Sitting comfort in vibration environment: Inter-axis equivalence and equivalent comfort contours for fore-aft,lateral,vertical,and pitch motion

Abstract

The method recommended in current standards for evaluating vibration-induced discomfort in cabin environments was determined separately for excitation at the seat pan, backrest, and floor. However, passengers typically sit with a backrest and experience vibrations at multiple human-seat interfaces simultaneously. In this study, 18 seated subjects with a backrest support were exposed to single-axis fore-aft, lateral, vertical, and pitch vibration between 0.5 and 20 Hz at six magnitudes in a controlled environment chamber, and evaluated discomfort using the magnitude estimation method. Equivalent comfort contours were identified, revealing the effect of vibration frequency and direction. A new index reflecting the equivalence of vibrations in different directions was then defined, based on the equivalent comfort contours. Results showed that the current standard overestimates the sensitivity of fore-aft vibration relative to vertical vibration for 0.5–2.5 Hz and underestimates the sensitivity of lateral vibration relative to vertical vibration for 1.25–20 Hz and the sensitivity of pitch vibration relative to vertical vibration for 0.5–4.0 Hz.

Keywords

vibration discomfort whole-body vibration inter-axis equivalence human vibration

Highlights

• Equivalent comfort contours for the sitting condition with a backrest was defined.

• A new index reflecting equivalence of vibration in different directions was derived.

• Sensitivity of vibration in different directions relative to vertical was determined.

• ISO 2631-1 may overestimate fore-aft vibration relative to vertical for 0.5–2.5 Hz.

Introduction

For the passengers in vehicle cabins, vibration-induced discomfort primarily stems from translational vibrations below 20 Hz.^1–4 Additionally, low-frequency pitch vibration has also been shown to significantly influence discomfort.⁵ Understanding discomfort due to vibration across different axes is crucial for accurately predicting and optimizing comfort in a vibration environment.

Vibration-induced discomfort of humans has been widely studied. To quantify the effect of vibration on discomfort, a common experimental method is to expose subjects in an environment containing vibration with predesigned frequencies and intensities to obtain their subjective discomfort responses (e.g., discomfort ratings). Stevens’ power law is then applied to link subjective responses and objective vibration amplitude. A group of curves, with each describing equal discomfort sensation across frequencies, which are called equivalent comfort contours, are then defined.^6–8 These curves explicitly present the human sensitivity to vibration frequency and intensity and form the fundamental basis deriving the series of frequency weightings in the standard ISO 2631-1.⁹

To evaluate vibration-induced discomfort of humans, a large number of studies have been carried out and the sensitive frequencies of the human body subject to single-axis vibration have been determined. For a seated human body, the sensitive frequencies to vertical and pitch vibration are considered to be around 5 Hz and 0.5 Hz,^5,7 respectively. The sensitive frequencies to fore-aft and lateral vibration are both found to be around 2 Hz.^6,8 However, when assessing discomfort in the cabin environment containing multi-axis vibrations, it is equally essential to determine the frequency dependence of discomfort resulting from vibrations within one direction and between different directions, while the latter remains inadequately studied.

The international standard ISO 2631-1⁹ employs multiplying factors to quantify the relative importance of vibration direction on discomfort. However, studies have suggested that these multiplying factors fail to effectively represent the relative sensitivity of the human body.^10,11 Specifically, Mansfield and Maeda¹² experimentally demonstrated that the method in ISO 2631-1 underestimates lateral vibration sensitivity, prompting their proposal of optimized multiplying factors. These findings underscore the need for further investigation into inter-axis equivalence in multi-axis vibration environments to better quantify directional vibration effects on discomfort.

Existing studies on vibration sensitivity have primarily focused on translational vibrations and seated postures without backrest support. For instance, Griefahn and Bröde¹³ examined the relative sensitivity to translational vibrations in various directions by adjusting the magnitude of the test excitation to match the discomfort level resulting from the reference excitation. Similarly, Thuong and Griffin¹⁴ applied an equivalent approach to standing postures. However, in real-world environments such as vehicle cabins, occupants are typically seated with backrest support and experience vibrations at multiple locations simultaneously. To date, there seems no systematic research investigating the relative sensitivity of the human body in this seated posture with backrest contact. Critically, backrest contact introduces additional vibration stimuli, which can alter the frequency dependence of the subjective response to both translational¹⁵ and pitch vibrations.⁵ Quantifying this sensitivity is essential for accurate discomfort evaluation in operational cabin environments.

