Transmission Of Vertical Vibration Research Articles

Transmission of vertical vibration through a seat cushion at the seat pan: Effect of foam physical properties during different excitation magnitudes

The vibration characteristics of car seats directly influence the ride comfort. Polyurethane foam is the key part of a seat, and its physical parameters have an important impact on the seat. In this study, the influence of the foam thickness and foam hardness on the vibration characteristics of seat cushion with different excitation magnitudes was investigated by using transmissibility and seat effective amplitude transmissibility (SEAT) value. First, vibration tests were carried out at a vertical vibration simulator with width-limited white noise vibration frequencies from 0.5 to 20 Hz with root-mean-square (r.m.s.) values of 0.4, 0.8, and 1.2 m/s2, the acceleration at the platform and the body-foam interfaces were measured to calculate the transmissibility, and the influence of the foam physical properties on the transmissibility was analyzed. Then, the SEAT value was introduced to assess the vibration isolation efficiency of the foam cushion, and the influence of the foam physical properties of the foam cushion on the vibration isolation efficiency was analyzed. With increasing thickness of the foam and decreasing hardness of the foam at the seat pan, the peak transmissibility increased and the resonance frequency decreased. The SEAT values show that increasing the foam thickness is beneficial to the improvement of the vibration isolation efficiency of the seat, but there is a diminishing return; the combination of physical parameters of low hardness and high thickness could make the vibration isolation performance of the seat better. In addition, the nonlinearity of human-seat system during different vibration magnitude was found.

Gender and Anthropometric Effects on Seat-to-Head Transmissibility Responses to Vertical Whole-Body Vibration of Humans Seated on an Elastic Seat

This study investigated the effects of gender and ten different anthropometric parameters on the vertical vibration transmission from seat to the head of the body seated on an elastic seat. The seat-to-head transmissibility (STHT) responses in the vertical and fore-aft directions of 58 participants (31 males and 27 females) were measured under three levels of vertical vibration (root mean square acceleration: 0.25, 0.50, and 0.75 m/s2) in the 0.50–20 Hz range, when sitting on a viscoelastic seat with and without a vertical back support, and with hands on a steering wheel. Apart from the important effects of elastic coupling between the body and seat, the results show distinctly different vertical and fore-aft STHT responses from the two genders. Moreover, the gender effect was strongly coupled with back support and excitation conditions. The primary resonance frequencies of male subjects were higher than those of female subjects, while the peak vertical STHT magnitudes were comparable. Owing to the strong coupled effects of gender and anthropometric dimensions, the study is designed to reduce the coupling by considering datasets for subjects with comparable chosen dimensions. Among the various anthropometric dimensions considered, the body mass and fat mass revealed strong influences on the primary resonance frequency, which was similar for male and female subjects with comparable body mass index and body fat mass. The vertical STHT magnitude of the two genders with the same lean body mass was also nearly identical. The peak fore-aft STHT magnitudes of the male subjects were notably higher than those of the female subjects with comparable anthropometric dimensions with the exception of the body mass.

Simulating 3D Human Postural Stabilization in Vibration and Dynamic Driving

In future automated vehicles we will often engage in non-driving tasks and will not watch the road. This will affect postural stabilization and may elicit discomfort or even motion sickness in dynamic driving. Future vehicles will accommodate this with properly designed seats and interiors, whereas comfortable vehicle motion will be achieved with smooth driving styles and well-designed (active) suspensions. To support research and development in dynamic comfort, this paper presents the validation of a multi-segment full-body human model, including visuo-vestibular and muscle spindle feedback, for postural stabilization. Dynamic driving is evaluated using a “sickening drive”, including a 0.2 Hz 4 m/s2 slalom. Vibration transmission is evaluated with compliant automotive seats, applying 3D platform motion and evaluating 3D translation and rotation of pelvis, trunk and head. The model matches human motion in dynamic driving and reproduces fore–aft, lateral and vertical oscillations. Visuo-vestibular and muscle spindle feedback are shown to be essential, in particular, for head–neck stabilization. Active leg muscle control at the hips and knees is shown to be essential to stabilize the trunk in the high-amplitude slalom condition but not with low-amplitude horizontal vibrations. However, active leg muscle control can strongly affect 4–6 Hz vertical vibration transmission. Compared to the vibration tests, the dynamic driving tests show enlarged postural control gains to minimize trunk and head roll and pitch and to align head yaw with driving direction. Human modelling can enable the insights required to achieve breakthrough comfort enhancements, while enabling efficient developments for a wide range of driving conditions, body sizes and other factors. Hence, modelling human postural control can accelerate the innovation of seats and vehicle motion-control strategies for (automated) vehicles.

