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.     

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.     

Determination of reference values of apparent mass responses of seated occupants of different body masses under vertical vibration with and without a back support

The biodynamic response of human body seated without a back support and exposed to vertical whole-body vibration have been standardized in ISO 5982 and DIN 45676 in terms of driving-point mechanical impedance and apparent mass. A comparison of ranges defined in two standards, however, reveal considerable differences in both the magnitude and phase. Greater differences are more evident for the three body mass groups, which suggests the lack of adequate reference values of biodynamic responses of seated human subjects of different body masses. In this experimental study, the biodynamic responses of seated humans within three different body mass ranges are characterized under different magnitudes of vibration and three different sitting postures in an attempt to define reference values of apparent mass for applications in mechanical-equivalent model development and anthropodynamic manikin design. Laboratory measurements were performed with adult male subjects of total body mass in the vicinity of 55, 75 and 98 kg (nine subjects for each mass group) seated with and without an inclined back support and exposed to three different magnitudes of white-noise vertical vibration (0.5, 1.0 and 2.0 m/s² unweighted rms acceleration) in the frequency range between 0.5 and 20 Hz. The measured data were analyzed to derive the mean magnitude and phase responses for the three body masses, posture and excitation conditions. The mean magnitude responses of subjects within three mass groups were compared with idealized ranges defined in ISO 5982 and mean values described in DIN 45676 for no back support condition. The results revealed significant differences between the mean measured and standardized magnitudes, suggesting that the current standardized values do not describe the biodynamic responses of seated occupant of different masses even for the back not supported condition. The mean measured responses revealed most important effect of body mass, irrespective of the sitting posture. The reference values of apparent mass responses of seated body subject to vertical whole-body vibration are thus defined for three mass groups and different back support conditions that may be considered applicable for ranges of excitations considered. The responses of the body seated without a back support, also revealed notable influences of excitation magnitude, particularly on the primary peak frequencies.     

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.     

Frequency-dependence of discomfort caused by vibration and mechanical shocks

The frequency content of a mechanical shock is not confined to its fundamental frequency, so it was hypothesised that the frequency-dependence of discomfort caused by shocks with defined fundamental frequencies will differ from the frequency-dependence of sinusoidal vibration. Subjects experienced vertical vibration and vertical shocks with fundamental frequencies from 0.5 to 16 Hz and magnitudes from ±0.7 to ±9.5 ms^–2. The rate of growth of discomfort with increasing magnitude of motion decreased with increasing frequency of both motions, so the frequency-dependence of discomfort varied with the magnitudes of both motions and no single frequency weighting will be ideal for all magnitudes. At the frequencies of sinusoidal vibration producing greatest discomfort (4–16 Hz), shocks produced less discomfort than vibration with same peak acceleration or unweighted vibration dose value. Frequency-weighted vibration dose values provided the best predictions of the discomfort caused by different frequencies and magnitudes of vibration and shock.

Practitioner Summary: Human responses to vibration and shock vary according to the frequency content of the motion. The ideal frequency weighting depends on the magnitude of the motion. Standardised frequency-weighted vibration dose values estimate discomfort caused by vibration and shock but for motions containing very low frequencies the filtering is not optimum.     

Difference thresholds for the perception of whole-body vertical vibration: dependence on the frequency and magnitude of vibration

When seeking to reduce vibration in transport it is useful to know how much reduction is needed for the improvement to be noticeable. This experimental study investigated whether relative difference thresholds for the perception of whole-body vertical vibration by seated persons depend on the frequency or magnitude of vibration. Relative difference thresholds for sinusoidal seat vibration were determined for 12 males at three vibration magnitudes and eight frequencies (2.5, 5, 10, 20, 40, 80, 160, 315 Hz) using the three-down-one-up method in conjunction with a two-interval-forced-choice procedure. The median relative difference thresholds were in the range 9.5% to 20.3%. There appeared to be a frequency-dependence at the lowest vibration magnitude, such that higher frequencies had higher difference thresholds. The relative difference thresholds depended on the vibration magnitude only at 2.5 and 315 Hz. The influence of both vibration frequency and vibration magnitude on the measured difference thresholds suggests that vision (at 2.5 Hz) and hearing (at 315 Hz) contributed to the perception of changes in vibration magnitude.     

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.     

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.     

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.     

Characterisation of the human-seat coupling in response to vibration

Characterising the coupling between the occupant and vehicle seat is necessary to understand the transmission of vehicle seat vibration to the human body. In this study, the vibration characteristics of the human body coupled with a vehicle seat were identified in frequencies up to 100 Hz. Transmissibilities of three volunteers seated on two different vehicle seats were measured under multi-axial random vibration excitation. The results revealed that the human-seat system vibration was dominated by the human body and foam below 10 Hz. Major coupling between the human body and the vehicle seat-structure was observed in the frequency range of 10–60 Hz. There was local coupling of the system dominated by local resonances of seat frame and seat surface above 60 Hz. Moreover, the transmissibility measured on the seat surface between the human and seat foam is suggested to be a good method of capturing human-seat system resonances rather than that measured on the human body in high frequencies above 10 Hz.Practitioner Summary: The coupling characteristics of the combined human body and vehicle seat system has not yet been fully understood in frequencies of 0.5–100 Hz. This study shows the human-seat system has distinctive dynamic coupling characteristics in three different frequency regions: below 10 Hz, 10–60 Hz, and above 60 Hz.     

