Assessments of two dynamic manikins for laboratory testing of seats under whole-body vibration

The aptness of two anthropodynamic manikins for assessing vibration isolation effectiveness of suspension seats is evaluated through laboratory measurements. The evaluations were performed using five different suspension seats exposed to idealized white noise (0.5–20 Hz) and target vehicle excitations along the vertical axis using a whole-body vehicular vibration simulator. The measurements were performed to derive acceleration transmissibility and seat effective amplitude transmissibility (SEAT) characteristics of seats loaded with: human subjects of body masses in the vicinity of 55, 75 and 98 kg; manikins configured to same masses; and equivalent rigid masses. The dynamic responses of the manikins were also measured under different magnitudes of white-noise excitations and expressed in terms of apparent mass. The relative applicability of the manikins for selected seats was evaluated by comparing the measures with those obtained for the seat–human and seat–mass systems. The comparisons suggested that the SEAT measures attained with manikins are comparable with those obtained with equivalent rigid mass, irrespective of the body mass, for the low natural frequency seats (2 Hz) considered in the study. Both the manikins and the equivalent rigid masses, however, provided an overestimate of isolation effectiveness of seats, when compared to those with human subjects. The manikins resulted in better estimates of SEAT values for high natural frequency seats than the rigid mass. The dynamic responses of manikins were also compared with the ranges of standardized values reported in ISO-5982 and DIN-45676. The results revealed considerable differences between the biodynamic responses of manikins and the standardized ranges.     

Seated body apparent mass response to vertical whole body vibration: Gender and anthropometric effects

The gender and anthropometric effects on apparent mass characteristics of the seated body exposed to vertical vibration are investigated through laboratory measurements. The study was conducted on 31 male and 27 female subjects, exposed to three levels of vertical vibration (0.25, 0.50 and 0.75 m/s² rms acceleration) in the 0.50 to 20 frequency range, while seated without a back support and against a vertical back support. The apparent mass responses were analyzed by grouping datasets in three ranges of mass-, build- and stature-related parameters for the male and female subjects. Comparisons of responses of male and female subjects with comparable anthropometric properties showed distinctly different biodynamic responses of the two genders. The primary resonance frequency of male subjects was significantly (p < 0.001) higher than the female subjects of comparable body mass but the peak magnitude was comparable for both the gender groups. The male subjects showed greater softening with increasing excitation magnitude compared to the female subjects, irrespective of the sitting condition. The male subjects showed significantly higher peak magnitude response than those of the female subjects for the same anthropometric properties, except for the total and lean body mass. The peak magnitude was linearly correlated with the body mass, body mass index, body fat and hip circumference (r² > 0.7), irrespective of the back support and excitation conditions for both the genders.Relevance to the industryThe apparent mass responses of the human body exposed to whole-body vibration form an essential basis for an understanding of mechanical-equivalent properties of the body, developments in frequency-weightings for assessment of exposure risks and anthropodynamic manikins for assessment of seats. The effects of gender and anthropometric parameters on the AM response are vital for seeking better seat designs, and anthropodynamic manikins for assessments of seating for male as well as female workers.     

Response of the seated human body to whole-body vertical vibration: biodynamic responses to sinusoidal and random vibration

The dependence of biodynamic responses of the seated human body on the frequency, magnitude and waveform of vertical vibration has been studied in 20 males and 20 females. With sinusoidal vibration (13 frequencies from 1 to 16 Hz) at five magnitudes (0.1–1.6 ms^? 2 r.m.s.) and with random vibration (1–16 Hz) at the same magnitudes, the apparent mass of the body was similar with random and sinusoidal vibration of the same overall magnitude. With increasing magnitude of vibration, the stiffness and damping of a model fitted to the apparent mass reduced and the resonance frequency decreased (from 6.5 to 4.5 Hz). Male and female subjects had similar apparent mass (after adjusting for subject weight) and a similar principal resonance frequency with both random and sinusoidal vibration. The change in biodynamic response with increasing vibration magnitude depends on the frequency of the vibration excitation, but is similar with sinusoidal and random excitation.     