Analysis of the similarity design and vibration transmission characteristics of typical support structures of an aero-engine

In the vibration test of an entire aero-engine, the magnitude and phase of the unbalanced vector of the internal rotor must be identified based on the vibration signal of the measuring point on the casing. Therefore, in addition to understanding the vibration transmission law between the high- and low-pressure rotors under unbalanced excitation, the vibration transmission law of the support structure must be studied urgently. However, few studies have investigated the vibration transfer characteristics of typical support structures. In this study, the similarity design of typical support structures was first performed, and the structural parameters of the core member squirrel cage were determined using theoretical calculations. Subsequently, the bush and spring elements were used to establish the connection between the inner and outer rings of the bearing to realise the equivalent simulation of the bearing stiffness. Using this method, refined finite element models of elastic and rigid support structures were established, and the accuracy of the model was verified based on low-speed rotating vibration and hammering tests. Furthermore, the unbalanced vibration transmission law of typical support structures was studied, and the vertical vibration transmission law from an aero-engine bearing pedestal to the panel was established with the vibration transmission rate as the quantitative index. Finally, considering the vital role of the squirrel cage, the influence of the local stiffness degradation of the squirrel cage on the unbalanced vibration transmission of the elastic support structure was studied. The research methods and results of this study can provide a basis for aero-engine assembly as well as manufacturing and structural performance evaluation.

Study on vertical vibration and transmission characteristics of railway ballast using impact hammer test

The vertical vibration and transmission characteristics of ballast are key factors that affect the dynamic stability of railway track structures and control the settlement of ballasted beds. Therefore, the following study was conducted to explore this topic. Firstly, through an impact hammer test on a ballast sensor with embedding chip, the vertical vibration data of the ballast was accurately measured. Therefore, the vertical vibration characteristics of a single ballast can be studied. Then, the vertical vibration characteristics at different positions in the stack were obtained by embedding ballast sensors into a ballasted stack. Finally, combined with field tests, a discrete element numerical model was established, then the vibration transmission speed and diffusion angle in a ballasted stack were calculated. The results of this study show that the damping ratio of ballast particles is less than 0.1, and the natural frequency is above 1000 Hz. The damping ratio and natural frequency of ballasts are greatly affected by their shape. The damping ratio of a ballasted stack is greater than that of ballast particles, and its natural frequency is lower. This indicates that the ballasted stack has the attributes of a soft material. The vertical acceleration transmission rate of ballasts is lower at frequencies below 257.94 Hz. This shows that the vibration suppression ability of the ballasted bed is better in the lower frequency range. As the depth increases, the vertical vibration transmission speed of the ballast gradually decreases, as does the accumulated external force. In the impact hammer test of a ballasted box, the average vertical vibration transmission speed was calculated to be 0.88 mm/μs, and the ballast vibration was transmitted downward at a diffusion angle of 35.32°–54.51° from the direction of gravity.

Vibration transmission simulation model of a seated vehicle passenger

The paper presents development of vertical vibration simulation for a seated passenger in a moving vehicle is resulting from the bounce effect of the vehicle under various conditions. Although extensive research has been conducted in this field of study, the existing analysis were conducted on either the suspension of vehicle or the human body and not both. In this paper, the simulation model consists of three sub-systems, namely, vehicle suspension, seat suspension and human body model in which the vertical vibration is transmitted. By incorporating these sub-systems into the simulation, a correlation between mechanical and biological aspects can be formed between the three sub-systems. The transmission of vertical vibration in the validated simulation model provides a more realistic approach which can result to a better comparison to the real-life scenario. Parametric analysis of passive suspension system shows that lower mass ratio, higher stiffness ratio and lower damping coefficient results in better ride comfort. The incorporation of variable damper into the suspension system shows significant improvement in settling time, peak displacement and velocity, lesser discomfort rating and higher safety in passenger body.

