EFFECT OF BACKREST INCLINATION ON APPARENT MASS AT THE SEAT AND THE BACKREST DURING VERTICAL WHOLE-BODY VIBRATION

Transcription

1 EFFECT OF BACKREST INCLINATION ON APPARENT MASS AT THE SEAT AND THE BACKREST DURING VERTICAL WHOLE-BODY VIBRATION Mingming Yang, Yi Qiu, and Michael J. Griin Human Factors Research Unit Institute o Sound and Vibration Research University o Southampton Southampton SO17 1BJ United Kingdom my8g11@soton.ac.uk Abstract Biodynamic models indicate that dynamic spinal orces depend on the biodynamic behaviour o the body, which varies with backrest inclination. With random vertical vibration (. to Hz at 1. ms - r.m.s.), this study measured the vertical in-line apparent mass and the ore-and-at cross-axis apparent mass at the seat pan and the backrest with 1 subjects sitting with dierent rigid lat backrests (vertical, 1,, 3, and no backrest). With the vertical backrest, the eect o contact at a lumbar support (at L) or a thoracic support (at T5) was investigated. Inclining the backrest tended to increase the resonance requency and decrease the apparent mass at the resonance in the vertical in-line apparent mass measured at the seat pan. With an inclined backrest, the principal peak in the vertical in-line apparent mass at the seat pan was broader, and the resonance requencies in the ore-andat cross-axis apparent mass and the vertical in-line apparent mass diered, suggesting changes in the motions o the thoracic and lumbar spine. With increasing inclination o the backrest, the overall dynamic orces exposed to the subjects in the vertical and ore-and-at directions increased in the requency range 6 to 15 Hz. It is concluded that varying the inclination o a backrest alters the motions o body parts and the ore-and-at and vertical dynamic orces at the seat pan and the backrest. 1. Introduction Drivers and passengers o many types o vehicle sit with their backs supported by a backrest. Backrest support can reduce the need or muscle activity to maintain posture in static conditions (Bennett et al., 1989) and stabilise the body so as to reduce the need or muscle activity in dynamic conditions (Oliveira et al., 1). A backrest can modiy the vibration transmitted through the body (e.g., Paddan and Griin, 1988) and so may aect the discomort caused by vibration (e.g., Basri and Griin, 13). The inclination o a seat backrest also inluences the vibration transmitted to the body (e.g., Pope et al., 1998) and the discomort caused by vibration (e.g., Basri and Griin, 13). Compared to sitting without a backrest, the use o backrest has been reported to reduce spinal loads during whole-body vertical vibration (.3 to 3 Hz at 1. ms - r.m.s.) and inclining the backrest urther reduces the orces measured in-vivo with vertebral body replacements (Rohlmann et al., 1). Presented at the 5 th United Kingdom Conerence on Human Responses to Vibration, held at ISVR, University o Southampton, Southampton, England, 9-1 September 15.

2 The orces in the lumbar spine can be predicted rom the sum o static spinal orces (caused by gravity) and dynamic spinal orces (induced by vertical vibration) using a simple biodynamic model (e.g., Yang et al., 13, 14). Such models suggest the dynamic spinal orces depend on the vibration transmitted to the upper body. This led to the current experimental investigation o the eects o a backrest on biodynamic responses. Compared to sitting without a backrest, a vertical backrest tends to increase the resonance requency in the vertical apparent mass and decrease the apparent mass at resonance (Toward and Griin, 9; Qiu and Griin, 1). In part, this may be because a backrest changes the curvature o the spine and, thereore, the dynamic response o the body (Griin, 199). Increased backrest inclination tends to urther increase the resonance requency and urther decrease the apparent mass at resonance (Toward and Griin, 9). The ore-and at cross-axis apparent mass is also aected by contact with a vertical backrest and whether the eet are supported (Nawayseh and Griin, 4). When sitting supported by a vertical backrest, the resonance requency in the ore-and-at cross-axis apparent mass seems to be correlated with the resonance requency in the vertical in-line apparent mass (e.g., Nawayseh and Griin, 4; Qiu and Griin, 1). The ore-and-at cross-axis apparent mass at the seat has not been reported with inclined backrests. During vertical whole-body vibration, there can be considerable orces at a vertical backrest in both the vertical and ore-and-at directions, with both the vertical in-line apparent mass and the ore-andat cross-axis apparent mass at the backrest having resonances around 5 Hz (e.g., Nawayseh and Griin, 4). Dynamic orces in the vertical and ore-and-at directions have not been reported with an inclined backrest. The objective o this study was to investigate the vertical in-line apparent mass and ore-and-at cross-axis apparent mass at the seat pan and the backrest and how backrest inclination aects the overall dynamic orces when seated. It was hypothesised that with increasing inclination o a backrest the ore-and-at cross-axis apparent mass at the seat pan would increase, because there would be more excitation o the body in the ore-and-at direction. The measured data were required or the development biodynamic models o the response o the seated human body to vertical whole-body vibration and predict spinal orces when sitting with dierent backrests.. Methods.1 Apparatus Vertical vibration was generated by a 1-m vertical vibrator. A rigid seat with an adjustable rigid backrest was mounted on the platorm o the vibrator (Figure 1). An aluminium alloy and plywood backrest was mounted on the rigid seat so that it could be adjusted to inclinations rom degrees (vertical) to 6 degrees. When vertical, the backrest extended rom 1 mm to 7 mm above the seat pan surace. To produce backrest contact in either the lumbar region or the thoracic region when sitting with a vertical backrest, the subjects were asked to adjust the position o their pelvis on the seat to provide the required contact location.