Biodynamic response analysis of semi-supine human under varying vertical excitations

The biodynamic responses of semi-supine humans exposed to varying vertical vibration magnitudes (0.125–1.0 m/s² r.m.s.) are studied employing a multi-body modeling approach. The model comprises five rigid segments: the head, upper torso, lower torso, thigh, and leg. The viscoelastic property of tissues at joints and body-support interface are incorporated using the Kelvin-Voigt model. The dynamic model parameters identified through optimization are employed to capture the transmissibility responses of different body segments at varying vibration magnitudes. The Monte-Carlo simulation is performed to ascertain the effect of uncertainty of the model parameter and body mass on the biodynamic responses at different vibration magnitudes. The calibrated model accurately predicts the decrease in the primary resonance frequency with the increase in vibration magnitude. This nonlinearity is also apparent in vertical transmissibility responses of all the body segments. The effect of uncertainty of model parameters and body mass on the transmissibility responses is prominent near resonance frequency, while their effect on the apparent mass response is consistent across the entire frequency spectrum. The Monte-Carlo simulation illustrates higher dispersion in the transmissibility responses of the head and thorax at 1.0 m/s² r.m.s. compared to at 0.125 m/s² r.m.s. Therefore effective restraint systems are required at the head and thorax to counter the impact of high vibration magnitudes experienced during spaceflight.     

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

This study examined how the apparent mass and transmissibility of the human body depend on the magnitude of fore-and-aft vibration excitation and the presence of vertical vibration. Fore-and-aft and vertical acceleration at five locations along the spine, and pitch acceleration at the pelvis, were measured in 12 seated male subjects during fore-and-aft random vibration excitation (0.25–20 Hz) at three vibration magnitudes (0.25, 0.5 and 1.0 ms⁻² r.m.s.). With the greatest magnitude of fore-and-aft excitation, vertical vibration was added at 0.25, 0.5, or 1.0 ms⁻² r.m.s. Forces in the fore-and-aft and vertical directions on the seat surface were measured to calculate apparent masses. Transmissibilities and apparent masses during fore-and-aft excitation showed a principal resonance around 1 Hz and a secondary resonance around 2–3 Hz. Increasing the magnitude of fore-and-aft excitation, or adding vertical excitation, decreased the magnitudes of the resonances. At the primary resonance frequency, the dominant mode induced by fore-and-aft excitation involved bending of the lumbar spine and the lower thoracic spine with shear deformation of tissues at the ischial tuberosities. The relative contributions to this mode from each body segment (especially the pelvis and the lower thoracic spine) varied with vibration magnitude. The nonlinearities in the apparent mass and transmissibility during dual-axis excitation indicate coupling between the principal mode of the seated human body excited by fore-and-aft excitation and the cross-axis influence of vertical excitation.Relevance to industryUnderstanding movements of the body during exposure to whole-body vibration can assist the optimisation of seating dynamics and help to control the effects of the vibration on human comfort, performance, and health. This study suggests cross-axis nonlinearity in biodynamic responses to vibration should be considered when optimising vibration environments.     

Effects of elastic seats on seated body apparent mass responses to vertical whole body vibration

Apparent mass (AM) responses of the body seated with and without a back support on three different elastic seats (flat and contoured polyurethane foam (PUF) and air cushion) and a rigid seat were measured under three levels of vertical vibration (overall rms acceleration: 0.25, 0.50 and 0.75 m/s²) in the 0.5 to 20 Hz range. A pressure-sensing system was used to capture biodynamic force at the occupant-seat interface. The results revealed strong effects of visco-elastic and vibration transmissibility characteristics of seats on AM. The response magnitudes with the relatively stiff air seat were generally higher than those with the PUF seats except at low frequencies. The peak magnitude decreased when sitting condition was changed from no back support to a vertical support; the reduction however was more pronounced with the air seat. Further, a relatively higher frequency shift was evident with soft seat compared with stiff elastic seat with increasing excitation.     

Modelling and simulation of locomotive driver''s seat vertical suspension vibration isolation system

The paper describes the simulation of a vertical seat suspension system with a variable damper. The model presented describes a real damper with bushings and is an extension of the classical linear SDOF oscillatory system. Transfer functions were identified from laboratory measurements and the mechano-mathematical model produced was validated by field measurements. The seat cushion parameters were identified from laboratory measurements and combined with standardized vertical (z-axis) seated human body models (ISO 5982 and DIN 45676). These models, together with an inert mass human body model, were used to predict the vibration mitigation performance of the seat–occupant system. The results were compared to data obtained from field measurements under real operating conditions. It was found that the use of the inert mass human body model resulted in the smallest differences between predicted and measured system vibration isolation performance for the field excitation in the frequency band up to 4.5 Hz, where most of the vibratory energy was present in the field. Hence this simplified model is suggested for prediction of vibration influence on locomotive driver under field conditions.

