Assessing the discomfort of dual-axis whole-body vibration

This paper reports on an experiment designed to provide information fundamental to the prediction of the discomfort of multi-axis vibration. Seated subjects were exposed to various level and phase combinations of 3·15 Hz vertical (a_z) and 3·15 Hz lateral (a_y) sinusoidal vibration. One part of the experiment determined the levels of two single-axis vibrations (a_zanda_y separately) which produced similar discomfort to a selection of dual-axis vibrations. In another part of the experiment subjects adjusted the level of a 3·15 Hz motion in one of the two axes to produced similar discomfort to each of seven levels of the same frequency in the other axis.It was concluded that for dual-axis motions of the type investigated the discomfort is not greatly influenced by the phase between the two single-axis components producing the motion. Thus, the discomfort caused by the circular motion given by the combinations of the two sinusoidal components differing in phase by 90 degrees is similar to that caused by the translational motion produced by the same components combined with zero phase shift. The results confirm that a meaningful estimate of the relative discomfort produced by dual-axis stimuli can be determined from the levels of a single-axis reference motion appropriately adjusted by subjects. The level of a single-axis motion giving similar discomfort to each of the dual-axis conditions in the experiment was well approximated by the root-mean-square of the two levels of this single-axis motion equivalent to the two separate components of each dual-axis motion.     

The vibration discomfort of standing persons: 0.5-16-Hz fore-and-aft, lateral, and vertical vibration

To minimise the discomfort of standing people caused by vibration of a floor, it is necessary to know how their sensitivity to vibration depends on the frequency of the vibration. This study was designed to determine how the discomfort of standing people exposed to horizontal and vertical vibration depends on vibration frequency over the range 0.5-16 Hz. Using the method of magnitude estimation, sixteen subjects judged the discomfort caused by fore-and-aft, lateral, and vertical sinusoidal vibration at each of the sixteen preferred one-third octave centre frequencies from 0.5 to 16 Hz at each of nine magnitudes. Subjects also reported the main cause of their discomfort. Equivalent comfort contours were constructed, reflecting the effect of frequency on subject sensitivity to vibration acceleration. With horizontal vibration, at frequencies between 0.5 and 3.15 Hz the discomfort was similar when the vibration velocity was similar, whereas at frequencies between 3.15 and 16 Hz the discomfort was similar when the vibration acceleration was similar. At frequencies less than 3.15 Hz, the subjects experienced problems with their stability, whereas at higher frequencies vibration discomfort was mostly experienced from sensations in the legs and feet. With vertical vibration, discomfort was felt in the lower-body and upper-body at all frequencies. The frequency weightings in current standards for predicting the vibration discomfort of standing persons have been greatly influenced by the findings of studies with seated subjects: the weightings are consistent with the experimentally determined frequency-dependence of discomfort caused by vertical vibration but inconsistent with the experimentally determined frequency-dependence of discomfort caused by horizontal vibration. The results suggest that the responses of seated and standing people are similar for vertical vibration, but differ for horizontal vibration, partly due to greater instability in standing persons.     

The horizontal apparent mass of the standing human body

The driving-point dynamic responses of standing people (e.g. their mechanical impedance or apparent mass) influence their dynamic interactions with structures on which they are supported. The apparent mass of the standing body has been reported previously for vertical excitation but not for lateral or fore-and-aft excitation. Twelve standing male subjects were exposed to fore-and-aft and lateral random vibration over the frequency range 0.1-5.0 Hz for 180 s at four vibration magnitudes: 0.016, 0.0315, 0.063, and 0.125 m s⁻² rms. With lateral excitation at 0.063 m s⁻² rms, subjects also stood with three separations of the feet. The dynamic forces measured at the driving-point in each of the three translational axes (i.e. fore-and-aft, lateral and vertical) showed components not linearly related to the input vibration, and not seen in previous studies with standing subjects exposed to vertical vibration or seated subjects exposed to vertical or horizontal vibration. A principal peak in the lateral apparent mass around 0.5 Hz tended to decrease in both frequency and magnitude with increasing magnitude of vibration and increase with increasing separation of the feet. The fore-and-aft apparent mass appeared to peak at a frequency lower than the lowest frequency used in the study.     