Vibration transmission and energy dissipation through the gear-shaft-bearing-housing system subjected to impulse force on gear

Abstract In this work, an eight-degree-of-freedom (DOF) dynamic model of the gear-shaft-bearing-housing system is established and the vertical vibration transmission and energy dissipation characteristics through the multiple transmitting interfaces under the impulse force due to gear fault are studied. The elastic deformations at the interfaces between gear and shaft, inner race and outer race, outer race and housing are formulated by the corresponding contact stiffness. The housing compliance is also included. A half-sine impulse force with two characteristic parameters as amplitude and time duration, which are associated with the defect type and size, is employed to represent the effect of gear fault on the system dynamics. The acceleration responses for different transmitting components as gear, inner race, outer race and housing are calculated for different impulse time duration, different impulse force amplitudes and shaft rotating speeds. The vibration transmission and energy dissipation through the multiple interfaces are characterized by the defined vibration transmission ratio and energy dissipation ratio. Obvious attenuation in acceleration magnitude is observed between the transmitting components from gear to housing. The maximum attenuation occurs at the transmission from inner race to outer race, while the minimum is between the outer race and the housing. The time duration of the impulse force determines the resonance and also the vibration transmission characteristics of the system. The energy dissipation increases nonlinearly with the amplitude of the applied impulse force. Results also suggest that the interface between inner race and outer race, and the interface between gear and shaft dissipated about 60% and 40% of the total energy, are the main sources of energy dissipation in the system. However, the shaft rotating speed has limited effect on the vertical impulse vibration amplitude, vibration transmission and energy dissipation. Experimental validation is performed, which supports the characteristics obtained from numerical results.

Transmission of fore-and-aft vibration to the seat pan, the backrest and the headrest of a car seat

Measurements of the transmission of vibration from the floor beneath a seat to interfaces between the seat and the human body are used to characterise the dynamic performance of the seat. Most studies of seat transmissibility concern the transmission of vertical vibration through seat pan cushions, but fore-and-aft vibration at a seat pan and backrest can also cause discomfort. This study investigated the transmission of fore-and-aft vibration through a car seat to surfaces on the seat pan cushion, the backrest cushion and the headrest, and also to the seat frame at these three locations. The study sought to understand the influences of the seat frame and the cushion foam and to provide data for dynamic modelling of the seat. The fore-and-aft transmissibility of the seat was measured with 12 human subjects and an SAE J826 manikin, using 120-s periods of fore-and-aft random vibration (0.25-40 Hz) at three magnitudes (0.4 m/s2 r.m.s., 0.8 m/s2 r.m.s. and 1.2 m/s2 r.m.s.). With the manikin, there were three resonances (at 3.5 Hz, 12 Hz and 20 Hz) in the transmissibilities from the seat base to the seat pan frame and the seat pan cushion, and to the backrest frame and the backrest cushion. With the human subjects, the transmissibilities from the seat base to all six locations on the seat showed a principal resonance around 4 Hz. With increasing magnitude of the vibration, the principal resonance frequency in all the seat transmissibilities decreased. It is concluded that fore-and-aft resonances in the seat transmissibilities, especially to the backrest, are likely to affect vibration discomfort. There are large differences between the fore-and-aft transmissibility of a seat with a manikin and those with human subjects, consistent with the human body having dynamics very different from those of a rigid mass. Non-linearities in the seat transmissibilities with the manikin and with the human subjects may be explained by non-linearity in the biodynamics of the body and the responses of the seat and the manikin.

Transmission of vertical vibration through a seat: Effect of thickness of foam cushions at the seat pan and the backrest