Relevance to the industry

The developed model using various seated human body models in the vertical direction revealed that an inert mass instead of the human body model may be sufficient for reliable prediction of seat vibration mitigation properties in rail vehicles. The developed model and findings reported here assisted in development of an improved locomotive driver's seat.     

Analysis of non-linear response of the human body to vertical whole-body vibration

The human response to vibration is typically studied using linear estimators of the frequency response function, although different literature works evidenced the presence of non-linear effects in whole-body vibration response. This paper analyses the apparent mass of standing subjects using the conditioned response techniques in order to understand the causes of the non-linear behaviour. The conditioned apparent masses were derived considering models of increasing complexity. The multiple coherence function was used as a figure of merit for the comparison between the linear and the non-linear models. The apparent mass of eight male subjects was studied in six configurations (combinations of three vibration magnitudes and two postures). The contribution of the non-linear terms was negligible and was endorsed to the change of modal parameters during the test. Since the effect of the inter-subject variability was larger than that due to the increase in vibration magnitude, the biodynamic response should be more meaningfully modelled using a linear estimator with uncertainty rather than looking for a non-linear modelling.     

Comparisons of apparent mass responses of human subjects seated on rigid and elastic seats under vertical vibration

The apparent mass (AM) responses of human body seated on elastic seat, without and with a vertical back support, are measured using a seat pressure sensing mat under three levels of vertical vibration (0.25, 0.50 and 0.75 m/s² rms acceleration) in 0.50–20 Hz frequency range. The responses were also measured with a rigid seat using the pressure mat and a force plate in order to examine the validity of the pressure mat. The pressure mat resulted in considerably lower AM magnitudes compared to the force plate. A correction function was proposed and applied, which resulted in comparable AM from both measurement systems for the rigid seat. The correction function was subsequently applied to derive AM of subjects seated on elastic seat. The responses revealed lower peak magnitude and corresponding frequency compared to those measured with rigid seat, irrespective of back support and excitation considered.     

Response of the seated human body to whole-body vertical vibration: discomfort caused by sinusoidal vibration

Frequency weightings for predicting vibration discomfort assume the same frequency-dependence at all magnitudes of vibration, whereas biodynamic studies show that the frequency-dependence of the human body depends on the magnitude of vibration. This study investigated how the frequency-dependence of vibration discomfort depends on the acceleration and the force at the subject–seat interface. Using magnitude estimation, 20 males and 20 females judged their discomfort caused by sinusoidal vertical acceleration at 13 frequencies (1–16 Hz) at magnitudes from 0.1 to 4.0 ms^? 2 r.m.s. The frequency-dependence of their equivalent comfort contours depended on the magnitude of vibration, but was less dependent on the magnitude of dynamic force than the magnitude of acceleration, consistent with the biodynamic non-linearity of the body causing some of the magnitude-dependence of equivalent comfort contours. There were significant associations between the biodynamic responses and subjective responses at all frequencies in the range 1–16 Hz.

Practitioner Summary: Vertical seat vibration causes discomfort in many forms of transport. This study provides the frequency-dependence of vibration discomfort over a range of vibration magnitudes and shows how the frequency weightings in the current standards can be improved.     

Modal analysis of human body vibration model for Indian subjects under sitting posture

Need and importance of modelling in human body vibration research studies are well established. The study of biodynamic responses of human beings can be classified into experimental and analytical methods. In the past few decades, plenty of mathematical models have been developed based on the diverse field measurements to describe the biodynamic responses of human beings. In this paper, a complete study on lumped parameter model derived from 50th percentile anthropometric data for a seated 54- kg Indian male subject without backrest support under free un-damped conditions has been carried out considering human body segments to be of ellipsoidal shape. Conventional lumped parameter modelling considers the human body as several rigid masses interconnected by springs and dampers. In this study, concept of mass of interconnecting springs has been incorporated and eigenvalues thus obtained are found to be closer to the values reported in the literature. Results obtained clearly establish decoupling of vertical and fore-and-aft oscillations.     