Magnitude-dependence of equivalent comfort contours for fore-and-aft, lateral and vertical whole-body vibration

It is currently assumed that the same frequency weightings, derived from studies of vibration discomfort, can be used to evaluate the severity of vibration at all vibration magnitudes from the threshold of vibration perception to the vibration magnitudes associated with risks to health. This experimental study determined equivalent comfort contours for the whole-body vibration of seated subjects over the frequency range 2-315 Hz in each of the three orthogonal axes (fore-and-aft, lateral and vertical). The contours were determined at vibration magnitudes from the threshold of perception to levels associated with severe discomfort and risks to health.At frequencies greater than 10 Hz, thresholds for the perception of vertical vibration were lower than thresholds for fore-and-aft and lateral vibration. At frequencies less than 4 Hz, thresholds for vertical vibration were higher than thresholds for fore-and-aft and lateral vibration. The rate of growth of sensation with increasing vibration magnitude was highly dependent on the frequency and axis of vibration. Consequently, the shapes of the equivalent comfort contours depended on vibration magnitude. At medium and high vibration magnitudes, the equivalent comfort contours were reasonably consistent with the frequency weightings for vibration discomfort in current standards (i.e. W_b and W_d). At low vibration magnitudes, the contours indicate that relative to lower frequencies the standards underestimate sensitivity at frequencies greater than about 30 Hz. The results imply that no single linear frequency weighting can provide accurate predictions of discomfort caused by a wide range of magnitudes of whole-body vibration.     

Magnitude-dependence of equivalent comfort contours for fore-and-aft, lateral, and vertical vibration at the foot for seated persons

Vibration at the feet can contribute to discomfort in many forms of transport and in some buildings. Knowledge of the frequency-dependence of discomfort caused by foot vibration, and how this varies with vibration magnitude, will assist the prediction of discomfort caused by vibration. With groups of 12 seated subjects, this experimental study determined absolute thresholds for the perception of foot vibration and quantified the discomfort caused by vibration at the foot. The study investigated a wide range of magnitudes (from the threshold of perception to levels associated with severe discomfort) over a wide range of frequencies (from 8 to 315 Hz in one-third octave steps) in each of the three orthogonal translational axes (fore-and-aft, lateral, and vertical). The effects of gender and shoes on absolute thresholds for the perception of vertical vibration at the foot were also investigated. Within each of the three axes, the vibration acceleration corresponding to the absolute thresholds for the perception of vibration, and also all contours showing conditions producing equivalent discomfort, were highly frequency-dependent at frequencies greater than about 40 Hz. The acceleration threshold contours were U-shaped at frequencies greater than 80 Hz in all three axes of excitation, suggesting the involvement of the Pacinian channel in vibration perception. At supra-threshold levels, the frequency-dependence of the equivalent comfort contours in each of the three axes was highly dependent on vibration magnitude. With increasing vibration magnitude, the conditions causing similar discomfort across the frequency range approximated towards constant velocity. Thresholds were not greatly affected by wearing shoes or subject gender. The derived frequency weightings imply that no single linear frequency weighting can provide accurate predictions of discomfort caused by a wide range of magnitudes of foot vibration.     

Vertical and dual-axis vibration of the seated human body: Nonlinearity,cross-axis coupling,and associations between resonances in transmissibility and apparent mass

