Equal sensation curves for whole-body vibration expressed as a function of driving force

Previous studies have shown that the seated human is most sensitive to whole-body vertical vibration at about 5 Hz. Similarly, the body shows an apparent mass resonance at about 5 Hz. Considering these similarities between the biomechanical and subjective responses, it was hypothesized that, at low frequencies, subjective ratings of whole-body vibration might be directly proportional to the driving force. Twelve male subjects participated in a laboratory experiment where subjects sat on a rigid seat mounted on a shaker. The magnitude of a test stimulus was adjusted such that the subjective intensity could be matched to a reference stimulus, using a modified Bruceton test protocol. The sinusoidal reference stimulus was 8-Hz vibration with a magnitude of 0.5 m/s2 rms (or 0.25 m/s2 rms for the 1-Hz test); the sinusoidal test stimuli had frequencies of 1, 2, 4, 16, and 32 Hz. Equal sensation contours in terms of seat acceleration showed data similar to those in the literature. Equal sensation contours in terms of force showed a nominally linear response at 1, 2, and 4 Hz, but an increasing sensitivity at higher frequencies. This is in agreement with a model derived from published subjective and objective fitted data.     

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.     

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.     

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.     

Dynamic and subjective responses of seated subjects exposed to simultaneous vertical and fore-and-aft whole-body vibration: The effect of the phase between the two single-axis components

Subjective and dynamic responses of seated subjects exposed to simultaneous vertical and fore-and-aft sinusoidal whole-body vibration were investigated. The effect of the phase difference between the vertical and the fore-and-aft vibration on the responses was of a particular interest in this study. Fifteen subjects were exposed to dual-axis vibrations at six frequencies (2.5-8 Hz) and at eight phases between the two single-axis components (0-315°). The magnitude of vibration in each axis was constant at 0.7 m s⁻² rms. Discomfort caused by vibration was measured by the method of magnitude estimation. The motion of the body were measured at the head and three locations along the spine with accelerometers attached to the body surface. The most significant effect of the phase between the two single-axis components on the discomfort was observed at 5 Hz: about 40% difference in the median discomfort estimate caused by changing the phase. The transmissibilities from vertical seat vibration to vertical motions of the spine varied from 0.5 to 2.0 by changing the phase between the two single-axis components at frequencies from 2.5 to 5 Hz. The effect of the phase observed in the dynamic response was not predicted by the superposition of the responses to each single-axis vibration. The discomfort caused by the dual-axis vibration tended to be correlated better with the combinations of the dynamic responses measured in the two axes than with the dynamic responses in a single axis.     

EVALUATING THE VIBRATION ISOLATION OF SOFT SEAT CUSHIONS USING AN ACTIVE ANTHROPODYNAMIC DUMMY

Seat test standards require human subjects to be used for measuring the vibration isolation of vehicle seats. Anthropodynamic dummies, based on passive mass-spring- damper systems, have been developed for testing seats but their performance has been limited at low excitation magnitudes by non-linear phenomena, such as friction in the mechanical components that provide damping. The use of an electrodynamic actuator to generate damping forces, controlled by feedback from acceleration and force transducers, may help to overcome these limitations and provide additional benefits. The transmissibilities of five foam cushions have been measured using an actively controlled anthropodynamic dummy, in which damping and spring forces were supplied by an electrodynamic actuator. The dummy could be set up to approximate alternative single-degree-of-freedom and two-degree-of-freedom apparent mass models of the seated human body by varying motion feedback parameters. Cushion transmissibilities were also measured with nine human subjects, having an average seated weight similar to the dummy. At frequencies greater than 4 Hz, mean cushion transmissibilities measured with subjects were in closer agreement with the transmissibilities obtained with a two degree-of-freedom dummy than with a single degree-of-freedom dummy. However, at frequencies between 2 and 4 Hz, cushion transmissibilities obtained with the two-degree-of-freedom dummy showed consistently larger differences from mean transmissibilities with subjects than single-degree-of-freedom dummies, indicating a need for further development of human apparent mass models to account for the effects of magnitude and spectral content of the input motion. Vertical vibration isolation efficiencies (SEAT values) of the five foams were measured with four input motions, including three motions measured in a car. The SEAT values obtained using the active dummy were highly correlated with the median SEAT values obtained with the nine human subjects, with the two-degree-of-freedom apparent mass dummy giving the highest agreement.     