Feasibility analysis of low-cost flexible resistive sensors for measurements of driving point mechanical impedance of the hand-arm system

This study explored the feasibility of the flexible resistive (FlexiForce) force sensors for measurement of the hand-arm biodynamic response. Two FlexiForce sensors were installed on an instrumented handle to measure the palm-handle and finger–handle interface dynamic forces. The measurements were performed with six subjects grasping a 38 mm diameter instrumented handle with nine different combinations of grip (10, 30 and 50 N) and push (25, 50 and 75 N) forces and two levels of broad-band random vibration (1.5 and 3.0 m/s² weighted rms acceleration) in the 4–1000 Hz frequency range. The data acquired from the instrumented handle was analyzed to determine the palm and finger impedance responses, which served as the reference values to evaluate feasibility of the FlexiForce sensors. The comparisons revealed very similar trends, while the impedance magnitude responses obtained from the FlexiForce sensors were substantially lower in the entire frequency range than the reference values, except at very low frequencies. A correction function was subsequently developed and applied to the FlexiForce measured data, which resulted in similar hand-arm impedance response trends compared to the reference values. It was concluded that the low-cost FlexiForce sensors could be applied for measurements of biodynamic responses of the hand-arm system in real tool handles in the field. Due to the physiological risks associated with prolonged exposure to tool vibration the applicability of a low-cost biodynamic response measurement system can be used as a preventative measure for such risks.Relevance to industryThe measurement of hand–handle interface forces is vital for assessing the hand-transmitted vibration exposure and the biodynamic responses of the hand-arm system to vibration. The low cost and flexible sensors, proposed in the study, could be conveniently applied to the curved surfaces of real power tool handles in the field. The most significant benefit of the sensors lies with its negligible mass and thereby the instrumented handle inertia-induced errors in the biodynamic responses can be eliminated.     

Subjective discomfort caused by vertical whole-body vibration in the frequency range 2–100 Hz

Current standards assume the same frequency weightings for discomfort at all magnitudes of vibration, whereas biodynamic and psychological studies show that the frequency-dependence of objective and subjective responses of the human body depends on the magnitude of vibration. This study investigated the discomfort of seated human body caused by vertical whole-body vibration over the frequency range 2–100?Hz at relatively high magnitudes from 1.0 to 2.5?ms^?2 r.m.s. Twenty-eight subjects (15 males and 13 females) judged the discomfort using the absolute magnitude estimation method. The rate of growth of discomfort with increasing vibration magnitude was highly dependent on the frequency, so the shapes of the equivalent comfort contours depended on the magnitude of vibration and no single frequency weighting would be appropriate for all magnitudes. The equivalent comfort contours indicated that the standards and previous relevant studies underestimated the vibration discomfort at frequencies greater than about 30?Hz.

Practitioner Summary: The discomfort caused by vertical vibration at relatively high frequencies can be severe, particularly at relatively great magnitudes in transport. This study provides the frequency-dependence of vibration discomfort at 2–100?Hz, and shows how the frequency weightings in the current standards can be improved at relatively high frequencies.     

Whole-body vertical biodynamic response characteristics of the seated vehicle driver: Measurement and model development

The vertical driving-point mechanical impedance characteristics applicable to seated vehicle drivers are measured in the 0.625–10 Hz frequency range with excitation amplitudes ranging from 1.0 to 2.0 m s⁻² using a whole-body vehicular vibration simulator. The measurements are performed for seated subjects with feet supported and hands held in a driving position. Variations in the seated posture, backrest angle, and nature and amplitude of the vibration excitation are introduced within a prescribed range of likely conditions to illustrate their influence on the driving-point mechanical impedance of seated vehicle drivers. Within the 0.75–10 Hz frequency range and for excitation amplitudes maintained below 4 m s⁻², a four-degree-of-freedom linear driver model is proposed for which the parameters are estimated to satisfy both the measured driving-point mechanical impedance and the seat-to-head transmissibility characteristics defined from a synthesis of published data for subjects seated erect without backrest support. The parameter identification technique involves the solution of a multivariable optimization function comprising the sum of squared magnitude and phase errors associated with both the mechanical impedance and seat-to-head transmissibility target values, subject to limit constraints identified from the anthropometric and biomechanical data. The model response, however, is found to provide a closer agreement with the mechanical impedance target values than that with the seat-to-head transmissibility. From the model, the main body resonant frequencies computed on the basis of both biodynamic response functions are found to be within close bounds to that expected for the human body.

Relevance to industry

The development of an appropriate analytical seated vehicle driver model should provide means of estimating the forces and motions being transmitted within the body under specific vehicular vibration environments. Furthermore, its use in conjunction with a corresponding model for the vehicle seat should allow the prediction of the driver's vibration exposure levels and the seat's ability to attenuate the vibration in particular vehicles.     

