A BODY MASS DEPENDENT MECHANICAL IMPEDANCE MODEL FOR APPLICATIONS IN VIBRATION SEAT TESTING

A three degree-of-freedom model is proposed to predict the biodynamic responses of the seated human body of different masses. A baseline model is initially derived to satisfy both the mean apparent mass and seat-to-head transmissibility responses proposed in ISO/DIS 5982:2000 applicable for mean body mass of 75 kg. The validity of the resultant generic mass dependent model is verified by comparing the apparent mass and driving-point mechanical impedance responses computed for total body masses of 55, 75 and 90 kg with the range of idealized values proposed for body masses within the 49-93 kg range. Considering the lack of data that could be found to define the apparent mass/mechanical impedance of subjects with different body masses when applying the experimental conditions defined in ISO/DIS 5982:2000, an attempt is made to adapt the parameters of the base model to fit the measured apparent mass data applicable to groups of automobile occupants within different mass ranges. This is achieved through constrained parametric optimization which consists of minimizing the sum of squared errors between the computed response and the mean apparent mass data measured for automobile occupants within four mass groups: less than 60 kg, 60·5-70·5 kg, 70·5-80 kg and above 80 kg. The results show a reasonably good agreement between the model responses and the measured apparent mass data, particularly at frequencies below 10 Hz. The results suggest that the proposed mass dependent model can effectively predict the apparent mass responses of automobile occupants over a wide range of body masses and for two different postures: passenger (hands-in-lap) and driver (hands-on-steering wheel) postures.     

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.     

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.     

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.     

EFFECTS OF POSTURE AND VIBRATION MAGNITUDE ON APPARENT MASS AND PELVIS ROTATION DURING EXPOSURE TO WHOLE-BODY VERTICAL VIBRATION

The effect of variations in posture and vibration magnitude on apparent mass and seat-to-pelvis pitch transmissibility have been studied with vertical random vibration over the frequency range 1·0-20 Hz. Each of 12 subjects was exposed to 27 combinations of three vibration magnitudes (0·2, 1·0 and 2·0m/s² r.m.s.) and nine sitting postures (“upright”, “anterior lean”, “posterior lean”, “kyphotic”, “back-on”, “pelvis support”, “inverted SIT-BAR” (increased pressure beneath ischial tuberosities), “bead cushion” (decreased pressure beneath ischial tuberosities) and “belt” (wearing an elasticated belt)).Peaks in the apparent masses were observed at about 5 and 10 Hz, and in the seat-to-pelvis pitch transmissibilities at about 12 Hz. In all postures, the resonance frequencies in the apparent mass and transmissibility decreased with increased vibration magnitude, indicating a non-linear softening system. There were only small changes in apparent mass or transmissibility with posture, although peaks were lower for the apparent mass in the “kyphotic” posture and were lower for the transmissibility in the “belt” posture. The changes in apparent mass and transmissibility caused by changes in vibration magnitude were greater than the changes caused by variation in posture.     

EFFECT OF MUSCLE TENSION ON NON-LINEARITIES IN THE APPARENT MASSES OF SEATED SUBJECTS EXPOSED TO VERTICAL WHOLE-BODY VIBRATION

In subjects exposed to whole-body vibration, the cause of non-linear dynamic characteristics with changes in vibration magnitude is not understood. The effect of muscle tension on the non-linearity in apparent mass has been investigated in this study. Eight seated male subjects were exposed to random and sinusoidal vertical vibration at five magnitudes (0·35-1·4 m/s² r.m.s.). The random vibration was presented for 60 s over the frequency range 2·0-20 Hz; the sinusoidal vibration was presented for 10 s at five frequencies (3·15, 4·0, 5·0, 6·3 and 8·0 Hz). Three sitting conditions were adopted such that, in two conditions, muscle tension in the buttocks and the abdomen was controlled. It was assumed that, in these two conditions, involuntary changes in muscle tension would be minimized. The force and acceleration at the seat surface were used to obtain apparent masses of subjects. With both sinusoidal and random vibration, there was statistical support for the hypothesis that non-linear characteristics were less clear when muscle tension in the buttocks and the abdomen was controlled. With increases in the magnitude of random vibration from 0·35 to 1·4 m/s² r.m.s., the apparent mass resonance frequency decreased from 5·25 to 4·25 Hz with normal muscle tension, from 5·0 to 4·38 Hz with the buttocks muscles tensed, and from 5·13 to 4·5 Hz with the abdominal muscles tensed. Involuntary changes in muscle tension during whole-body vibration may be partly responsible for non-linear biodynamic responses.     