3 A orce plate (Kistler 981 B) consisting o our tri-axial quartz transducers at the our corners o a rectangular welded steel rame (6 mm x 4 mm) was secured on the supporting surace o the seat to measure the dynamic orces in vertical and ore-and-at directions at the seat pan interace. Another orce plate, consisting our tri-axial orce transducers (Kistler 96) at the our corners o a rectangular plywood rame (6 mm x 5 mm) was mounted on the backrest. The signals rom the orce transducers were ampliied by Kistler 573 charger ampliiers. One single-axis piezo-resistive accelerometer (Entran EGCSY-4D-1) was mounted at the centre o the orce plate on the seat pan to measure the vertical acceleration. Two more single-axis piezoresistive accelerometers (Entran EGCSY-4D-1) were mounted at the middle o the backrest rame to measure the acceleration normal to the backrest surace and parallel to the backrest surace. The signals measured at the our corners o the orce plate at the seat pan were summed to give two signals corresponding to the vertical and ore-and-at orces. The orce signals rom each corner o the backrest in directions normal and parallel to the backrest surace were acquired individually. All orces and acceleration signals were acquired with a 16-channel HVLab data acquisition system at a sampling rate o 56 samples per second via 1-Hz anti-aliasing ilters. Adjustable backrest F n F p Force transducers at backrest Force plate at seat F xs F Two accelerometers at backrest Single-axis accelerometer at seat a Figure 1 Seat on vibrator with a subject sitting against a º-inclined backrest. Experimental design Twelve healthy male subjects with median age 9 years (range to 34 years), median height cm (range 16 to 184 cm) and median weight 69 kg (range 6 to 1 kg) participated in the experiment. During the experiment subjects sat in the ollowing conditions: (i) upright without backrest contact (i.e., NB); (ii) against the vertical backrest with contact at either L or T5 (i.e., B L and B T5 );