Difference thresholds for intensity perception of whole-body vertical vibration: effect of frequency and magnitude

Difference thresholds for seated subjects exposed to whole-body vertical sinusoidal vibration have been determined at two vibration magnitudes [0.1 and 0.5 ms(-2) root mean square (r.m.s.)] and at two frequencies (5 and 20 Hz). For 12 subjects, difference thresholds were determined using the up-and-down transformed response method based on two-interval forced-choice tracking. At both frequencies, the difference thresholds increased by a factor of five when the magnitude of the vibration increased from 0.1 to 0.5 ms(-2) r.m.s. The median relative difference thresholds, Weber fractions (deltaI/I), expressed as percentages, were about 10% and did not differ significantly between the two vibration magnitudes or the two frequencies. It is concluded that for the conditions investigated the difference thresholds for whole-body vibration are approximately consistent with Weber's Law. A vibration magnitude will need to be reduced by more than about 10% for the change to be detectable by human subjects; vibration measurements will be required to detect reductions of less than 10%.     

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.     

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.     

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.     

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.     

SEATED OCCUPANT APPARENT MASS CHARACTERISTICS UNDER AUTOMOTIVE POSTURES AND VERTICAL VIBRATION

The biodynamic apparent mass response characteristics of 24 human subjects (12 males and 12 females) seated under representative automotive postures with hands-in-lap (passengers) and hands-on-steering wheel (drivers) are reported. The measurements were carried out under white noise vertical excitations of 0·25, 0·5 and 1·0m/s²r.m.s. acceleration magnitudes in the 0·5-40Hz frequency range and a track measured input (1·07m/s²). The measured data have been analyzed to study the effects of hands position, body mass, magnitude and type of vibration excitation, and feet position, on the biodynamic response expressed in terms of apparent mass. A comparison of the measured response of subjects assuming typical automotive postures involving inclined cushion, inclined backrest and full use of backrest support with data determined under different postural conditions and excitation levels revealed considerable differences. The biodynamic response of automobile occupants seated with hands in lap, peaks in the 6·5-8·6Hz frequency range, which is considerably higher than the reported range of fundamental frequencies (4·5-5Hz) in most other studies involving different experimental conditions. The peak magnitude tends to decrease considerably for the driving posture with hands-on-steering wheel, while a second peak in the 8-12 Hz range becomes more apparent for this posture. The results suggest that biodynamic response of occupants seated in automotive seats and subject to vertical vibration need to be characterized, as a minimum, by two distinct functions for passenger and driving postures. A higher body mass, in general, yields higher peak magnitude response and lower corresponding frequency for both postures. The strong dependence of the response on the body mass is further demonstrated by grouping the measured data into four different mass ranges: less than 60 kg, between 60·5 and 70 kg, between 70·5 and 80 kg, and above 80 kg. From the results, it is concluded that hands position and body mass have the most significant influence on the apparent mass response under automotive posture and vibration.     

Factors affecting perception thresholds of vertical whole-body vibration in recumbent subjects: Gender and age of subjects, and vibration duration

Some factors that may affect human perception thresholds of the vertical whole-body vibrations were investigated in two laboratory experiments with recumbent subjects. In the first experiment, the effects of gender and age of subjects on perception were investigated with three groups of 12 subjects, i.e., young males, young females and old males. For continuous sinusoidal vibrations at 2, 4, 8, 16, 31.5 and 63 Hz, there were no significant differences in the perception thresholds between male and female subjects, while the thresholds of young subjects tended to be significantly lower than the thresholds of old subjects. In the second experiment, the effect of vibration duration was investigated by using sinusoidal vibrations, at the same frequencies as above, modulated by the Hanning windows with different lengths (i.e., 0.5, 1.0, 2.0 and 4.0 s) for 12 subjects. It was found that the peak acceleration at the threshold tended to decrease with increasing duration of vibration. The perception thresholds were also evaluated by the running root-mean-square (rms) acceleration and the fourth power acceleration method defined in the current standards. The differences in the threshold of the transient vibrations for different durations were less with the fourth power acceleration method. Additionally, the effect of the integration time on the threshold was investigated for the running rms acceleration and the fourth power acceleration. It was found that the integration time that yielded less differences in the threshold of vibrations for different durations depended on the frequency of vibration.     