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.     

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.     

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.     

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.     

Equivalent comfort contours for vertical seat vibration: effect of vibration magnitude and backrest inclination

This study determined how backrest inclination and the frequency and magnitude of vertical seat vibration influence vibration discomfort. Subjects experienced vertical seat vibration at frequencies in the range 2.5-25 Hz at vibration magnitudes in the range 0.016-2.0 ms(-2) r.m.s. Equivalent comfort contours were determined with five backrest conditions: no backrest, and with a stationary backrest inclined at 0° (upright), 30°, 60° and 90°. Within all conditions, the frequency of greatest sensitivity to acceleration decreased with increasing vibration magnitude. Compared to an upright backrest, around the main resonance of the body, the vibration magnitudes required to cause similar discomfort were 100% greater with 60° and 90° backrest inclinations and 50% greater with a 30° backrest inclination. It is concluded that no single frequency weighting provides an accurate prediction of the discomfort caused by vertical seat vibration at all magnitudes and with all backrest conditions. PRACTITIONER SUMMARY: Vertical seat vibration is a main cause of vibration discomfort for drivers and passengers of road vehicles. A frequency weighting has been standardised for the evaluation of vertical seat vibration when sitting upright but it was not known whether this weighting is suitable for the reclined sitting postures often adopted during travel.     

The vibration discomfort of standing people: evaluation of multi-axis vibration

Few studies have investigated discomfort caused by multi-axis vibration and none has explored methods of predicting the discomfort of standing people from simultaneous fore-and-aft, lateral and vertical vibration of a floor. Using the method of magnitude estimation, 16 subjects estimated their discomfort caused by dual-axis and tri-axial motions (octave-bands centred on either 1 or 4 Hz with various magnitudes in the fore-and-aft, lateral and vertical directions) and the discomfort caused by single-axis motions. The method of predicting discomfort assumed in current standards (square-root of the sums of squares of the three components weighted according to their individual contributions to discomfort) provided reasonable predictions of the discomfort caused by multi-axis vibration. Improved predictions can be obtained for specific stimuli, but no single simple method will provide accurate predictions for all stimuli because the rate of growth of discomfort with increasing magnitude of vibration depends on the frequency and direction of vibration.     

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.     

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.     

Finite element modelling of human-seat interactions: vertical in-line and fore-and-aft cross-axis apparent mass when sitting on a rigid seat without backrest and exposed to vertical vibration

Biodynamic models representing distributed human-seat interactions can assist seat design. This study sought to develop a finite element (FE) model representing the soft tissues of the body supported by seating and the vertical in-line apparent mass and the fore-and-aft cross-axis apparent mass of the seated human body during vertical vibration excitation. The model was developed with rigid parts representing the torso segments, skeletal structures (pelvis and femurs) and deformable parts representing the soft tissues of the buttocks and the thighs. The model had three vibration modes at frequencies less than 15 Hz and provided reasonable vertical in-line apparent mass and fore-and-aft cross-axis apparent mass. The model can be developed to represent dynamic interactions between the body and a seat over a seat surface (e.g. dynamic pressure distributions and variations in seat transmissibility over the seat surface).     

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

This study determined how backrest inclination and the frequency of vibration influence the perception and discomfort of vibration applied parallel to the back (vertical vibration when sitting upright, horizontal vibration when recumbent). Subjects experienced backrest vibration at frequencies in the range 2.5 to 25 Hz at vibration magnitudes up to 24 dB above threshold. Absolute thresholds, equivalent comfort contours, and the principal locations for feeling vibration were determined with four backrest inclinations: 0° (upright), 30°, 60° and 90° (recumbent). With all backrest inclinations, acceleration thresholds and equivalent comfort contours were similar and increased with increasing frequency at 6 dB per octave (i.e. velocity constant). It is concluded that backrest inclination has little effect on the frequency dependence of thresholds and equivalent comfort contours for vibration applied along the back, and that the W _d frequency weighting in current standards is appropriate for evaluating z-axis vibration of the back at all backrest inclinations.

Statement of Relevance: To minimise the vibration discomfort of seated people, it is necessary to understand how discomfort varies with backrest inclination. It is concluded that the vibration on backrests can be measured using a pad between the backrest and the back, so that it reclines with the backrest, and the measured vibration evaluated without correcting for the backrest inclination.