Apparent mass of small children: experimental measurements

A test facility and protocol were developed for measuring the seated, vertical, whole-body vibration response of small children of less than 18 kg in mass over the frequency range from 1 to 45 Hz. The facility and protocol adhered to the human vibration testing guidelines of BS7085 and to current codes of ethics for research involving children. Additional procedures were also developed which are not currently defined in the guidelines, including the integral involvement of the parents and steps taken to maximize child happiness. Eight children were tested at amplitudes of 0.8 and 1.2 m/s(2) using band-limited, Gaussian, white noise acceleration signals defined over the frequency interval from 1 to 50 Hz. Driving point apparent mass modulus and phase curves were determined for all eight children at both test amplitudes. All results presented a single, principal, anti-resonance, and were similar to data reported for primates and for adult humans seated in an automotive posture which provided backrest support. The mean frequency of the apparent mass peak was 6.25 Hz for the small children, as compared to values between 6.5 - 8.5 Hz for small primates and values between 6.5 - 8.6 Hz for adults seated with backrest support. The peak value of the mean, normalized, apparent mass was 1.54 for the children, which compares to values from 1.19 to 1.45 reported in the literature for small primates and 1.28 for adults seated with backrest support. ISO standard 5982, which specifies a mean, normalized, apparent mass modulus peak of 1.50 at a frequency of 4.0 Hz for adults seated without backrest support, provides significant differences.     

Apparent mass of small children: experimental measurements

A test facility and protocol were developed for measuring the seated, vertical, whole-body vibration response of small children of less than 18 kg in mass over the frequency range from 1 to 45 Hz. The facility and protocol adhered to the human vibration testing guidelines of BS7085 and to current codes of ethics for research involving children. Additional procedures were also developed which are not currently defined in the guidelines, including the integral involvement of the parents and steps taken to maximize child happiness. Eight children were tested at amplitudes of 0.8 and 1.2 m/s² using band-limited, Gaussian, white noise acceleration signals defined over the frequency interval from 1 to 50 Hz. Driving point apparent mass modulus and phase curves were determined for all eight children at both test amplitudes. All results presented a single, principal, anti-resonance, and were similar to data reported for primates and for adult humans seated in an automotive posture which provided backrest support. The mean frequency of the apparent mass peak was 6.25 Hz for the small children, as compared to values between 6.5 – 8.5 Hz for small primates and values between 6.5 – 8.6 Hz for adults seated with backrest support. The peak value of the mean, normalized, apparent mass was 1.54 for the children, which compares to values from 1.19 to 1.45 reported in the literature for small primates and 1.28 for adults seated with backrest support. ISO standard 5982, which specifies a mean, normalized, apparent mass modulus peak of 1.50 at a frequency of 4.0 Hz for adults seated without backrest support, provides significant differences.     

Vibrations transmitted from human hands to upper arm,shoulder, back,neck, and head

Some powered hand tools can generate significant vibration at frequencies below 25 Hz. It is not clear whether such vibration can be effectively transmitted to the upper arm, shoulder, neck, and head and cause adverse effects in these substructures. The objective of this study is to investigate the vibration transmission from the human hands to these substructures. Eight human subjects participated in the experiment, which was conducted on a 1-D vibration test system. Unlike many vibration transmission studies, both the right and left hand-arm systems were simultaneously exposed to the vibration to simulate a working posture in the experiment. A laser vibrometer and three accelerometers were used to measure the vibration transmitted to the substructures. The apparent mass at the palm of each hand was also measured to help in understanding the transmitted vibration and biodynamic response. This study found that the upper arm resonance frequency was 7–12 Hz, the shoulder resonance was 7–9 Hz, and the back and neck resonances were 6–7 Hz. The responses were affected by the hand-arm posture, applied hand force, and vibration magnitude. The transmissibility measured on the upper arm had a trend similar to that of the apparent mass measured at the palm in their major resonant frequency ranges. The implications of the results are discussed.Relevance to industryMusculoskeletal disorders (MSDs) of the shoulder and neck are important issues among many workers. Many of these workers use heavy-duty powered hand tools. The combined mechanical loads and vibration exposures are among the major factors contributing to the development of MSDs. The vibration characteristics of the body segments examined in this study can be used to help understand MSDs and to help develop more effective intervention methods.     

