Elsevier

Journal of Biomechanics

Volume 61, 16 August 2017, Pages 176-182
Journal of Biomechanics

Dynamic forces over the interface between a seated human body and a rigid seat during vertical whole-body vibration

https://doi.org/10.1016/j.jbiomech.2017.07.015Get rights and content

Abstract

Biodynamic responses of the seated human body are usually measured and modelled assuming a single point of vibration excitation. With vertical vibration excitation, this study investigated how forces are distributed over the body-seat interface. Vertical and fore-and-aft forces were measured beneath the ischial tuberosities, middle thighs, and front thighs of 14 subjects sitting on a rigid flat seat in three postures with different thigh contact while exposed to random vertical vibration at three magnitudes. Measures of apparent mass were calculated from transfer functions between the vertical acceleration of the seat and the vertical or fore-and-aft forces measured at the three locations, and the sum of these forces. When sitting normally or sitting with a high footrest, vertical forces at the ischial tuberosities dominated the vertical apparent mass. With feet unsupported to give increased thigh contact, vertical forces at the front thighs were dominant around 8 Hz. Around 3–7 Hz, fore-and-aft forces at the middle thighs dominated the fore-and-aft cross-axis apparent mass. Around 8–10 Hz, fore-and-aft forces were dominant at the ischial tuberosities with feet supported but at the front thighs with feet unsupported. All apparent masses were nonlinear: as the vibration magnitude increased the resonance frequencies decreased. With feet unsupported, the nonlinearity in the apparent mass was greater at the front thighs than at the ischial tuberosities. It is concluded that when the thighs are supported on a seat it is not appropriate to assume the body has a single point of vibration excitation.

Introduction

Studies of human responses to whole-body vibration have mostly considered the seated body to have a single principal vibration input beneath the pelvis, and standards for assessing vibration severity require that vibration acceleration is measured on seat surfaces beneath the ischial tuberosities (British Standards Institution, 1987, International Organization for Standardization, 1997). Similarly, methods of measuring and predicting the transmission of vibration through seats assume that only the transmission of vibration to the ischial tuberosities is of interest.

The transmission of vibration through a seat depends on the dynamic characteristics of the body supported on the seat (Fairley and Griffin, 1986, Wei and Griffin, 1998a, Tufano and Griffin, 2012). The tissues of the body vary over the area of contact with a seat, so the transmission of vibration through a seat cushion and into the body can be expected to vary over this area. The perception of vibration also depends on the transmitted vibration and the physiology of the tissues being excited, so understanding of the discomfort caused by the vibration of a seat pan is currently limited by assuming the body is excited at only one location (i.e., beneath the ischial tuberosities).

The apparent mass of the seated human body (the transfer function between the overall dynamic forces over the sitting surface to the acceleration beneath the ischial tuberosities) indicates how the forces acting to the body vary with the frequency of the vibration excitation. The vertical apparent mass of the body is similar to the sitting mass at very low frequencies (e.g., 0.25 Hz). With increasing frequency of vibration, the vertical apparent mass increases to a peak at a principal resonance around 5 Hz and then decreases (e.g., Fairley and Griffin, 1989, Wang et al., 2004, Mansfield and Maeda, 2007, Toward and Griffin, 2011, Zhou and Griffin, 2014, Dewangan et al., 2015). Simple models with one or two degrees of freedom can represent the vertical apparent mass of the body (e.g., Fairley and Griffin, 1989, Wei and Griffin, 1998b, Toward and Griffin, 2010), but the movements of the body during whole-body vibration are much more complex than the movements of such simple models.

At the principal vertical resonance around 5 Hz the entire body moves vertically with deformation of the soft tissues beneath the ischial tuberosities (Kitazaki and Griffin, 1997, Kitazaki and Griffin, 1998, Pankoke et al., 1998, Matsumoto and Griffin, 2001), so local forces beneath the ischial tuberosities can be expected to show a peak at this frequency. However, the body has other modes of vibration involving pitch and fore-and-aft motion of the pelvis at frequencies less than 10 Hz (Kitazaki and Griffin, 1997, Kitazaki and Griffin, 1998, Pankoke et al., 1998) with deformation and forces beneath the ischial tuberosities and the thighs that will vary with the frequency of vibration. In this study, the transfer function between the vertical acceleration of the seat and the dynamic force measured over a local area of contact with a rigid flat seat is called the ‘localised apparent mass’.

The apparent mass of the human body is nonlinear: as the vibration magnitude increases the principal resonance frequency decreases (e.g., Fairley and Griffin, 1989, Matsumoto and Griffin, 2002, Rakheja et al., 2002, Nawayseh and Griffin, 2003, Huang and Griffin, 2008, Zhou and Griffin, 2014). It is unknown whether localised apparent masses measured along the thighs also show nonlinear behaviour.

This study was designed to identify how localised apparent masses measured over the seat-body interface contribute to the overall apparent mass of the seated human body. It was hypothesised that the localised vertical apparent mass at the thighs would have a principal resonance frequency that is different from the resonance frequency in the localised vertical apparent mass at the ischial tuberosities. It was also hypothesised that the nonlinearity in the localised vertical apparent mass at the thighs would differ from the nonlinearity in the localised vertical apparent mass measured at the ischial tuberosities.

Section snippets

Equipment

A rigid seat with a flat horizontal surface was secured to the platform of a 1 m vertical electro-hydraulic vibrator (Fig. 1). An accelerometer (Entran EGCSY-240D-10) was mounted beneath the centre of the seat pan to measure the acceleration of the vibration. A multi-axis force plate (Kistler 9281B) was secured to the seat frame to measure the overall force on the seat surface. Two tri-axial load cells (Kistler 9602) supported a rectangular wooden plate at the front area of the force plate to

Overall and localised vertical in-line apparent masses

The overall vertical apparent mass of the body and the localised vertical apparent masses at the ischial tuberosities, the middle thighs, and the front thighs are shown for individual subjects in Fig. 3. The median apparent masses are shown in Fig. 4. The same trends were observed with all three magnitudes of vibration (i.e., 0.25, 0.5 and 1.0 m s−2 r.m.s.).

In all three postures, there was no significant difference in the frequency of the principal resonance in the overall vertical apparent mass

Vertical in-line apparent masses

At all frequencies the localised vertical apparent mass was greater at the ischial tuberosities than at either the middle thighs or the front thighs, except from 8 to 10 Hz in the feet hanging posture where the localised vertical apparent mass was greater at the front thighs than at the other two locations (Fig. 4). This shows that the localised vertical apparent mass at the ischial tuberosities dominates the overall vertical apparent mass of the human body except between 8 and 10 Hz in the feet

Conflict of interest statement

None declared.

References (26)

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