4 (iii) against the backrest inclined by 1º, º or 3º with contact only at the thoracic region o the back (i.e., B 1, B and B 3 ). In all six conditions, the eet were supported on an adjustable ootrest to obtain average thigh contact. The hands rested on the lap. In each condition, the subjects were exposed to 6-s periods o random vertical vibration with approximately lat constant-bandwidth acceleration spectra (. to Hz at 1. ms - r.m.s.). The experiment was approved by the Ethics Committee o the Faculty o Engineering and the Environment at the University o Southampton (approval number 1434)..3 Data analysis.3.1 Mass cancellation For the calculation o the orces at the seat and the backrest, the eect o the mass o the orce plates on the measured dynamic orces was eliminated by mass cancellation in the time-domain. The acceleration time-history was multiplied by the mass o the orce platorm above the orce sensors and the resulting orce subtracted rom the measured orce. With inclined backrests, mass cancellation was perormed on the dynamic orces in the directions normal and parallel to the backrest surace. In the normal and the parallel direction, the time history o the acceleration was multiplied by the mass o the plate and then subtracted rom the measured orce time history in the same direction..3. Transer unctions Various measures o apparent mass were calculated rom transer unctions between dynamic orce and acceleration using the cross spectral density method. For the vertical in-line apparent mass at the seat pan, M z (), the measured orce and acceleration were in the same direction (i.e., vertical). For the ore-and-at cross-axis apparent mass at the seat pan, M x (), the measured ore-and-at orce was perpendicular to the vertical acceleration at the seat pan. The two apparent masses at the seat pan, M z () and M x (), and the associated coherencies, C z () and C x (), were calculated as: F Mz( ), ( ) F xs Mx ( ), ( ) C C z x ( ) ( ) F, G ( ) G ( ) a F F xs (1) G ( ) G ( ) a Fxs where, G ( ) is the auto-spectra o the vertical acceleration at the seat pan, a (t), and G Fxs a G F ( ) are the auto-spectra o vertical and ore-and-at orces measured at the seat pan, F (t) and F xs (t), and G a F ( ) and G a F ( ) are the cross-spectra between a (t) and F (t) and between a (t) xs and F xs (t). The orce transducers at the backrest measured the dynamic orces in directions normal to the surace o the backrest, F n, and parallel to the surace o the backrest, F p. These orces were

5 combined, ater adjusting or the inclination o the backrest, so as to calculate the orces in the vertical and ore-and-at directions (i.e., the same coordinates used or calculating the vertical in-line and oreand-at cross-axis apparent mass at the seat pan). For a backrest inclination angle α, the orce time histories in the vertical and ore-and-at directions were calculated as: F F zb xb ( t) F n ( t) F n ( t)sin F p ( t)cos F ( t)cos p ( t)sin, () where F n (t) and F p (t) are the orce time-histories measured by the orce transducers in the local coordinate system, and F zb (t) and F xb (t) are the orces adjusted to the vertical and ore-and-at directions, respectively. The vertical in-line apparent mass at the back, M zzb (), was given by the transer unction between F zb (t) and a (t). The ore-and-at cross-axis apparent mass at the back, M xzb (), was given by the transer unction between F xb (t) and a (t). The two apparent masses at the back, M zzb () and M xzb (), and the associated coherencies, C zzb (), C xzb (), were calculated as: F zb Mzzb( ), Czzb ( ) ( ) F xb Mxzb ( ), Cxzb ( ) ( ) F zb, G ( ) G ( ) a Fzb F xb (3) G ( ) G ( ) a Fxb where GF zb and GF xb are the auto-spectra o the calculated vertical orce F zb (t) and the calculated ore-and-at orce F xb (t) at the backrest; zb and xb are the cross-spectra between a (t) and F zb (t) and between a (t) and F xb (t)..3.3 Statistical analysis F Non-parametric statistical tests (Friedman two-way analysis o variance or k-related samples and Wilcoxon matched-pairs signed-ranks test or two-related samples) were used. The Spearman rank order correlation was employed in to investigate associations between variables. 3. Results 3.1 Apparent mass at the seat pan Vertical in-line apparent mass The median vertical apparent masses o the 1 subjects in each o the six sitting conditions (without backrest and with the vertical backrest at L or T5 or the backrest inclined by 1, and 3º) are shown in Figure. The vertical apparent mass in the upright sitting posture shows a principal resonance at about 5 Hz. Some subjects also showed a secondary resonance around 8 to 1 Hz. These indings are consistent with previous studies (e.g., Fairley and Griin, 1989). F