The perception of vehicle ride comfort is influenced by the dynamic performance of full-depth foam used in many vehicle seats. The effects of the thickness of foam on the dynamic stiffness (i.e., stiffness and damping as a function of frequency) of foam cushions with three thicknesses (60, 80, and 100 mm), and the vibration transmitted through these cushions at the seat pan and the backrest were measured with 12 subjects (6 males and 6 females). With increasing thickness, the stiffness and the damping of the foam decreased. With increasing thickness of foam at the seat pan, the resonance frequencies around 4 Hz in the vertical in-line and fore-and-aft cross-axis transmissibilities of the seat pan cushion and the backrest cushion decreased. For the conditions investigated, it is concluded that the thickness of foam at a vertical backrest has little effect on the vertical in-line or fore-and-aft cross-axis transmissibilities of the foam at either the seat pan or the backrest. The frequencies of the primary resonances around 4 Hz in the vertical in-line transmissibility and the fore-and-aft cross-axis transmissibility of foam at the seat pan were highly correlated. Compared to sitting on a rigid seat pan with a foam backrest, sitting with foam at both the seat pan and the backrest reduced the resonance frequency in the vertical in-line transmissibility of the backrest foam and increased the associated transmissibility at resonance, while the fore-and-aft cross-axis transmissibility of the backrest was little affected. Compared to sitting without a backrest, sitting with a rigid vertical backrest increased the resonance frequency of the fore-and-aft cross-axis transmissibility of the seat pan cushion and increased the transmissibility at resonance. Relevance to industryThe transmissibility of a seat is determined by the dynamic properties of the occupant of the seat and the dynamic properties of the seat. This study shows how the thicknesses of foam at a seat pan and foam at a backrest affect the in-line and cross-axis transmissibilities of the foams at the seat pan and the backrest. The findings have application to the design of vehicle seats to minimise the transmission of vibration to the body.

The application of SEAT values for predicting how compliant seats with backrests influence vibration discomfort

The extent to which a seat can provide useful attenuation of vehicle vibration depends on three factors: the characteristics of the vehicle motion, the vibration transmissibility of the seat, and the sensitivity of the body to vibration. The ‘seat effective amplitude transmissibility’ (i.e., SEAT value) reflects how these three factors vary with the frequency and the direction of vibration so as to predict the vibration isolation efficiency of a seat. The SEAT value is mostly used to select seat cushions or seat suspensions based on the transmission of vertical vibration to the principal supporting surface of a seat. This study investigated the accuracy of SEAT values in predicting how seats with backrests influence the discomfort caused by multiple-input vibration. Twelve male subjects participated in a four-part experiment to determine equivalent comfort contours, the relative discomfort, the location of discomfort, and seat transmissibility with three foam seats and a rigid reference seat at 14 frequencies of vibration in the range 1–20 Hz at magnitudes of vibration from 0.2 to 1.6 ms−2 r.m.s. The ‘measured seat dynamic discomfort’ (MSDD) was calculated for each foam seat from the ratio of the vibration acceleration required to cause similar discomfort with the foam seat and with the rigid reference seat. Using the frequency weightings in current standards, the SEAT values of each seat were calculated from the ratio of overall ride values with the foam seat to the overall ride values with the rigid reference seat, and compared to the corresponding MSDD at each frequency. The SEAT values provided good predictions of how the foam seats increased vibration discomfort at frequencies around the 4-Hz resonance but reduced vibration discomfort at frequencies greater than about 6.3 Hz, with discrepancies explained by a known limitation of the frequency weightings.

Noise reduction performance of wheel and rail vibration absorbers

The rolling noise reduction effectiveness of wheel and rail vibration absorbers was evaluated at Trimet in Portland, Oregon. Tests included tangent ballast and concrete tie track and curved track slab track with bi-block concrete ties. Under-car noise data were recorded throughout the system with and without wheel vibration absorbers. Results of the rolling noise tests are summarized for various combinations of treated and untreated rails and wheels. The wheel and especially the rail vibration absorbers significantly reduced rail vibration at audio frequencies, but had little effect on wayside rolling noise. Wayside noise at tangent track was slightly higher with rail vibration absorbers than without. However, the “singing rail” noise was eliminated entirely. The “singing rail” vertical vibration transmission spectrum had a pass-band characteristic as expected for periodic supports. The vibration data indicate that above 250 Hz the wheel was the dominant source of noise relative to the rail. A reduction of stick-slip noise was observed over most curves, though results were inconsistent.