EFFECTS RELATED TO RANDOM WHOLE-BODY VIBRATION AND POSTURE ON A SUSPENDED SEATWITH AND WITHOUT BACKREST

WBV-exposures are often linked with forced postures as prolonged sitting, bent forward sitting, or sitting without a backrest. No quantitative data are available to describe the exposure-effect relationships for different conditions of seating, posture, and the biological variability of workers. Experiments and subsequent predictions of forces acting within the spine during WBV can help to improve the assessment of the health risk. An experimental study was performed with 39 male subjects sitting on a suspension seat with or with no backrest contact. They were exposed to random whole-body vibration with a weighted r.m.s. value of 0·6 m/s² at a relaxed or a forward bending posture. A two-dimensional finite element model was used for the calculation of the internal spinal load. The model simulates the human response on a suspension driver seat. Individual exposure conditions were considered by including the transfer functions between the seat cushion and the seat base as well as between the backrest and the seat base for the calculation of the vibration input to the buttocks and to the back respectively. The average peak seat transmissibility was higher for the seat with the backrest, but the peak seat-to-head transmissibility was higher for the seat without the backrest for both postures. The peak transmissibilities between the accelerations at the seat base and the compressive forces at L5/S1 were highest for the seat without the backrest during the bending posture. Various biological effects can result from identical exposures combined with different backrest contact and postures. The backrest contact and posture conditions should not be neglected in the assessment of health risk caused by whole-body vibration.     

The transmission of vertical vibration through seats: Influence of the characteristics of the human body

The transmission of vibration through a seat depends on the impedance of the seat and the apparent mass of the seat occupant. This study was designed to determine how factors affecting the apparent mass of the body (age, gender, physical characteristics, backrest contact, and magnitude of vibration) affect seat transmissibility. The transmission of vertical vibration through a car seat was measured with 80 adults (41 males and 39 females aged 18-65) at frequencies between 0.6 and 20 Hz with two backrest conditions (no backrest and backrest), and with three magnitudes of random vibration (0.5, 1.0, and 1.5 m s^-2 rms). Linear regression models were used to study the effects of subject physical characteristics (age, gender, and anthropometry) and features of their apparent mass (resonance frequency, apparent mass at resonance and at 12 Hz) on the measured seat transmissibility. The strongest predictor of both the frequency of the principal resonance in seat transmissibility and the seat transmissibility at resonance was subject age, with other factors having only marginal effects. The transmissibility of the seat at 12 Hz depended on subject age, body mass index, and gender. Although subject weight was strongly associated with apparent mass, weight was not strongly associated with seat transmissibility. The resonance frequency of the seat decreased with increases in the magnitude of the vibration excitation and increased when subjects made contact with the backrest. Inter-subject variability in the resonance frequency and transmissibility at resonance was less with greater vibration excitation, but was largely unaffected by backrest contact. A lumped parameter seat-person model showed that changes in seat transmissibility with age can be predicted from changes in apparent mass with age, and that the dynamic stiffness of the seat appeared to increase with increased loading so as to compensate for increases in subject apparent mass associated with increased sitting weight.     

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.     