The vertical apparent mass of the human body exhibits nonlinearity, with the principal resonance frequency reducing as the vibration magnitude increases. Measures of the transmission of vibration to the spine and the pelvis have suggested complex modes are responsible for the dominant resonance during vertical excitation, but the modes present with dual-axis excitation have not been investigated. This study was designed to examine how the apparent mass and transmissibility of the human body depend on the magnitude of vertical excitation and the addition of fore-and-aft excitation, and the relation between the apparent mass and the transmissibility of the 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 male subjects sitting with their hands on their laps during random vertical vibration excitation (over the range 0.25–20 Hz) at three vibration magnitudes (0.25, 0.5 and 1.0 m s^?2 rms). At the highest magnitude of vertical excitation (1.0 m s^?2 rms) the effect of adding fore-aft vibration (at 0.25, 0.5, and 1.0 m s^?2 rms) was investigated. The forces in the vertical and fore-and-aft directions on the seat surface were also measured so as to calculate apparent masses. Resonances in the apparent mass and transmissibility to the spine and pelvis in the fore-and-aft and vertical directions, and pitch transmissibility to the pelvis, shifted to lower frequencies as the magnitude of vertical excitation increased and as the magnitude of the additional fore-and-aft excitation increased. The nonlinear resonant behaviour of the apparent mass and transmissibility during dual-axis vibration excitation suggests coupling between the principal mode associated with vertical excitation and the cross-axis influence of fore-and-aft excitation. The transmissibility measures are consistent with complex modes contributing to motion of the body at the principal resonance: pitch motions of the upper thoracic and lumbar spine, and vertical and fore-aft motion of the pelvis and spine. The mode varies with the magnitude of vertical and fore-and-aft excitation.     

Analyses of biodynamic responses of seated occupants to uncorrelated fore-aft and vertical whole-body vibration

The apparent mass and seat-to-head-transmissibility response functions of the seated human body were investigated under exposures to fore-aft (x), vertical (z), and combined fore-aft and vertical (x and z) axis whole-body vibration. The coupling effects of dual-axis vibration were investigated using two different frequency response function estimators based upon the cross- and auto-spectral densities of the response and excitation signals, denoted as H₁ and H_v estimators, respectively. The experiments were performed to measure the biodynamic responses to single and uncorrelated dual-axis vibration, and to study the effects of hands support, back support and vibration magnitude on the body interactions with the seatpan and the backrest, characterized in terms of apparent masses and the vibration transmitted to the head. The data were acquired with 9 subjects exposed to two different magnitudes of vibration applied along the individual x- and z-axis (0.25 and 0.4 m/s² rms), and along both the axis (0.28 and 0.4 m/s² rms along each axis) in the 0.5-20 Hz frequency range. The two methods resulted in identical single-axis responses but considerably different dual-axis responses. The dual-axis responses derived from the H_v estimator revealed notable effects of dual-axis vibration, as they comprised both the direct and cross-axis responses observed under single axis vibration. Such effect, termed as the coupling effect, was not evident in the dual-axis responses derived using the commonly used H₁ estimator. The results also revealed significant effects of hands and back support conditions on the coupling effects and the measured responses. The back support constrained the upper body movements and thus showed relatively weaker coupling compared to that observed in the responses without the back support. The effect of hand support was also pronounced under the fore-aft vibration. The results suggest that a better understanding of the seated human body responses to uncorrelated multi-axis whole-body vibration could be developed using the power-spectral-density based H_v estimator.     

The vibration of inclined backrests: perception and discomfort of vibration applied normal to the back in the x-axis of the body