The objective of this study was to quantify the relative contribution of fore-aft, lateral, vertical and pitch vibrations to discomfort in a seated posture with backrest support. To this end, a carefully controlled experiment was conducted, exposing participants to vibrations in these four directions at predefined frequencies and amplitudes. The magnitude estimation method was employed to obtain the ratings regarding discomfort. Stevens’ power law was then applied to derive the discomfort contour for vibration in each direction and then to further derive the inter-axis equivalence for vibration across directions. The hypothesis was that inter-axis equivalence of discomfort caused by vibration across directions would depend on both the frequency and amplitude of the vibration input.

Method

Vibration stimuli

The experiment employed sinusoidal vibrations in fore-aft, lateral, vertical, and pitch directions as excitation stimuli. For each direction, stimuli were generated at seventeen one-third octave center frequencies (0.5–20 Hz) with six amplitude levels (0.2, 0.4, 0.6, 0.8, 1.0, 1.2 m/s² or rad/s² r.m.s., frequency unweighted). All stimuli featured a 5-s duration with 0.5-s cosine-windowed onset/offset transitions. Stimuli used in the experiment were generated by a Matlab program and then reproduced by the SERVOTEST vibration test system.

Apparatus

The stimuli were produced in a six-axis vibrator located at a semi-anechoic chamber in the Research Laboratory for Sound, Vibration and Human Factors, Zhejiang University. An environmental chamber was installed on the vibrator to simulate the cabin environment. During the laboratory experiment, the indoor temperature was maintained between 24 and 26°C, and the relative humidity was kept between 40% and 60%. A rigid seat was installed at the center of environmental chamber. The rigid seat was used so as to eliminate the influence of the dynamic characteristics of the seat on the human perception of vibration. An emergency stop controller was held in the hands of the subjects during the experiment and was used to stop the movement of the vibrator when necessary. The schematic diagram of the vibrator was shown in Figure 1.

Figure 1.

The experimental setup: (a) Exterior view; (b) interior view; (c) layout of the apparatus.

Subjects

All subjects were students of Zhejiang University, totaling 18 individuals, with an average age of 23.5 years (standard deviation = 3.2 years), an average height of 173 cm (standard deviation = 5.8 cm), and an average weight of 72 kg (standard deviation = 4.4 kg). All the subjects were informed of the experimental procedure and confirmed that they had no physical illnesses related to vibration or cognitive impairment. Prior to the formal commencement of the experiment, each subject provided written informed consent and was trained to get familiarized with the test procedure. During the whole test, the subjects required to maintain an upright seated posture with their backs against the seat backrest. The angle between the thighs and legs was about 90°. The experimental study was approved by the Ethics Committee at Zhejiang University (approval ID: 202589).

Procedure

As shown in Figure 2, there are 102 stimuli (6 levels of amplitudes and 17 frequencies) for each direction of vibration, and therefore 408 stimuli in total. The stimuli were presented in a random order during the test.

Figure 2.

Diagram of the procedure.

At the end of each vibration exposure, a rating of subjective discomfort was assigned to each stimulus using the magnitude estimation method. In this method, subjects could assign arbitrary numerical values to represent the level of discomfort they perceived. For instance, when a subject rated stimuli 1 as 100, they might assign a rating of 200 to stimuli 2 if it felt twice as discomfort, or 50 if it felt half as discomfort. This method has been widely used to quantify vibration-induced subjective discomfort.^7,15–18

To examine the differences between discomfort due to different stimuli, the Friedman two-way analysis of variance and the Wilcoxon matched-pairs signed-ranks tests were used.

Analysis

Equivalent comfort contours

Stevens’ power law is often used to characterize the relationship between objective magnitude $φ$ and subjective magnitude $ψ$ , as follows:

ψ = k φ^{n}

(1)

where n is the growth of sensation and k is a constant. For each frequency in each direction of vibration, n and k can be determined by linear regression based on equation (1). For normalization, the subjective magnitude rated by each subject was divided by the median of the subjective ratings to all the stimuli and then multiplied by 100. This allows the subjective ratings of each subject to be scaled to a similar scale for comparison.

Equation (1) can be rewritten as:

φ = {(\frac{ψ}{k})}^{\frac{1}{n}}

(2)

The comfort contour was obtained in the following procedure: first, for each direction of vibration, $φ$ and $ψ$ can be determined by experiment, then n and k can be derived from linear regression at each frequency; second, substituting n and k into equation (2), the acceleration φ can be calculated at different levels of subjective ratings ψ (i.e., 63, 80, 100, 125, 160, and 200).