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.     

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.     

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.     

Perturbation parameters associated with nonlinear responses of the head at small amplitudes

The head-neck system has multiple degrees of freedom in both its control and response characteristics, but is often modeled as a single joint mechanical system. In this study, we have attempted to quantify the perturbation parameters that would elicit nonlinear responses in a single degree-of-freedom neuromechanical system at small amplitudes and velocities of perturbation. Twelve healthy young adults seated on a linear sled randomly received anterior-posterior sinusoidal translations with +/-15 mm and +/-25 mm peak displacements at 0.81, 1.76, and 2.25 Hz. Head angular velocity and angular position data were examined using a nonlinear phase-plane analysis. Poincare sections of the phase plane were computed and Lyapunov exponents calculated to measure divergence (chaotic behavior) or convergence (stable behavior) of system dynamics. Variability of head angular position and velocity across the entire phase plot was compared to that of the Poincare sections to quantify spatial-temporal irregularity. Multiple equilibrium points and positive Lyapunov exponents revealed chaotic behavior at 0.81 Hz at both amplitudes whereas responses at 1.76 and 2.25 Hz exhibited periodic oscillations, clustered phase points, and negative Lyapunov exponents. However, intersubject variability increased at the lowest frequency and a few subjects presented chaotic behavior at all frequencies. An inverted pendulum with position and velocity threshold nonlinearity was adopted as a simplistic model of the head and neck. Simulations with the model resulted in features similar to those observed in the experimental data. Our principal finding was that increasing the perturbation amplitude had a stabilizing effect on the behavior across frequencies. Nonlinear behaviors observed at the lowest stimulus frequency might be attributed to fluctuations in control between the multiple sensory inputs. Although this study has not conclusively pointed toward any single mechanism as responsible for the responses observed, it has revealed clear directions for further investigation. To examine if changing the sensory modalities would elicit a significant change in the nonlinear behaviors observed here, further experiments that target a patient population with some sort of sensory deficit are warranted.     

电力变压器绕组振动声纹特性分析*

为更加准确分析变压器绕组的状态特征,本文提出一种基于多物理场耦合仿真的变压器绕组振动声纹特性分析方法。根据实验条件,建立变压器绕组振动噪声模型,考虑变压器绝缘油在噪声传播过程中的作用,对S13-M-200/10型号的油浸式变压器进行短路实验,测量油箱表面的振动加速度以及周围空间的声音信号。仿真结果与实测数据对比分析,油箱表面的振动加速度集中频率为100Hz,空间声音信号集中频率为100Hz和200Hz,验证仿真模型的有效性。最后,建立变压器机械故障的仿真模型,分析得到变压器发生机械故障时,声音信号中100Hz频率分量减少,200Hz频率分量增加,为变压器绕组故障诊断提供依据。     

Intensity difference limens at high frequencies

Thresholds for amplitude modulation detection were obtained from four subjects at frequencies of 2, 4, 6, 8, and 10 kHz for sensation levels of 15, 30, 45, and 60 dB and modulation rates of 2, 4, and 8 Hz. High-frequency difference limens calculated from amplitude modulation thresholds were found to change nonmonotonically as a function of sensation level, independent of modulation rate. This nonmonotonic relation stemmed mainly from a gradual reduction of the difference limen at the lowest sensation level with increasing frequency. Difference limens for pulsed tone discrimination were also measured in two of the subjects at 2, 6, and 10 kHz and sensation levels of 15, 30, 45, and 60 dB. The relation between intensity discrimination and sensation level was similar to that found for amplitude modulation detection. These findings are interpreted as indicating that the nonmonotonic relation between sensation level and intensity resolution is a general characteristic of stimulus processing at higher frequencies.     

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.