The vibration of backrests contributes to the discomfort of drivers and passengers. A frequency weighting exists for evaluating the vibration of vertical backrests but not for reclined backrests often used during travel. This experimental study was designed to determine how backrest inclination and the frequency of vibration influence perception thresholds and vibration discomfort when the vibration is applied normal to the back (i.e. fore-and-aft vibration when seated upright and vertical vibration when fully reclined). Twelve subjects experienced the vibration of a backrest (at each of the 11 preferred one-third octave centre frequencies in the range 2.5–25 Hz) at vibration magnitudes from the threshold of perception to 24 dB above threshold. Initially, absolute thresholds for the perception of vibration were determined with four backrest inclinations: 0° (upright), 30°, 60° and 90° (recumbent). The method of magnitude estimation was then used to obtain judgements of vibration discomfort with each of the four backrest angles. Finally, the relative discomfort between the four backrest angles, and the principal locations for feeling vibration discomfort in the body, were determined. With all backrest inclinations, absolute thresholds for the perception of vibration acceleration were dependent on the frequency of vibration. As the backrest inclination became more horizontal, the thresholds increased at frequencies between 4 and 8 Hz. For all backrest inclinations, the rate of growth of discomfort with increasing magnitude of vibration was independent of the frequency of vibration, so the frequency-dependence of discomfort was similar over the range of magnitudes investigated (0.04–0.6 m s^?2 rms). With an upright backrest, the discomfort caused by vibration acceleration tended to be greatest at frequencies less than about 8 Hz. With inclined backrests (at 30°, 60°, and 90°), the equivalent comfort contours were broadly similar to each other, with greatest discomfort caused by acceleration around 10 or 12.5 Hz. At frequencies from 4 to 8 Hz, 30–40 percent greater magnitudes of vibration were required with the three inclined backrests to cause discomfort equivalent to that caused by the upright backrest. It is concluded that with an upright backrest the frequency weighting W_c used in current standards is appropriate for predicting the discomfort caused by fore-and-aft backrest vibration. With inclined and horizontal backrests, a weighting similar to frequency weighting W_b (used to predict discomfort caused by vertical seat vibration) appears more appropriate.     

Comparison of the apparent masses and cross-axis apparent masses of seated humans exposed to single- and dual-axis whole-body vibration

Humans are exposed to whole-body vibration in many types of environment. In almost all cases, the vibration to which the human is exposed comprises multi-axis vibration, such that vibration occurs in all directions simultaneously. Despite the complex nature of vibration to which humans are exposed in the workplace, almost all laboratory studies investigating the biomechanical response of the person have been completed using single-axis simulators. This paper presents a study whereby 15 male subjects were exposed to single-axis whole-body vibration in the x-, y- and z-directions and dual-axis vibration in the xy-, xz-, and yz-directions using a 6 degree-of-freedom vibration simulator. All vibration magnitudes were 0.4 ms⁻² rms in each axis. Acceleration and force was measured in the x-, y-, and z-direction during all trials. Subjects sat in two postures (‘back-on’ and ‘back-off’) on a flat rigid seat. Apparent masses measured using single-axis and dual-axis vibration stimuli showed comparable results; similarly, cross-axis apparent masses (i.e. the ratio of the force in one direction to the acceleration in another direction) were almost identical for the single- and dual-axis vibration stimuli. All results were in agreement with data previously published using single-axis vibration. In most cases, the peaks in the apparent mass and the cross-axis apparent mass occurred at a slightly lower frequency for the dual-axis vibration than for the single-axis vibration. It is hypothesised that this change is due to a nonlinear effect, analogous to that which occurs with increasing vibration magnitude for single-axis vibration.     

Non-linear dual-axis biodynamic response to vertical whole-body vibration

Seated human subjects have been exposed to vertical whole-body vibration so as to investigate the non-linearity in their biodynamic responses and quantify the response in directions other than the direction of excitation. Twelve males were exposed to random vertical vibration in the frequency range 0.25-25 Hz at four vibration magnitudes (0.125, 0.25, 0.625, and 1.25 m s⁻² r.m.s.). The subjects sat in four sitting postures having varying foot heights so as to produce differing thigh contact with the seat (feet hanging, feet supported with maximum thigh contact, feet supported with average thigh contact, and feet supported with minimum thigh contact). Forces were measured in the vertical, fore-and-aft, and lateral directions on the seat and in the vertical direction at the footrest.The characteristic non-linear response of the human body with reducing resonance frequency at increasing vibration magnitudes was seen in all postures, but to a lesser extent with minimum thigh contact. Appreciable forces in the fore-and-aft direction also showed non-linearity, while forces in the lateral direction were low and showed no consistent trend. Forces at the feet were non-linear with a multi-resonant behaviour and were affected by the position of the legs.The decreased non-linearity with the minimum thigh contact posture suggests the tissues of the buttocks affect the non-linearity of the body more than the tissues of the thighs. The forces in the fore-and-aft direction are consistent with the body moving in two directions when exposed to vertical vibration. The non-linear behaviour of the body, and the considerable forces in the fore-aft direction should be taken into account when optimizing vibration isolation devices.     