Inter-axis equivalence coefficients

The inter-axis equivalence was defined as the ratio of discomfort caused by two vibrations in different directions.¹⁴ Adopted in this study, the inter-axis equivalence coefficients of the discomfort of the fore-aft, lateral, and pitch vibration can be defined as (taking the discomfort of vertical vibration as the reference):

K_{z / i} (f) = \frac{φ_{z} (f)}{φ_{i} (f)}

(3)

where the subscript z and i represent the vibrations in vertical, and in fore-aft, lateral, and pitch directions, respectively;

φ_{z} (f)

and

φ_{i} (f)

represent the acceleration of vibration at

f

Hz in z and i directions which cause equal discomfort. The inter-axis equivalence coefficients

K_{z / i} (f)

characterize the ratio of the acceleration of the z-axis to that of the i-axis with equal discomfort. For example, if the

K_{z / i} (5) = 2.65

, it means at 5 Hz, the discomfort resulting from vertical vibration with magnitude of 2.65 m/s² is equal to the discomfort caused by fore-aft vibration with magnitude of 1 m/s².

K_{z / i} (f)

can be determined by substituting equations (2) into (3) as follows:

K_{z / i} (f) = \frac{{(\frac{ψ_{j}}{k_{z (f)}})}^{\frac{1}{n_{z (f)}}}}{{(\frac{ψ_{j}}{k_{i (f)}})}^{\frac{1}{n_{i (f)}}}}

(4)

where

ψ_{j}

was subjective magnitude,

ψ_{j = 1, 2, \dots, 6} =

{63, 80, 100, 125, 160, 200} in this study. The magnitude of inter-axis equivalence coefficients

K_{z / i} (f)

can be interpreted as follows: if the magnitude is greater than 1, it indicates that compared with the vibration in i-direction at f Hz, the human body is less sensitive to the vibration in z-direction (i.e., to cause equal discomfort, the acceleration of the z-axis vibration needs to be greater than that of the i-direction vibration), and vice versa.

Results

Growth of sensation

The median growth of sensation (n) and constants (k) for fore-aft, lateral, vertical, and pitch vibration of the subject sitting with a backrest are shown in Table 1, and the box plot of the growth of sensation (n) are shown in Figure 3. For each direction of vibration, the growth of sensation (n) is significantly dependent on frequency (p < 0.05, Friedman). A greater growth of sensation indicates that discomfort increases more rapidly with the increase of vibration magnitude.

Table 1.

Median exponents (n) and constants (k) for vibration in each direction.

Frequency (Hz)	Fore-aft		Lateral		Vertical		Pitch
Frequency (Hz)	k	n	k	n	k	n	k	n
0.5	131	0.78	208	0.93	130	0.57	197	0.67
0.63	117	0.75	180	0.82	116	0.58	162	0.81
0.8	106	0.73	156	0.78	110	0.67	141	0.84
1	132	0.74	169	0.68	116	0.67	136	0.62
1.25	122	0.58	153	0.7	103	0.7	137	0.75
1.6	137	0.78	179	0.73	105	0.71	158	0.69
2	150	0.91	169	0.69	108	0.68	150	0.75
2.5	153	0.76	141	0.58	109	0.78	152	0.74
3.15	158	0.6	126	0.48	106	0.73	150	0.52
4	147	0.59	117	0.71	138	1	112	0.66
5	149	0.55	108	0.51	163	0.7	131	0.74
6.3	146	0.51	102	0.59	158	0.53	132	0.58
8	125	0.44	104	0.47	149	0.47	120	0.57
10	109	0.59	91	0.46	139	0.41	112	0.57
12.5	104	0.49	88	0.43	138	0.49	106	0.59
16	108	0.59	94	0.46	141	0.47	106	0.6
20	106	0.33	112	0.59	141	0.39	102	0.58

Figure 3.

Box plot of growth of sensation (n) of vibration in different directions.

Equivalent comfort contours

The equivalent comfort contours are presented in Figure 4. For all the directions of vibration at six magnitudes, the level of the equivalent comfort contours is highly dependent on vibration frequency (p < 0.001, Friedman; Figure 4).

Figure 4.

Contours of comfort for vibration in different directions from the “absolute” magnitudes (ψ) 63–200 in 0.5–20 Hz. The minimum and maximum magnitudes of the physical stimuli used in this study are represented by dotted lines.