Transmission of Vertical Vibration to the Human Foot and Ankle

The load absorbing capability of the foot and ankle system (FAS) was characterized by measuring the transmissibility and the phase delay at the medial malleolus and the tibial tuberosity. The FAS of twenty subjects were exposed to sinusoidal vertical excitation (10-50 Hz with 5 Hz increments and peak to peak acceleration of 17.9 m/s(2)) while sitting as a function of the external mass (0, 2.3, and 4.5 kg) and the foot postures (midstance, plantarflexion, and dorsiflexion). The results showed that the FAS plays important role in vibration transmission of lower leg. Adding extra mass affected a resonant frequency at the medial malleolus: 15-25, 30-35, and 35 Hz for with no additional mass, 2.3, and 4.5 kg, respectively. However, the changed postures of the FAS did not show significant effect on the resonant frequency. The applied mass affected the stiffness increase of the FAS and consequently resulted in the increase of the resonant frequency. This result supports the assertion that the resonant frequency of overweight or obese persons is similar to the major frequency component (25-35 Hz) of the heel strike.

Measurement of transmission of vibration through the human spine using skin-mounted inertial sensors

The purpose of this study was to examine the feasibility of measuring the transmission of vibration using skin mounted inertial sensors and to assess the dynamic properties of the human spine during activities of daily living. Two inertial sensors were attached to skin overlying the first thoracic vertebra (T1) and another one over the first sacral vertebra (S1) with double sided adhesive tape. Subjects walked along a straight line, and up and down stairs at a self selected, comfortable speed. Transmissibility of vertical vibration was calculated as the ratio of the power spectral density of the acceleration signal at T1 over that at S1, over the frequency range of 0.5–12Hz. Cross correlation and coherence of the acceleration signals between the two T1 sensors were performed to evaluate the similarity of the data after correction. Cross correlation of signals between trials was also performed to examine the repeatability of the signals. Cross correlation coefficients were found to be very high (>0.9). Inter-trial consistency of the signals of all sensors was also high (>0.9). It is concluded that skin measurement of transmission of vertical vibration is feasible with the inertial sensors and correction method presented. Different physical activities seem to elicit different frequency characteristics of 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.

Apparent mass of the human body in the vertical direction: Effect of seat backrest

The transmission of vibration through a seat depends on various characteristics of the seat and the dynamic response of the human body. The dynamic response of the body can be represented by its apparent mass, but the effect of the seat on the apparent mass of the body is not well understood. This study was designed to quantify the effect of foam and rigid backrests on the vertical apparent mass of the human measured at the seat surface supporting the body. The apparent masses of 12 subjects were measured during exposure to random vertical vibration (1.0 ms −2 rms from 0.125 to 40 Hz) in a seat with a rigid backrest, in the same rigid seat with three thicknesses of foam backrest (50, 100 and 150 mm), and in the same seat with no backrest. The backrests were inclined at various angles: 0°, 5°, 10°, 15°, 20°, 25° and 30° for the rigid and 100 mm foam backrests, and 0°, 10°, 20° and 30° for the 50 and 150 mm foam backrests. With all vertical backrests (i.e., 0° inclination), there were resonances in the apparent mass of the body around 5 and 10 Hz. With no backrest, the apparent mass was increased at frequencies less than the resonance frequency but decreased at frequencies between 8 and 20 Hz, relative to the apparent mass with the vertical rigid and foam backrests. With the rigid backrest, the primary resonance frequencies in the apparent mass increased with increasing backrest inclination. With the foam backrests, the resonance frequencies decreased with increasing backrest inclination. At frequencies less than the primary resonance, the apparent mass decreased with increasing backrest inclination, particularly with the rigid backrest. Between 8 and 15 Hz, the apparent mass decreased with increasing inclination, most notably with the foam backrests. At inclinations less than 30°, there was little effect of foam thickness on the apparent mass, but at 30° an increase in the thickness of the foam decreased the frequency of the first resonances. Since contact with backrests and the characteristics of backrests influence the vertical apparent mass of the seated body, backrests should be expected to influence the transmission of vertical vibration through a supporting seat cushion.