Effect of phase on discomfort caused by vertical whole-body vibration and shock--experimental investigation

An experimental study has investigated the effect of "phase" on the subjective responses of human subjects exposed to vertical whole-body vibration and shock. The stimuli were formed from two frequency components: 3 and 9 Hz for continuous vibrations and 3 and 12 Hz for shocks. The two frequency components, each having 1.0 ms(-2) peak acceleration, were combined to form various waveforms. The effects of the vibration magnitude on the discomfort caused by the input stimuli were also investigated with both the continuous vibrations and the shocks. Various objective measurements of acceleration and force at the seat surface, the effects of different frequency weightings and second and fourth power evaluations were compared with judgments of the discomfort of the stimuli. It was found that a 6% to 12% increase in magnitude produced a statistically significant increase in discomfort with both the continuous vibrations and the shocks. Judgments of discomfort caused by changes in vibration magnitude were highly correlated with all of the objective measurements used in the study. The effects on discomfort of the phase between components in the continuous vibrations were not statistically significant, as predicted using evaluation methods with a power of 2. However, small changes in discomfort were correlated with the vibration dose value (VDV) of the Wb frequency-weighted acceleration. The effect of phase between frequency components within the shocks was statistically significant, although no objective measurement method used in the study was correlated with the subjective judgments.     

Power absorbed during whole-body fore-and-aft vibration: Effects of sitting posture,backrest, and footrest

Although the discomfort or injury associated with whole-body vibration cannot be predicted directly from the power absorbed during exposure to vibration, the absorbed power may contribute to understanding of the biodynamics involved in such responses. From measurements of force and acceleration at the seat, the feet, and the backrest, the power absorbed at these three locations was calculated for subjects sitting in four postures (feet hanging, maximum thigh contact, average thigh contact, and minimum thigh contact) both with and without a rigid vertical backrest while exposed to four magnitudes (0.125, 0.25, 0.625, and 1.25 m s^?2 rms) of random fore-and-aft vibration. The power absorbed by the body at the supporting seat surface when there was no backrest showed a peak around 1 Hz and another peak between 3 and 4 Hz. Supporting the back with the backrest decreased the power absorbed at the seat at low frequencies but increased the power absorbed at high frequencies. Foot support influenced both the magnitude and the frequency of the peaks in the absorbed power spectra as well as the total absorbed power. The measurements of absorbed power are consistent with backrests being beneficial during exposure to low frequency fore-and-aft vibration but detrimental with high frequency fore-and-aft vibration.     

Fore-and-aft transmissibility of backrests: Variation with height above the seat surface and non-linearity

The transmissibility of a seat depends on the dynamic response of the human body (which varies between individuals, body locations, and vibration magnitudes) and the dynamic response of the seat (which varies according to seat design). In the fore-and-aft direction, the transmissibility of a seat backrest was therefore expected to vary with vertical position on the backrest. This experimental study with 12 subjects investigated how backrest transmissibility varied with both the vertical measurement position and the magnitude of vibration. The transmissibilities of the backrest of a car seat and a block of solid foam were measured at five heights above the seat surface with random fore-and-aft vibration at five magnitudes (0.1, 0.2, 0.4, 0.8 and 1.6 ms⁻² rms) over the range 0.25–20 Hz. The median transmissibilities exhibited resonances in the range 4–5 Hz for the car seat and in the range 3–6 Hz for the foam. The backrests showed clear changes in transmissibility with vertical position, but there were minimal changes in the resonance frequencies. For both backrests, the transmissibilities were greatest at the middle of the backrest. The least transmissibility was measured at the top of the car seat but at the bottom of the foam backrest. At each measurement position on both backrests, the transmissibility was non-linear with vibration magnitude: the resonance frequencies and transmissibilities at resonance decreased with increasing vibration magnitude. The variations in backrest transmissibility with vertical position and with vibration magnitude were sufficiently great to affect assessments of backrest dynamic performance. The results suggest that the fore-and-aft transmissibilities of backrests should be evaluated from more than one measurement location.     