Inter-axis equivalence

For median inter-axis equivalence coefficients with various “absolute” magnitudes (ψ, 63–200) between 0.5 and 20 Hz were shown in Figures 5–7, respectively. For vibration in all directions, the inter-axis equivalence was dependent on the subjective magnitudes and frequency.

Figure 5.

Median inter-axis equivalence coefficients for fore-aft relative to vertical vibration for various “absolute” discomfort magnitudes (ψ) between 0.5 and 20 Hz.

Figure 6.

Median inter-axis equivalence coefficients for lateral relative to vertical vibration for various “absolute” discomfort magnitudes (ψ) between 0.5 and 20 Hz.

Figure 7.

Median inter-axis equivalence coefficients for pitch relative to vertical vibration for various “absolute” magnitudes (ψ) between 0.5 and 20 Hz.

Figure 8 demonstrates the equivalence of fore-aft, lateral and pitch vibration relative to vertical vibration for the discomfort magnitudes of 100. Compared with exposure to vertical vibration, the seated human body exhibited greater sensitivity to fore-aft vibrations within 1.0–5.0 Hz, but showed reduced sensitivity above 5.0 Hz. Additionally, sensitivity to lateral and pitch vibrations was lower apart from frequencies between 0.5 and 3.5 Hz. The $K_{z / x}$ and $K_{z / p}$ showed a similar trend with frequency, but pitch vibration shows higher sensitivity than fore-aft vibration at 0.5–2.5 Hz.

Figure 8.

Median inter-axis equivalence coefficients for the “absolute” subjective magnitudes (ψ) at 100 over 0.5–20 Hz.

Discussion

Growth of sensation and equivalent comfort contours

In Figure 9, the median growth of sensation (n) for fore-aft, lateral, vertical, and pitch vibration of the human body sitting with a backrest was compared. For the vibrations in the same direction, there are significant differences among the growth of sensation in 0.5–20 Hz (p < 0.05, Friedman). For the vibration between different directions, except for 1, 2.5, and 5 Hz, there was no significant difference in the growth of sensation (p > 0.05, Friedman). Kitazaki and Griffin¹⁹ applied experimental study and found eight vibration modes of the body, including three modes at 1.1, 2.2, and 4.9 Hz, which corresponded to the frequencies at the growth of sensation dependent on the directions in this study. This may indicate that the difference between the growth of sensation for vibration in different directions may be related to the human body modes at the corresponding frequencies.

Figure 9.

Median growth of sensation (n) for vibration in different directions.

As shown in Figure 4, for the fore-aft, lateral, and vertical vibration, sensitivity to acceleration was greatest at 2.5, 1.6, and 6.3 Hz, respectively (ψ = 100), which were corresponding to the resonance of the apparent mass of human body sitting with a backrest reported in many studies.^20–24 It was indicated that the subjective sensation appears to correlate to the biodynamic response of seated human body. The sensitivity to acceleration was great at 0.5 and 3 Hz for the pitch vibration, which corresponds to the two resonance frequencies of the biodynamic response of seated human body subject to fore-aft vibration.²⁵ It implies that the human body may have a similar mechanism for sensing the pitch and fore-aft vibration. There were few studies on the biodynamics of the seated human body exposed to pitch vibration. Paddan and Griffin²⁶ used a light-weight bite-bar to investigate the Seat-to-head transmissibility of seated human exposed to pitch vibration, and the principal resonance was observed at 2 Hz. This result seems to be inconsistent with the frequency of the greatest growth of sensation for pitch vibration in this study. It may be due to the sense of weightlessness caused by pitch vibration at low frequency with high amplitude that makes the sensation of the subjects more sensitive, resulting in overestimating the growth of the sensation for pitch vibration at low frequency. This is worth investigating in future studies.

Figure 10 shows the comparison between the growth of sensation determined in this study compared with those reported in the previous studies.^5,6,15,27 The growth of sensation varied between studies, which may be caused by different experimental conditions, including seats (rigid flat or contoured), methods of subjective evaluation (absolute magnitude estimation or relative magnitude estimation), and feet support (fixed or moved with the vibrator).

Figure 10.

Comparison of growth of sensation (n) reported in various studies.