Transmission of vibration to the backrest of a car seat evaluated with multi-input models

The transmission of vibration to the occupant of a car seat has been studied using the multiple vibration inputs to the seat. Twelve input signals at the seat base (tri-axial vibration at the four corners) and six output signals (tri-axial vibration at the backrest and seat pan) were measured while driving. The results showed that vibration inputs to the seat varied between the four positions at the seat base. The two fore-aft input accelerations at the left-hand side of the seat base and the two fore-aft input accelerations at the right-hand side of the seat base were highly correlated with each other. There was also a high correlation between the two pairs of lateral acceleration inputs at the front and rear of the seat base. A computer program for studying seat vibration transmission via multi-input channels was developed to allow the calculation of seat transmissibility with up to 12 different inputs. The transmission of multi-axis seat base vibration to fore-aft seat backrest vibration was investigated using single-input, two-input, six-input and eight-input models. Results showed that the fore-aft vibration and the vertical vibration, but not lateral vibration, at the four corners of the seat base contributed to fore-aft vibration of the backrest. The primary peak of the fore-aft backrest transmissibility occurred around 4–5 Hz. The coherency was improved when using the multi-input models, although the characteristics of the transmissibility remained similar. The transmission of lateral vibration at the seat base to lateral vibration at the backrest was studied using single-input and two-input models. With single-input models, the transmission of lateral acceleration at the seat base to lateral acceleration at the backrest was amplified between 18 and 35 Hz, with a peak at 26 Hz. Coherency was greater at frequencies above 20 Hz than at lower frequencies. The coherency at low frequencies was increased with a two-input model. The transmission of vertical vibration to vertical vibration at the backrest was investigated using single-input, four-input and six-input models. The results showed that vertical acceleration at the four corners of the seat base was highly correlated with vertical acceleration at the backrest. The results are consistent with previous findings that a single-input model is not sufficient to study the transmission of vibration to the seat back in the horizontal directions, while for the transmission of vertical vibration a single-input model is probably sufficient, especially when low frequencies are of main concern.

Transmission of vibration to the backrest of a car seat evaluated with multi-input models

The transmission of vibration to the occupant of a car seat has been studied using the multiple vibration inputs to the seat. Twelve input signals at the seat base (tri-axial vibration at the four corners) and six output signals (tri-axial vibration at the backrest and seat pan) were measured while driving. The results showed that vibration inputs to the seat varied between the four positions at the seat base. The two fore-aft input accelerations at the left-hand side of the seat base and the two fore-aft input accelerations at the right-hand side of the seat base were highly correlated with each other. There was also a high correlation between the two pairs of lateral acceleration inputs at the front and rear of the seat base. A computer program for studying seat vibration transmission via multi-input channels was developed to allow the calculation of seat transmissibility with up to 12 different inputs. The transmission of multi-axis seat base vibration to fore-aft seat backrest vibration was investigated using single-input, two-input, six-input and eight-input models. Results showed that the fore-aft vibration and the vertical vibration, but not lateral vibration, at the four corners of the seat base contributed to fore-aft vibration of the backrest. The primary peak of the fore-aft backrest transmissibility occurred around 4–5 Hz. The coherency was improved when using the multi-input models, although the characteristics of the transmissibility remained similar. The transmission of lateral vibration at the seat base to lateral vibration at the backrest was studied using single-input and two-input models. With single-input models, the transmission of lateral acceleration at the seat base to lateral acceleration at the backrest was amplified between 18 and 35 Hz, with a peak at 26 Hz. Coherency was greater at frequencies above 20 Hz than at lower frequencies. The coherency at low frequencies was increased with a two-input model. The transmission of vertical vibration to vertical vibration at the backrest was investigated using single-input, four-input and six-input models. The results showed that vertical acceleration at the four corners of the seat base was highly correlated with vertical acceleration at the backrest. The results are consistent with previous findings that a single-input model is not sufficient to study the transmission of vibration to the seat back in the horizontal directions, while for the transmission of vertical vibration a single-input model is probably sufficient, especially when low frequencies are of main concern.