Effect of voluntary periodic muscular activity on nonlinearity in the apparent mass of the seated human body during vertical random whole-body vibration

The principal resonance frequency in the driving-point impedance of the human body decreases with increasing vibration magnitude—a nonlinear response. An understanding of the nonlinearities may advance understanding of the mechanisms controlling body movement and improve anthropodynamic modelling of responses to vibration at various magnitudes. This study investigated the effects of vibration magnitude and voluntary periodic muscle activity on the apparent mass resonance frequency using vertical random vibration in the frequency range 0.5-20 Hz. Each of 14 subjects was exposed to 14 combinations of two vibration magnitudes (0.25 and 2.0 m s⁻² root-mean square (rms)) in seven sitting conditions: two without voluntary periodic movement (A: upright; B: upper-body tensed), and five with voluntary periodic movement (C: back-abdomen bending; D: folding-stretching arms from back to front; E: stretching arms from rest to front; F: folding arms from elbow; G: deep breathing). Three conditions with voluntary periodic movement significantly reduced the difference in resonance frequency at the two vibration magnitudes compared with the difference in a static sitting condition. Without voluntary periodic movement (condition A: upright), the median apparent mass resonance frequency was 5.47 Hz at the low vibration magnitude and 4.39 Hz at the high vibration magnitude. With voluntary periodic movement (C: back-abdomen bending), the resonance frequency was 4.69 Hz at the low vibration magnitude and 4.59 Hz at the high vibration magnitude. It is concluded that back muscles, or other muscles or tissues in the upper body, influence biodynamic responses of the human body to vibration and that voluntary muscular activity or involuntary movement of these parts can alter their equivalent stiffness.     

Apparent mass of the human body in the vertical direction: Inter-subject variability

The biodynamic responses of the seated human body to whole-body vibration vary considerably between people, but the reasons for the variability are not well understood. This study was designed to determine how the physical characteristics of people affect their apparent mass and whether inter-subject variability is influenced by the magnitude of vibration and the support of a seat backrest. The vertical apparent masses of 80 seated adults (41 males and 39 females aged 18-65) were measured at frequencies between 0.6 and 20 Hz with four backrest conditions (no backrest, upright rigid backrest, reclined rigid backrest, reclined foam backrest) and with three magnitudes of random vibration (0.5, 1.0 and 1.5 m s^-2 rms). Relationships between subject physical characteristics (age, gender, weight, and anthropometry) and subject apparent mass were investigated with multiple regression models. The strongest predictor of the modulus of the vertical apparent mass at 0.6 Hz, at resonance, and at 12 Hz was body weight, with other factors having only a marginal effect. After correction for other variables, the principal resonance frequency was most consistently associated with age and body mass index. As age increased from 18 to 65 years, the resonance frequency increased by up to 1.7 Hz, and when the body mass index was increased from 18 to 34 kg m⁻² the resonance frequency decreased by up to 1.7 Hz. These changes were greater than the 0.9-Hz increase in resonance frequency between sitting without a backrest and sitting with a reclined rigid backrest, and greater than the 1.0-Hz reduction in resonance frequency when the magnitude of vibration increased from 0.5 to 1.5 m s⁻² rms. It is concluded that the effects of age, body mass index, posture, vibration magnitude, and weight should be taken into account when defining the vertical apparent mass of the seated human body.     

