joint elements, and 56 force elements imitate the trunk and neck muscles. The motion equations are derived by means of the dynamics of systems of rigid bodies, and the motions are simulated in three directions. The frequency-response functions between the accelerations of the seat and the head satisfactorily correspond to data reported in the literature. The spine forces are composed of a static part, due to body posture, and a vibration-induced part. The relation between the oscillating parts of the forces transmitted from seat to pelvis and the spine forces are also described by frequency-response functions. To assess the health risk the simulated spine forces must be compared with the strength of the spine, bearing in mind that this is dependent on the number of load cycles.


Frequency-response function Health risks Rigid bodies Simulation Spine forces Strength of the spine 


x, y, z

coordinates according to the basicentric system of ISO 2631-1


acceleration of the excitation


frequency of the excitation


vector of the generalised coordinates of the multibody system

\(\ddot q\)

second time derivative ofq

A andB

matrices of the equation of motion


stiffness matrix


frequency-response function between accelerations


frequency-response function between time dependent forces


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Copyright information

© IFMBE 1998

Authors and Affiliations

  1. 1.Institut für Arbeitsphysiologie an der Universität DortmundDortmundGermany

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