The comparison of the equivalent comfort contours (ψ = 100) with those from literature of the seated human body exposed to fore-aft, lateral, vertical, and pitch vibration in various studies is shown in Figure 11. The equivalent comfort contours for vertical vibration in all the studies were similar regardless of the usage of backrest support. It appears to suggest that additional input stimuli at vertical backrest had minimal effect on the discomfort resulting from vertical vibration, aligning with the findings of Basri and Griffin.¹⁵ For fore-aft, lateral and pitch vibration, the backrest support seems to cause varying degrees of changes in the comfort contours. Therefore, when evaluating the discomfort of occupants in vehicles, it is essential to take into account the influence of backrest vibrations in these directions.

Figure 11.

Comparison of contours of comfort reported in various studies.

Inter-axis equivalence

The equal comfort contours can be employed to evaluate the sensitivity to vibration of different frequencies within one direction. However, the sensitivity to vibration in different directions (inter-axis equivalence) is also worth studying; it is directly related to the evaluation of passenger vibration comfort in real traffic environment. As shown in Figures 5–7, the inter-axis equivalence coefficients were dependent on the subjective magnitude, which should be of concern when comparing the discomfort of different directions of vibrations. As marked with black circles in Figures 5–7, there was a common intersection point (around 6 Hz) in the inter-axis equivalent coefficients ( $K_{z / x}$ , $K_{z / y}$ and $K_{z / p}$ ) of ψ = {63, 80, 100, 125, 160, 200}. It means that the inter-axis equivalence coefficient calculated at this frequency (around 6 Hz) was not affected by the subjective magnitude.

The inter-axis equivalences reported in previous studies were summarized in Table 2. Griffin et al.²⁸ used the paired matching method with a vertical vibration reference to determine the equivalent comfort contours of the seated human body under single-axis fore-aft, lateral, and vertical vibration. The subjects in their study sat without backrest and with a non-vibrating footrest. It was indicated that the seated human body shows close sensitivity to the lateral vibration than the fore-aft vibration at 6.3 Hz. The same method was applied by Griefahn and Brode¹³ to identify the inter-axis equivalence coefficients between single-axis lateral, fore-aft and vertical vibration at 1.6, 3.15, 6.3, 8, and 12.5 Hz. During the whole experiment, all subjects sat without backrest support but with a footrest moving with the vibrator. The results demonstrated that the discomfort of the seated human body exposed to lateral vibration and fore-aft vibration was almost equal, both less than that under vertical vibration of 6.3 Hz. There seems to be certain differences between the inter-axis equivalence coefficients reported in other studies and in this study, which may be caused by the different methods used for subjective evaluation and different sitting posture of subjects. In the current study, considering the validity of the evaluation¹⁷ and the duration of the whole experiment, the magnitude estimation method was applied. Also, to better represent the real environment drivers and passengers exposed to vibration, the sitting posture with backrest and footstep support was used.

Table 2.

Median inter-axis equivalence coefficients at 6.3 Hz reported in various studies.

	Vibration input	$K_{z / x}$	$K_{z / y}$	$K_{z / p}$
In this study	Seat pan, back, and feet	0.68	0.42	0.58
Griefahn and Bröde (1997)	Seat pan and feet	0.60	0.58	—
Griffin et al. (1982)	Seat pan	0.55	0.63	—

The inter-axis equivalence coefficients with the discomfort of vertical vibration as the reference, $K_{z / i} (f)$ (i = x, y, p), were also calculated with frequency weightings and multiplying factors in accord with ISO 2631-1 as follows:

K_{z / x} = \frac{\sqrt{{(0.4 * W_{d})}^{2} + {(1 * W_{k})}^{2} + {(0.4 * W_{k})}^{2}}}{\sqrt{{(0.8 * W_{c})}^{2} + {(1 * W_{d})}^{2} + {(0.25 * W_{k})}^{2}}}

(5)

K_{z / y} = \frac{\sqrt{{(0.4 * W_{d})}^{2} + {(1 * W_{k})}^{2} + {(0.4 * W_{k})}^{2}}}{\sqrt{{(0.5 * W_{d})}^{2} + {(1 * W_{d})}^{2} + {(0.25 * W_{k})}^{2}}}

(6)

K_{z / p} = \frac{\sqrt{{(0.4 * W_{d})}^{2} + {(1 * W_{k})}^{2} + {(0.4 * W_{k})}^{2}}}{\sqrt{{(0.8 * W_{c})}^{2} + {(0.4 * W_{e})}^{2}}}

(7)