COMPARISON OF BIODYNAMIC RESPONSES IN STANDING AND SEATED HUMAN BODIES

The dynamic responses of the human body in a standing position and in a sitting position have been compared. The apparent mass and transmissibilities to the head, six locations along the spine, and the pelvis were measured with eight male subjects exposed to vertical whole-body vibration. In both postures, the principal resonance in the apparent mass occurred in the range 5–6 Hz, with slightly higher frequencies and lower apparent mass in the standing posture. There was greater transmission of vertical vibration to the pelvis and the lower spine and greater relative motion within the lower spine in the standing posture than in the sitting posture at the principal resonance and at higher frequencies. Transmissibilities from the supporting surface (floor or seat) to the thoracic region had similar magnitudes for both standing and sitting subjects. The lumbar spine has less lordosis and may be more compressed and less flexible in the sitting posture than in the standing posture. This may have reduced the relative motions between lumbar vertebrae and both the supporting vibrating surface and the other vertebrae in the sitting posture. The characteristics of the vibration transmitted to the pelvis may have differed in the two postures due to different transmission paths. Increased forward rotation of the pelvis in the standing posture may have caused the differences in responses of the pelvis and the lower spine that were observed between the two postures.

VERTICAL VIBRATION TRANSMISSION THROUGH THE LUMBAR SPINE OF THE SEATED SUBJECT—FIRST RESULTS

Seven fresh, not embalmed, cadavers (58·1±6·6 years, 73±10·3 kg, 170·7±6·5 cm) were submitted, in the week following their death (7·1±3·1 days), to a whole-body vertical broad-band white random vibration in the bandwidth 0·8 to 25 Hz of about 1·5 m/s2r.m.s. Two postures were tested using the same rigid seat, each one with and without a lumbar support: seated erect and seated as in a car. Vibration was monitored on the floor, the seating in the vertical direction (buttocks-to-head), the five lumbar vertebrae and the sternum: vertical (buttocks to head) and longitudinal (back to chest). Biaxial accelerometers were mounted rigidly on the anterior face of the vertebral body, after the removal of the abdominal viscera. Analogue recordings of each channel were passed through an antialising filter (Fc=40 Hz) then sampled at 80 Hz (4096 samples/channel). The inclination of each accelerometer (α) was measured on the lateral X-ray taken for every trial, then the data were set in order to be in the same reference (Z=z/cos α,X=xcos α). Spectral analysis was performed with a frequency resolution of 0·3 Hz, on the basis of Welch's method. Thirty one overlapping sections (256 samples per section using a Hanning window with an overlap rate of 128 samples) of the estimated periodograms were averaged. Transfer and coherence functions were than estimated between the vertical seating acceleration and the measured accelerations at the upper levels. The first results showed that the vertical vibration transmission was constant throughout the lumbar spine. Inter-subject variability was the major source of disparity. Resonance phenomena were observed between 4 and 9 Hz and depended on posture.

DYNAMIC RESPONSE OF THE STANDING HUMAN BODY EXPOSED TO VERTICAL VIBRATION: INFLUENCE OF POSTURE AND VIBRATION MAGNITUDE

The influence of the posture of the legs and the vibration magnitude on the dynamic response of the standing human body exposed to vertical whole-body vibration has been investigated. Motions were measured on the body surface at the first and eighth thoracic and fourth lumbar vertebrae (T1, T8 and L4), at the right and left iliac crests and at the knee. Twelve subjects took part in the experiment with three leg postures (normal, legs bent and one leg), and five magnitudes of random vibration (0·125–2·0 ms−2r.m.s.) in the frequency range from 0[msde]5–30 Hz. The main resonance frequencies of the apparent masses at 1·0 ms−2r.m.s. differed between postures: 5·5 Hz in the normal posture, 2·75 Hz in the legs bent posture and 3·75 Hz in the one leg posture. In the normal posture, the transmissibilities to L4 and the iliac crests showed a similar trend to the apparent mass at low frequencies. With the legs straight, no resonance was observed in the legs at frequencies below 15 Hz. In the legs bent posture, a bending motion of the legs at the knee and a pitching or bending motion of the upper-body appeared to contribute to the resonance of the whole body as observed in the apparent mass, with attenuation of vibration transmission to the upper body at high frequencies. In the one leg posture, coupled rotational motion of the whole upper-body about the hip joint may have contributed to the resonance observed in the apparent mass at low frequencies and the attenuation of vertical vibration transmission at high frequencies. The resonance frequency of the apparent mass in the normal posture decreased from 6·75–5·25 Hz with increasing vibration magnitude from 0·125 to 2·0 ms−2r.m.s. This “softening” effect was also found in the transmissibilities to many parts of the body that showed resonances.