Difference thresholds for vibration of the foot: Dependence on frequency and magnitude of vibration

The smallest change in vibration intensity for the change to be perceptible (i.e. intensity difference threshold) has not previously been reported for vibration of the foot. This study investigated the influence of vibration magnitude and vibration frequency on intensity difference thresholds for the perception of vertical sinusoidal vibration of the foot. It was hypothesised that relative intensity difference thresholds (i.e. Weber fractions) for 16-Hz vibration mediated by the non-Pacinian I (NPI) channel would differ from relative intensity difference thresholds for 125-Hz vibration mediated by the Pacinian (P) channel. Absolute thresholds, difference thresholds, and the locations of vibration sensation caused by vertical vibration of the right foot were determined for 12 subjects using the up-down-transformed-response method together with the three-down-one-up rule. The difference thresholds and locations of sensation were obtained at six reference magnitudes (at 6, 9, 12, 18, 24, 30 dB above absolute threshold—i.e. sensation levels, SL). For 16-Hz vibration, the median relative difference thresholds were not significantly dependent on vibration magnitude and were in the range 0.19 (at 30 dB SL) to 0.27 (at 9 dB SL). For 125-Hz vibration, the median relative difference thresholds varied between 0.17 (at 9 dB SL) and 0.34 (at 30 dB SL), with difference thresholds from 6 to 12 dB SL significantly less than those from 18 to 30 dB SL. At vibration magnitudes slightly in excess of absolute thresholds (i.e. 6-12 dB SL) there were no significant differences between Weber fractions obtained from the P channel (at 125 Hz) and the NPI channel (at 16 Hz). At 24 and 30 dB SL, the 125-Hz Weber fractions were significantly greater than the 16-Hz Weber fractions. Differences in the 125-Hz Weber fractions may have been caused by a reduction in the discriminability of the P channel at high levels of excitation, resulting in one or more NP channel mediating the difference thresholds at magnitudes greater than 18 dB SL. At high magnitudes, a change of channel mediating the Weber fractions may have been responsible for different Weber fractions with 16- and 125-Hz vibration.     

Apparent mass of the human body in the vertical direction: Effect of a footrest and a steering wheel

The apparent mass of the seated human body influences the vibration transmitted through a car seat. The apparent mass of the body is known to be influenced by sitting posture but the influence of the position of the hands and the feet is not well understood. This study was designed to quantify the influence of steering wheel location and the position of a footrest on the vertical apparent mass of the human body. The influences of the forces applied by the hands to a steering wheel and by the feet to a footrest were also investigated. Twelve subjects were exposed to whole-body vertical random vibration (1.0 m s⁻² rms over the frequency range 0.13-40.0 Hz) while supported by a rigid seat with a backrest reclined to 15°. The apparent mass of the body was measured with five horizontal positions and three vertical positions of a steering wheel and also with hands in the lap, and with five horizontal positions of a footrest. The influence of five forward forces (0, 50, 100, 150, 200 N) applied separately to the ‘steering wheel’ and the footrest were also investigated as well as a ‘no backrest’ condition. With their hands in their laps, subjects exhibited a resonance around 6.7 Hz, compared to 4.8 Hz when sitting upright with no backrest. In the same posture holding a steering wheel, the mass supported on the seat surface decreased and there was an additional resonance at 4 Hz. Moving the steering wheel away from the body reduced the apparent mass at the primary resonance frequency and increased the apparent mass around the 4 Hz resonance. As the feet moved forward, the mass supported on the seat surface decreased, indicating that the backrest and footrest supported a greater proportion of the subject weight. Applying force to either the steering wheel or the footrest reduced the apparent mass at resonance and decreased the mass supported on the seat surface. It is concluded that the positions and contact conditions of the hands and the feet affect the biodynamic response of the body in a car driving posture. As the biodynamic response influences the vibration transmitted through seats, these factors should be considered in dynamic models of vehicle seating.     

Seated occupant interactions with seat backrest and pan, and biodynamic responses under vertical vibration