6 Apparent mass (kg) Phase (rad) With the addition o the vertical backrest at T5, the vertical in-line apparent mass reduced at the 5-Hz resonance (p=.1). Similarly, with increasing inclination o the backrest (B T5, B 1, B and B 3 ), the vertical in-line apparent mass reduced at requencies around the 5-Hz resonance (p<.1, Friedman) and at lower requencies. Although over the our backrest inclinations (B T5, B 1, B and B 3 ) the resonance requency appears to increase, the change was not statistically signiicant (p=.1, Friedman). Even so, the resonance requency in the vertical apparent mass was signiicantly greater with the 3º backrest inclination than with each o the other backrest conditions (p<.5, Wilcoxon). Changing the location o contact with a vertical backrest rom L (B L ) to T5 (B T5 ) did not change the resonance requency or the apparent mass at the resonance in the vertical in-line apparent mass at the seat pan (p>.5, Wilcoxon). Dierences in the resonance requencies o the apparent mass and the apparent mass at resonance are summarised in Table 1. Table 1 Statistical signiicance o the eects o backrest inclination on the resonance requency in the vertical apparent mass at the seat pan and the modulus o the apparent mass at resonance. Wilcoxon matched-pairs signed ranks test. Resonance requency o vertical apparent mass at the seat pan Vertical apparent mass at the seat pan at the resonance requency NB B L B T5 B 1 B B 3 NB B L B T5 B 1 B B 3 NB - ns ns ns ns * NB - * * ** ** ** B L - ns ns ns * B L - ns * ** ** B T5 - ns ns * B T5 - ** ** ** B 1 - ns ** B 1 - ** ** B - * B - ** B 3 - B 3 - ns: not signiicant; * p.5; ** p Figure Vertical in-line apparent mass at the seat pan in dierent sitting conditions: normal upright sitting posture NB ( ); vertical backrest contact at L, B L ( ); vertical backrest contact at T5, B T5 ( ); contact with 1º inclined backrest, B 1 ( ); º inclined backrest, B ( ); 3º inclined backrest, B 3 ( ). Let: modulus; right: phase. Median values rom 1 subjects. With the backrest inclined to and 3 degrees, the vertical apparent mass at the resonance requency broadened (Figure ) and about 6 o the 1 subjects showed two peaks in the apparent

7 Apparent mass (kg) phase (rad) mass in the range 5 to 7.5 Hz. With increasing inclination o the backrest, the magnitude o the peak at the higher requency tended to be greater than the irst peak, especially when the backrest was inclined to 3º Fore-and-at cross-axis apparent mass The ore-and-at cross-axis apparent mass at the seat pan when sitting with no backrest showed a principal resonance around 5 Hz (Figure 3), similar to the resonance requency in the vertical in-line apparent mass at the seat pan. With the addition o the vertical backrest at either L or T5 there was no change in either the ore-andat cross axis apparent mass at resonance (p>.5, Wilcoxon) or the resonance requency (p>.5, Wilcoxon). When the contact location with the vertical backrest changed rom L to T5, there was no change in either the resonance requency o the ore-and-at cross-axis apparent mass at the seat pan or the apparent mass at this resonance (p>.5, Wilcoxon) Freqeuncy (Hz) Figure 3 Fore-and-at cross-axis apparent mass at the seat pan in dierent sitting conditions: normal upright sitting posture NB ( ); vertical backrest contact at L, B L ( ); vertical backrest contact at T5, B T5 ( ); contact with 1º inclined backrest, B 1 ( ); º inclined backrest, B ( ); 3º inclined backrest, B 3 ( ). Let: modulus; right: phase. Median values rom 1 subjects. Table Statistical signiicance o the eects o backrest inclination on the resonance requency in the ore-and-at cross-axis apparent mass at the seat pan and the modulus o the cross-axis apparent mass at resonance. Wilcoxon matched-pairs signed ranks test. Resonance requency o ore-and-at apparent mass at the seat pan Fore-and-at apparent mass at the seat pan at the resonance requency NB B L B T5 B 1 B B 3 NB B L B T5 B 1 B B 3 NB - ns ns ns ns * NB - ns ns * ns ns B L - ns ns * ** B L - ns ** ns ns B T5 - ns * ** B T5 - * ns ns B 1 - * ** B 1 - ns ns B - ** B - ns B 3 - B 3 - ns: not signiicant; * p.5; ** p.1.

