Biodynamics of the seated human body with dual-axis excitation: nonlinearity and cross-axis coupling.
University of Southampton, Institute of Sound and Vibration Research,
The apparent mass of the seated human body and the transmissibility to the upper-body (i.e., the spine and the pelvis) during vertical vibration excitation have been reported to have resonance frequencies around 5 Hz. With fore-and-aft excitation the apparent mass shows a first peak around 1 Hz and second mode around 2 to 3 Hz. Little is known about how the motion of the upper-body during excitation in one direction is affected by the addition of vibration in an orthogonal direction (i.e., the cross-axis coupling). The principal objective of the research reported in this thesis was to identify how the resonances in the apparent mass and transmissibility, and their association, depends on the magnitude of the inline vibration excitation and the addition of an orthogonal vibration excitation. The research was also designed to investigate the characteristics necessary in mathematical models that represent the cross-axis coupling and nonlinearity evident in the biodynamic responses of the human body.
The movement of the body (over the first, fifth and twelfth thoracic vertebrae, the third lumbar vertebra, and the pelvis) in the fore-and-aft and vertical directions (and in pitch at the pelvis) was measured in 12 seated male subjects during random vertical vibration excitation (over the range 0.25 to 20 Hz) at three vibration magnitudes (0.25, 0.5 and 1.0 ms-2 r.m.s.) and during fore-and-aft vibration excitation over the same frequency range and at the same three vibration magnitudes. At the highest magnitude of vertical excitation the effect of adding fore-aft excitation (at 0.25, 0.5, and 1.0 ms-2 r.m.s.) was investigated. Similarly, at the highest magnitude of fore-and-aft excitation the effect of adding vertical vibration (at 0.25, 0.5, and 1.0 ms-2 r.m.s.) was investigated. The forces in the fore-and-aft and vertical directions on the seat surface were also measured so as to calculate apparent masses. The subjects adopted a normal upright posture, an erect posture, and a slouched posture. Resonance frequencies in the apparent mass and transmissibility during vertical excitation decreased with increasing magnitude of vertical excitation and with the addition of fore-and-aft excitation. The modulus of the first peak in the apparent mass and transmissibility during fore-and-aft excitation decreased with increasing magnitude of fore-and-aft excitation and with the addition of vertical excitation. Complex vibration modes in the upper-body appear to be responsible for the resonances in both the vertical and the fore-and-aft apparent masses. Compared to the normal upright posture, the erect posture tended to increase the resonance frequency in the apparent mass and transmissibility associated with vertical excitation but decrease the resonance frequency in the apparent mass and transmissibility associated with fore-and-aft excitation. The association between resonances in the transmissibility to the upper body and the resonance in the apparent mass varied with vertical excitation but not with fore-aft excitation.
A seven degree-of-freedom multi-body model indicated that the resonance frequency in the vertical apparent mass on the seat and the vertical transmissibility to the upper-body with either vertical or dual-axis excitation is sensitive to the vertical stiffness of tissues beneath the pelvis and closely related to the vertical motion of the upper body. It has also been shown that the first mode of the fore-and-aft apparent mass and the fore-and-aft transmissibility can be attributed to the fore-and-aft movement of the upper-body due to the pelvis pitch, while the second mode can be attributed to the fore-and-aft movement of the upper-body caused by shear deformation of the pelvis tissue. It is suggested that a mathematical model developed with single-axis excitation can represent the biodynamic response with dual-axis excitation by changing these sensitive parameters (e.g., the stiffness of the tissue beneath the pelvis).
A finite element human body model with flexible bodies representing the tissue beneath the pelvis and thighs and rigid bodies representing other body segments provided sensible prediction of the first resonance frequencies and the associated modulus in the vertical inline and fore-and-aft cross-axis apparent mass on the seat and the transmissibility to the lumbar spine, as well as the pressure distribution on the seat surface. With the flexible bodies assigned the material properties of nonlinear low density foam, the model was allowed to reflect the softening effect (i.e., a reduce in the resonance frequency of the vertical apparent mass) when the when the magnitude of the vertical excitation was increased.
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