The inter-axis equivalence coefficients calculated with equations (5)–(7) along with those shown in Figure 8 were presented in Figure 12. When the value of $K_{z / i}$ calculated based on the method in standard is greater than the coefficients obtained in this study, it means that the method in standard for evaluating vibration comfort overestimates the relative sensitivity of the i-axis vibration relative to z-axis vibration, and vice versa. The inter-axis equivalence coefficients of lateral and pitch vibration relative to vertical vibration calculated in this study were close to those calculated by ISO 2631-1, with only slight underestimation of the sensitivity of lateral vibration in 1.25–20 Hz and pitch vibration in 0.5–4 Hz relative to vertical vibration. However, for the inter-axis equivalence coefficients of fore-aft vibration relative to vertical vibration, the ISO 2631-1 overestimates the sensitivity of fore-aft vibration relative to vertical vibration in the frequency range of 0.5–2.5 Hz but underestimates the sensitivity of fore-aft vibration relative to vertical vibration in the frequency range of 2.5–6.0 Hz. The observed results are consistent with the research findings on biomechanical responses. As reported by Qiu and Griffin,²² the primary resonance frequency of the apparent mass under vertical vibration exhibits a clear dependence on postural support: the primary resonance above 2.5 Hz with backrest support, and it shifts to the 0.5–2.5 Hz range in the absence of backrest support. In addition, the frequency weightings in ISO 2631-1 for the accelerations at the seat pan and the backrest were developed based on the experimental studies with vibration applied at the supporting surface individually, differing from the condition with simultaneous vibration. This may lead to biases when applying the ISO 2631-1 method to evaluate the discomfort due to multi-location vibrations.

Figure 12.

Comparison between median inter-axis equivalence coefficients measured in the current study and inter-axis equivalence coefficients calculated according to ISO 2631-1.

Application and limitation

In this study, the inter-axis equivalence coefficients were defined to reflect the relative importance of vibrations in different directions to discomfort. Such relative importance seems to differ from those calculated in accord with ISO 2631-1 following equations (5)–(7) (see Figure 12). It suggests that the method in ISO 2631-1 may need to be adjusted to better represent the relative importance of vibration across directions. The equivalent comfort contours and the inter-axis equivalence coefficients determined in this study can be used as references. The findings of this study provide practical guidance for seat design. Specifically, for vehicles subjected to significant vertical and pitch excitations (e.g., off-road or heavy-duty engineering vehicles), vibrational modes within the 2.5–6.0 Hz range should be mitigated in seat design to minimize adverse biomechanical responses.

The current study investigated the relative discomfort due to fore-aft, lateral, vertical, and pitch vibrations; however, in real transportation environment, vibrations in roll and yaw may also cause significant discomfort. Although ISO 2631-1 suggests the axis multiplying factors of 0.63 and 0.2 m/rad for roll and yaw vibration, respectively, to account for the overall contribution to discomfort compared to vertical seat vibration, detailed frequency-specific contributions remain unclear. Inter-axis discomfort equivalence needs to be further tested and expanded across different frequencies and vibration magnitudes in future. Moreover, both the equivalent comfort contours and the inter-axis equivalence coefficients determined in this study vary with the amplitude of excitation, which means the frequency dependency in the sensitivity regarding vibration discomfort would alter with vibration magnitude. This magnitude-frequency interaction necessitates further investigation to develop comprehensive discomfort evaluation methods for complex vibration environments.

Conclusion

For the human body sitting with a backrest exposed to single-axis fore-aft, lateral, vertical, and pitch vibration, the growth of sensation showed frequency dependency between 0.5 and 20 Hz in each direction.

This study established inter-axis equivalence coefficients to characterize discomfort relationships between fore-aft, lateral, vertical, and pitch vibrations, revealing their significant dependence on both vibration frequency and amplitude. Comparative analysis with ISO 2631-1 demonstrated that the standard potentially overestimates fore-aft vibration sensitivity relative to vertical vibration at 0.5–2.5 Hz while underestimating lateral vibration sensitivity at 1.25–20 Hz and pitch vibration sensitivity at 0.5–4 Hz, all relative to vertical vibration. These findings provide crucial reference data for more accurate evaluation of discomfort induced by complex multi-axis vibration environments in practical cabin environments, addressing current limitations in existing standards.

Footnotes

ORCID iDs

Yi Qiu

Xu Zheng

Chi Liu

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China under Grant T2192931, and by the Zhejiang Provincial Natural Science Foundation of China under Grant LQK26E050002.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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