8 Apparent mass(kg) Phase (rad) Comparing the ore-and-at cross-axis apparent mass measured at the seat pan with the vertical backrest at T5 and the three inclinations o the backrest (i.e., B 1, B and B 3 ), there was a change in the requency o the principal resonance (p<.1, Friedman), with a dierence between inclinations o 1º and º (p=.13, Wilcoxon; Table, Figure 3). However, the ore-and-at cross-axis apparent mass at resonance did not dier over the vertical backrest at T5 and the three inclinations o the backrest (p=.1335, Friedman). More detail on the dierences in the resonance requency o the ore-and-at apparent mass and the ore-and-at apparent mass at resonance are shown in Table. The ore-and-at cross-axis apparent mass at the seat pan increased at requencies less than the resonance requency when there was backrest contact at T5 (p=., Wilcoxon; analysed at.5 Hz), and increased urther with increasing inclination o the backrest (p=.1, Friedman; analysed at.5 Hz; Figure 3). 3. Apparent mass at the backrest 3..1 Vertical in-line apparent mass The vertical in-line apparent mass at the backrest showed a resonance in the requency range 4 to 5.5 Hz (Figure 4). The resonance requencies in the vertical in-line apparent mass at the backrest were similar with contact at L and T5 (p>.5, Wilcoxon), although the apparent mass at resonance was greater with contact at T5 than contact at L (p=.9, Wilcoxon) Figure 4 Vertical in-line apparent mass at the backrest in dierent sitting conditions: vertical backrest contact at L, B L ( ); vertical backrest contact at T5, B T5 ( ); contact with 1º inclined backrest, B 1 ( ); º inclined backrest, B ( ); 3º inclined backrest, B 3 ( ). Let: modulus; right: phase. Median values rom 1 subjects.

9 Apparent mass (kg) phase (rad) Comparing the vertical in-line apparent mass measured at the backrest with the vertical backrest at T5 and with the three inclinations o the backrest (i.e., B 1, B and B 3 ), there was a change in both the resonance requency (p=.6, Friedman) and the apparent mass at resonance (p<.1, Friedman). The resonance requency in the apparent mass increased between the vertical backrest at T5 and each o the three inclined backrest conditions (p<.5, Wilcoxon). However, the resonance requencies in the vertical in-line apparent mass did not dier with 1º, º and 3º inclination o the backrest (p=.146, Friedman). The vertical in-line apparent mass at the backrest increased at requencies less than the resonance requency as the inclination o the backrest increased (Figure 4). 3.. Fore-and-at cross-axis apparent mass In all backrest conditions, the median ore-and-at cross-axis apparent mass at the back showed a peak around 5 Hz (Figure 5). When contact with the vertical backrest changed rom L to T5, the ore-and-at cross-axis apparent mass at the back at resonance increased (p=.35, Wilcoxon) although the resonance requency did not change (p=.98, Wilcoxon). Comparing the ore-and-at cross-axis apparent mass measured with the vertical backrest at T5 and with the three inclinations o the backrest (i.e., B 1, B and B 3 ), there was a change in the resonance requency (p=.9, Friedman) and the apparent mass increased at all requencies as the backrest inclination increased Figure 5 Fore-and-at cross-axis apparent mass at the backrest in dierent sitting conditions: vertical backrest contact at L, B L ( ); vertical backrest contact at T5, B T5 ( ); contact with 1º inclined backrest, B 1 ( ); º inclined backrest, B ( ); 3º inclined backrest, B 3 ( ). Let: modulus; right: phase. Median values rom 1 subjects.