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

Previous studies have quantified the power absorbed in the seated human body during exposure to vibration but have not investigated the effects of body posture or the power absorbed at the back and the feet. This study investigated the effects of support for the feet and back and the magnitude of vibration on the power absorbed during whole-body vertical vibration. Twelve subjects were exposed to four magnitudes (0.125, 0.25, 0.625, and 1.25 m s⁻² rms) of random vertical vibration (0.25-20 Hz) while sitting on a rigid seat in four postures (feet hanging, maximum thigh contact, average thigh contact, and minimum thigh contact) both with and without a rigid vertical backrest. Force and acceleration were measured at the seat, the feet, and the backrest to calculate the power absorbed at these three locations. At all three interfaces (seat, feet, and back) the absorbed power increased in proportion to the square of the magnitude of vibration, with most power absorbed from vibration at the seat. Supporting the back with the backrest decreased the power absorbed at the seat at low frequencies but increased the power absorbed at high frequencies. Supporting the feet with the footrest reduced the total absorbed power at the seat, with greater reductions with higher footrests. It is concluded that contact between the thighs and the seat increases the power absorbed at the seat whereas a backrest can either increase or decrease the power absorbed at the seat.     

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: 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.     

SOME ASPECTS OF THE INVESTIGATION OF RANDOM VIBRATION INFLUENCE ON RIDE COMFORT

Contemporary vehicles must satisfy high ride comfort criteria. This paper attempts to develop criteria for ride comfort improvement. The highest loading levels have been found to be in the vertical direction and the lowest in lateral direction in passenger cars and trucks. These results have formed the basis for further laboratory and field investigations. An investigation of the human body behaviour under random vibrations is reported in this paper. The research included two phases; biodynamic research and ride comfort investigation. A group of 30 subjects was tested. The influence of broadband random vibrations on the human body was examined through the seat-to-head transmissibility function (STHT). Initially, vertical and fore and aft vibrations were considered. Multi-directional vibration was also investigated. In the biodynamic research, subjects were exposed to 0·55, 1·75 and 2·25 m/s² r.m.s. vibration levels in the 0·5- 40 Hz frequency domain. The influence of sitting position on human body behaviour under two axial vibrations was also examined. Data analysis showed that the human body behaviour under two-directional random vibrations could not be approximated by superposition of one-directional random vibrations. Non-linearity of the seated human body in the vertical and fore and aft directions was observed. Seat-backrest angle also influenced STHT. In the second phase of experimental research, a new method for the assessment of the influence of narrowband random vibration on the human body was formulated and tested. It included determination of equivalent comfort curves in the vertical and fore and aft directions under one- and two-directional narrowband random vibrations. Equivalent comfort curves for durations of 2·5, 4 and 8 h were determined.     

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.     

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.     

Modelling resonances of the standing body exposed to vertical whole-body vibration: Effects of posture

Lumped parameter mathematical models representing anatomical parts of the human body have been developed to represent body motions associated with resonances of the vertical apparent mass and the fore-and-aft cross-axis apparent mass of the human body standing in five different postures: ‘upright’, ‘lordotic’, ‘anterior lean’, ‘knees bent’, and ‘knees more bent’. The inertial and geometric parameters of the models were determined from published anthropometric data. Stiffness and damping parameters were obtained by comparing model responses with experimental data obtained previously.The principal resonance of the vertical apparent mass, and the first peak in the fore-and-aft cross-axis apparent mass, of the standing body in an upright posture (at 5–6 Hz) corresponded to vertical motion of the viscera in phase with the vertical motion of the entire body due to deformation of the tissues at the soles of the feet, with pitch motion of the pelvis out of phase with pitch motion of the upper body above the pelvis. Upward motion of the body was in phase with the forward pitch motion of the pelvis. Changing the posture of the upper body had minor effects on the mode associated with the principal resonances of the apparent mass and cross-axis apparent mass, but the mode changed significantly with bending of the legs. In legs-bent postures, the principal resonance (at about 3 Hz) was attributed to bending of the legs coupled with pitch motion of the pelvis in phase with pitch motion of the upper body. In this mode, extension of the legs was in phase with the forward pitch motion of the upper body and the upward vertical motion of the viscera.     

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.     

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.