Study of human–seat interface pressure distribution under vertical vibration

The influence of whole-body vertical vibration on the dynamic human–seat interface pressure is investigated using a flexible grid of pressure sensors. The ischium pressure and the overall pressure distribution at the human–seat interface are evaluated as functions of the magnitude and frequency of vibration excitation, and seated posture and height. The dynamic pressure at the seat surface is measured under sinusoidal vertical vibration of different magnitudes in the 1–10 Hz frequency range. Two methods based on ischium pressure and ischium force are proposed to study the influence of seat height, posture and characteristics of vibration. The results of the study reveal that the amplitude of dynamic pressure component increases with an increase in the excitation amplitude in almost entire frequency range considered in this study. The dynamic components of both the ischium pressure and the ischium force reveal peaks in the 4 to 5 Hz frequency band, the range of primary resonant frequency of the seated human body in the vertical mode. The mean values of the dynamic ischium pressure and the ischium force remain constant, irrespective of the excitation frequency and amplitude. The magnitudes of mean pressure and force at the human–seat interface, however, are dependent upon the seat height and the subject's posture. The inter-subject variability of the static ischium pressure and effective contact area are presented as functions of the subject weight and subject weight-to-height ratio. It was found that heavy subjects tend to induce low ischium pressure as a result of increased effective contact area.

Relevance to industry

Pressure distribution at the human–seat interface has been found to be an important factor affecting the seating comfort and work efficiency of various workers. The study of human–seat interface pressure distribution under vibration is specifically critical to the comfort, work efficiency and health of vehicle drivers, who are regularly exposed to vibration. The results reported in this paper will be useful to study dynamic response of the interface pressure and design vehicle seats.     

The effect of posture and vibration magnitude on the vertical vibration transmissibility of tractor suspension system

The efficiency of suspension seat can be influenced by several factors such as the input vibration, the dynamic characteristics of the seat and the dynamic characteristics of the human body. The objective of this paper is to study the effect of sitting postures and vibration magnitude on the vibration transmissibility of a suspension system of an agricultural tractor seat. Eleven (11) healthy male subjects participated in the study. All subjects were asked to sit on the suspension system. Four (4) different sitting postures were investigated – i) “relax”, ii) “slouch”, iii) “tense”, and iv) “with backrest support”. All subjects were exposed to random vertical vibration in the range of 1–20 Hz, at three vibration magnitudes - 0.5, 1.0 and 2.0 m/s² r.m.s for 60 s. The results showed that there were three pronounced peaks in the seat transmissibility, with the primary resonance was found at 1.75–2.5 Hz for every sitting postures. The “backrest” condition had the highest transmissibility resonance (1.46), while the “slouch” posture had the highest Seat Effective Amplitude Transmissibility (SEAT) values (64.7%). Changes in vibration magnitude for “relax” posture from 0.5 to 2.0 m/s² r.m.s resulted in greater reduction in the primary resonance frequency of seat transmissibility. The SEAT values decreased with increased vibration magnitude. It can be suggested that variations in posture and vibration magnitude affected the vibration transmission through the suspension system, indicating the non-linear effect on the interaction between the human body and the suspension system.Relevance to industry: Investigating the posture adopted during agricultural activities, and the effects of various magnitudes of vibration on the suspension system's performance are beneficial to the industry. The findings regarding their influence on the human body may be used to optimize the suspension system's performance.     

Apparent mass matrix of standing subjects exposed to multi-axial whole-body vibration

This paper describes the experimental characterisation of the apparent mass matrix of eight male subjects in standing position and the identification of nonlinearities under both mono-axial and dual-axis whole-body vibration. The nonlinear behaviour of the response was studied using the conditioned response techniques considering models of increasing complexity. Results showed that the cross-axis terms are comparable to the diagonal terms. The contribution of the nonlinear effects are minor and can be endorsed to the change of modal parameters during the tests. The nonlinearity generated by the vibration magnitude is more evident in the subject response, since magnitude-dependent effects in the population are overlaid by the scatter in the subjects’ biometric data. The biodynamic response is influenced by the addition of a secondary vibration axis and, in case of dual-axis vibrations, the overall magnitude has a marginal contribution.

Practitioner Summary: We have measured both the diagonal and cross-axis elements of the apparent mass matrix. The effect of nonlinearities and the simultaneous presence of vibration along two axes are smaller than the inter-subject variability.