10 4. Discussion 4.1 Eect o vertical and inclined backrests on the vertical in-line apparent mass at the seat pan An increase in the resonance requency o the vertical in-line apparent mass at the seat pan has been reported when the back is supported by a vertical backrest (Nawayseh and Griin, 4) with the resonance requency increasing urther i the backrest is inclined (Toward and Griin, 9). In the present study, there was a similar increasing trend in the resonance requency o the vertical in-line apparent mass at seat pan, although a statistically signiicant dierence was only ound with a 3º inclined backrest. As the backrest inclination increased, the vertical apparent mass measured at the seat pan decreased around the 5-Hz resonance and at lower requencies, presumably because more o the weight o the body was supported by the backrest. With increasing backrest inclination, the peak in the vertical apparent mass around the resonance broadened. With the backrest inclined to º or 3º, some subjects exhibited two peaks at requencies around the resonance (in the range 4 to 8 Hz). According to a modal analysis o the human body in an upright sitting posture without backrest (e.g., Kitazaki and Griin, 1997; Matsumoto and Griin, 1), the resonance requency (around 5 Hz) arises rom several body modes that are merged by the heavy damping o the body. The modes include pitch motion o the pelvis with bending o the spine combined with shear and axial deormation o buttocks tissues. The two peaks observed in the present study indicate that two or more body modes were excited in the range o 4 to 8 Hz and that increasing the inclination o the backrest separated the two modes. 4. Eect o vertical and inclined backrests on ore-and-at cross-axis apparent mass at the seat pan When sitting without a backrest, the principal resonance in the ore-and-at cross-axis apparent mass at the seat pan was correlated with the resonance requency in the vertical in-line apparent mass (p=<.1, Spearman). This correlation is consistent with the indings o some previous studies (Nawayseh and Griin, 4; Qiu and Griin, 1), and suggests that when sitting without a backrest the resonances evident in the vertical in-line apparent mass and the ore-and-at cross-axis apparent mass have a common cause. When sitting with a vertical backrest and supported at L or T5 (B L and B T5 ), the resonance requencies in the vertical in-line apparent mass and the ore-and-at cross-axis apparent mass were also correlated (B L, p=.1; B T5, p=.3; Spearman). However, with the backrest inclined (B 1, B and B 3 ), the correlation was no longer statistically signiicant (p>.5, Spearman). The resonance tended to be at a lower requency in the ore-and-at cross-axis apparent mass than in the vertical inline apparent mass, especially when the backrest was inclined by º and 3º (at º 4 Hz in the ore-and-at cross-axis and 5 Hz in the vertical in-line apparent mass; at 3º 4 Hz in the ore-and-at cross-axis and 5.5 Hz in the vertical in-line apparent mass; Figures and 3). The absence o correlations when the backrest was inclined indicate that dierent body motions then contribute to the resonances in the ore-and-at cross-axis apparent mass and the vertical in-line apparent mass.

11 4.3 Vertical in-line apparent mass and ore-and-at cross-axis apparent mass at the back When contact with the vertical backrest changed rom L (B L ) to T5 (B T5 ), both the vertical in-line apparent mass and the ore-and-at cross-axis apparent mass at the backrest increased at the resonance requency. The resonance in the ore-and-at cross-axis apparent mass at the back may be inluenced by the motions o head-neck system and ore-and-at motion o the spine (Nawayseh and Griin, 4). The increased ore-and-at cross-axis apparent mass at the backrest at resonance suggests more motion o the spine with the back support in the thoracic region (i.e., B T ), although the dierences are not large. With increasing inclination o the backrest, the vertical in-line apparent mass and the ore-and-at cross-axis apparent masses at the back increased. The increase in both apparent masses at low requencies indicates that more mass was supported on the backrest as the backrest inclination increased. The ore-and-at cross-axis apparent mass at the back tended to be greater than the vertical in-line apparent mass at the back. At the resonance, with increasing inclination o the backrest (rom B T5 to B 3 ) the median ore-and-at cross-axis apparent mass at the backrest increased rom to 4 kg whereas the median vertical in-line apparent mass at the backrest increased rom 4 to 1 kg (Figures 4 and 5). 4.4 Dynamic orces experienced by the seated body in the vertical and ore-and-at directions The measurements allow the calculation o how the sum o the vertical in-line and ore-and-at crossaxis orces at the seat and the backrest vary according to the nature o the backrest. The transer unctions between the vertical seat acceleration and the sums o the orces at the seat pan and the backrest in the vertical and ore-and-at directions were calculated in the requency domain or each subject to give the overall vertical in-line apparent mass and the overall ore-and-at cross-axis apparent mass (Figure 6). No dierence has been reported in the apparent mass at.78 Hz calculated rom the seat acceleration and the sum o vertical orces (at the seat pan and backrest) when sitting with and without a backrest (Nawayseh and Griin, 4). In the present study, irrespective o the backrest condition, the overall vertical apparent mass at very low requencies (e.g.,.5 Hz) was close to the static mass when sitting with no backrest (Figure 6). The slight dierences could be due to variations in the support rom the ootrest when the backrest varied. With increasing inclination o the backrest the overall vertical in-line dynamic orces showed no signiicant change at requencies up to 5 Hz but increased at higher requencies in the range 6 to 15 Hz (p<.1, Friedman). With increasing inclination o the backrest, the overall ore-and-at cross-axis dynamic orces increased in the requency range 5 to 15 Hz (p<.1, Friedman).