The relative interactions of the seated occupants with an inclined backrest were investigated in terms of apparent mass (APMS) responses at the two driving-points formed by the buttock-seat pan and the upper body-backrest under exposure to broad-band and road-measured vertical vibration. The measurements were performed using 24 adult subjects seated with full contact with the back support and two different positions of the hands (in lap and on steering wheel), while exposed to three different levels of broad band (0.25, 0.5 and 1.0 m/s² rms acceleration) vibration in the 0.5-40 Hz frequency range, and a track-measured vibration spectrum (1.07 m/s² rms acceleration). The forces developed on the seat pan and the backrest in directions normal to the supporting surfaces were measured to derive the APMS responses at both the driving-points. The results showed significant interactions of the upper body with the back support in a direction normal to the backrest, even though the vibration is applied along the vertical axis. At low frequencies, the backrest APMS magnitude was smaller than that measured at the seat pan, but it either exceeded or approached that of the seat pan APMS in the vicinity of the primary resonant frequencies. The results also suggested considerable effect of the hands position on the APMS magnitudes measured at both the driving-points. The effects of variations in the excitation type and magnitude, considered in this study, were observed to be small compared to those caused by the hands position and individual body masses. Owing to the strong effects of the body mass on the measured APMS responses at both driving-points, a total of 8 target data sets were identified corresponding to four mass groups (<60, 60.6-70, 70.5-80 and >80 kg) and two hands positions for formulating mechanical equivalent models. The model parameters identified for the target functions suggested that the models mass, stiffness and damping parameters increase with increasing body mass. The observed variations in the identified parameters could be applied for predicting the APMS responses reflected on the pan as well as backrest of the human occupants with specific body mass.     

An analytic model of the in-line and cross-axis apparent mass of the seated human body exposed to vertical vibration with and without a backrest

During vertical excitation of the seated human body there are vertical and fore-and-aft forces at the seat that are influenced by contact with a backrest, so it is desirable to take into account the effect of a backrest when developing models of the seated human body. Initially, a seven degree-of-freedom multi-body dynamic model was developed for the human body sitting with an upright posture unsupported by a backrest and exposed to vertical vibration. The model was optimized to fit the vertical apparent mass and the fore-and-aft cross-axis apparent mass measured on a seat. The model was then extended by the addition of vertical and fore-and-aft reaction forces to the upper lumbar spine to model the interaction between the human body and a backrest. By minimizing the least square error between experimental data and the analytical solution of the apparent masses on the seat and at the back, the human body model was able to represent both the vertical apparent mass and the fore-and-aft cross-axis apparent mass on the seat and at the back. Parameter sensitivity studies showed that the vertical apparent mass and the fore-and-aft cross-axis apparent mass on the seat and the backrest were all highly sensitive to the axial stiffness of the tissue beneath the pelvis. Pitch motion of the upper-body contributed to the vertical apparent mass and the fore-and-aft cross-axis apparent mass on the seat. The apparent mass at the back was more sensitive to the stiffness and damping of the lower back than the properties of the upper back.     

Fore-and-aft transmissibility of backrests: Effect of backrest inclination,seat-pan inclination,and measurement location

Car seats have inclined backrests and inclined seat-pans, but there has been little study of how the inclinations of the surfaces of a seat influence the transmission of fore-and-aft vibration through the backrest. The effects of backrest inclination and seat-pan inclination on the fore-and-aft transmissibilities of two seats (a car seat and a rigid seat with solid foam backrest) have been investigated in the laboratory. With 12 subjects, each seat was exposed to random fore-and-aft vibration in the frequency range 0.25–20 Hz with a vibration magnitude of 0.4 ms⁻² rms. At six vertical locations on each backrest, the fore-and-aft transmissibilities of the backrests were measured with four backrest inclinations (90° (i.e. vertical), 105°, 100°, and 105°) and up to four seat-pan inclinations (0° (i.e. horizontal), 5°, 10°, and 15°). At all six measurement locations, there was a resonance of both backrests at about 4 Hz, which increased in frequency with increasing backrest inclination for the car seat but showed little change with inclination for the foam backrest. The inclination of the backrest had more influence at the bottom that at the top of the backrest of the car seat, but showed little variation with position on the foam backrest. Variations in seat-pan inclination had little influence on the resonance frequencies of either backrest at any location. Inclining the backrest and the seat-pan increased the transmissibility at resonance with the car seat, but produced little change with the foam backrest. It is concluded that both the backrest inclination and the seat inclination can affect the fore-and-aft transmissibility of backrests but, with moderate changes of inclination, the effects are not large.