12 Apparent mass (kg) phase (rad) Apparent mass (kg) phase (rad) Figure 6 Overall vertical in-line apparent mass (top row) and overall ore-and-at cross-axis apparent mass (bottom row) in dierent sitting conditions: normal upright sitting posture NB ( ); vertical backrest contact at L, B L ( ); vertical backrest contact at T5, B T5 ( ); contact with 1º inclined backrest, B 1 ( ); º inclined backrest, B ( ); 3º inclined backrest, B 3 ( ). Let: modulus; right: phase. Median values rom 1 subjects. 5. Conclusion Contact with an inclined backrest reduces the mass o the body supported on the seat pan but increases the ore-and-at dynamic shearing orce between body and the seat pan. The presence o an inclined backrest alters the body motions and resonance requencies in the vertical in-line and ore-and-at cross-axis apparent mass measured at the seat pan. When there is no backrest or a vertical backrest, the resonance requency in the ore-and-at crossaxis apparent mass at the seat pan is correlated with the resonance requency in the vertical in-line apparent mass at the seat pan. However, the two resonances became less correlated with increasing inclination o the backrest, suggesting dierent body modes may contribute to the vertical in-line and ore-and-at cross-axis apparent mass when the backrest is inclined. 6. Acknowledgements This work was undertaken on contract ROD HQ SG 34//8/5 in association with the Institute o Naval Medicine. The assistance o Dr GS Paddan is grateully acknowledged.

13 7. Reerences Basri B and Griin MJ (13) Predicting discomort rom whole-body vertical vibration when sitting with an inclined backrest, Applied Ergonomics, Volume 44, Issue 3, Bennett DL, Gillis DK, Portney LG, Romanow M and Sanchez AS (1989) Comparison o integrated electromyographic activity and lumbar curvature during standing and sitting in three chairs, Physical Therapy, 69 (11), Fairley TE and Griin MJ (1989) The apparent mass o the seated human body: vertical vibration. Journal o Biomechanics,, Griin MJ, Handbook o Human Vibration, Academic Press Limited, London, 199. Kitazaki S and Griin MJ (1997) A modal analysis o whole-body vertical vibration, using a inite element model o the human body, Journal o Sound and Vibration,, Mansield NJ and Griin MJ () Eects o posture and vibration magnitude on apparent mass and pelvis rotation during exposure to whole-body vertical vibration, Journal o Sound and Vibration, 53(1), Matsumoto Y and Griin MJ (1) Modelling the dynamic mechanisms associated with the principal resonance o the seated human body, Clinical Biomechanics, 16, Nawayseh N and Griin MJ (4) Tri-axial orces at the seat and backrest during whole-body vertical vibration, Journal o Sound and Vibration, 77, Oliveira CG, Simpson DM and Nadal J (1) Lumbar back muscle activity o helicopter pilots and whole-body vibration, Journal o Biomechanics 34, Paddan GS and Griin MJ (1988) The transmission o translational seat vibration to the head I. Vertical seat vibration, Journal o Biomechanics, Vol.1. No.3. pp Pope MH, Wilder DG and Magnusson M (1998) Possible mechanisms o low back pain due to wholebody vibration, Journal o Sound and Vibration, 15(4), Qiu Y and Griin MJ (1) Biodynamic response o the seated human body to single-axis and dualaxis vibration: Eect o backrest and non-linearity, Industrial Health, 5, Rohlmann A, Hinz B, Blüthner R, Graichen F and Bergmann G (1) Loads on a spinal implant measured in vivo during whole-body vibration, Eur Spine J, 19, Toward MGR and Griin MJ (9) Apparent mass o the human body in the vertical direction: Eect o seat backrest, Journal o Sound and Vibration, 37, Wang W., Rakheja S., and Boileau P.E. (4) Eects o sitting postures on biodynamic response o seated occupants under vertical vibration, International Journal o Industrial Ergonomics, 34, Yang M, Qiu Y and Griin MJ (13) Developing a simple mathematical model o the seated human body to predict spinal orces caused by vertical vibration, 48th UK conerence on human response to vibration, Ascot, UK,16th 18th September. Yang M, Qiu Y and Griin MJ (14) Biodynamic modelling o spinal orces caused by vertical vibration in three sitting postures, 49th UK conerence on human response to vibration, Buxton, UK, 9th 11th September.