Despite the presence of multi-axis vibration in many vehicles, biodynamic responses of the human body are mostly studied under single-axis conditions. In this study, the fore-aft, lateral, and vertical apparent masses were measured under tri-axis translational excitation with various in-line (“primary-axis”) and cross-axis (“secondary-axes”) magnitudes and backrest inclinations (0°, 10°, and 20°). The softening effect of increasing the primary-axis magnitude was reduced by higher secondary-axes magnitudes, and the effect of secondary-axes magnitudes was similarly attenuated by higher primary-axis magnitudes. With tri-axis vibration, the fore-aft peak modulus at the seat pan first fell, then rose with the increasing backrest inclination as under single-axis conditions, whereas the resonance frequency lost the non-monotonic pattern. Backrest effects on fore-aft and lateral apparent masses were insignificant with single-axis vibration but became significant with tri-axis vibration. These findings suggest that incorporating multi-axis vibration and backrest inclination may improve the accuracy of ride comfort evaluation for realistic driving conditions.

Active noise control (ANC) systems in vehicle cabins are conventionally validated through real-time prototypes in road tests. However, the escalating complexity of ANC algorithms and the inherent variability of real-world testing conditions frequently lead to high experimental costs and inefficiencies, significantly impeding the broader implementation of in-vehicle ANC systems. This challenge underscores a significant deficiency in the field: the absence of a high-fidelity approach to facilitate the validation of algorithms under reproducible conditions. This article introduces a sound field reproduction (SFR) method based on the multichannel pressure matching least squares (MCPMLSs) algorithm for in-vehicle ANC system evaluation. The SFR-ANC system is further proposed, integrating a feedback-equalization-optimized SFR subsystem with dual parallel ANC subsystems powered by broadband and narrowband adaptive algorithms. The hybrid system was implemented through a loudspeaker array and active headrest integration, designed to achieve accurate in-vehicle sound environment reproduction and localized cancellation. The system's performance was evaluated using ear zone noise collected inside a real vehicle as disturbance signals within an acoustic laboratory. Experimental results validate the system's accuracy in reproducing authentic noise environments and the noise canceling performances both in stable and transient conditions. The proposed approach establishes a reproducible testing protocol for standardized subjective-objective assessment of in-vehicle ANC performance.

Occupants of off-road vehicle are often exposed to multi-axis translational vibration combined with pitch vibration during operations. Understanding the dynamic behaviors of the seated human body exposed to multi-axis vibration is essential for vibration reduction designs of off-road vehicles. In this study, the apparent masses of thirteen subjects were measured under different combinations of fore-aft (x), lateral (y), vertical (z), and pitch (p) vibrations, and the contribution of vibration in each direction to the apparent mass was quantified. Two principal findings regarding vibration transmission path and characteristics were obtained. First, the dynamic forces at the seat pan were predominantly governed by the corresponding in-line vibration component under both multi-axis and single-axis conditions. Second, the primary resonance frequencies of the apparent mass in the x-, y-, and z-directions under multi-axis vibration differed significantly from those under single-axis vibration (p<0.05, Wilcoxon), whereas addition of pitch vibration did not significantly alter the primary resonance frequencies in any direction. This mechanism explains the poor correlation between unweighted overall vibration magnitude (the previous approach) and resonance frequencies (mean Spearman coefficients: rx=-0.40, ry=-0.38 and rz=-0.41). To improve the predictive accuracy for vibration magnitude-induced resonance shifts, axis-weighted overall vibration magnitudes were derived via an optimization algorithm. The optimized weighting scheme yielded substantially higher correlations (rx=-0.54, ry=-0.64 and rz=-0.54), offering a reliable basis for predicting the resonances of seated human body to prevent frequency coincidence and subsequent coupled resonance between the seat and the occupant.

The ride comfort of high-speed trains under the vibro-acoustic coupled environment is a critical factor influencing passenger experience. However, the cross-modal interaction mechanisms between vibration and noise remain complex and not fully understood. This study investigated the subjective discomfort response to coupled vibration and noise excitations simulated from actual high-speed train operations. A psychophysical experiment was conducted using a 6-DOF vibration simulation platform and a high-fidelity binaural acoustic reproduction system. Subjective ratings from 12 participants were collected using the absolute magnitude estimation (AME) method under full-factorial combined conditions. Objective-subjective correlation models were constructed based on Response Surface Methodology, achieving high predictive accuracy (R2 > 0.9). The results indicate that noise plays a dominant role in combined discomfort, as confirmed by Sobol global sensitivity analysis. A significant nonlinear interaction between vibration and noise was revealed, characterized by a unique bidirectional "effect reversal" phenomenon: Increasing noise levels transitioned from exacerbating to suppressing vibration discomfort (synergistic-to-masking), whereas increasing vibration amplitudes shifted from masking to worsening noise discomfort (masking-to-synergistic). Furthermore, a "cross-modal tolerance shift" was identified, where the acceptability threshold for one physical field is passively elevated by the high intensity of the other. These findings elucidate the dynamic modulation mechanism of human multimodal perception and provide a theoretical basis for the optimization of vibro-acoustic environments in next-generation high-speed trains.

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.

Magnetorheological dampers have been widely applied in automotive suspension and seating systems due to their rapid response and tunable damping characteristics. This study aims to develop accurate mechanical models of the magnetorheological dampers, which are essential for the design of semi-active vibration control systems. Both forward and inverse dynamic models were established to characterize the nonlinear mechanical behavior of the damper. The forward dynamic model was formulated based on the Bouc-Wen hysteresis model. For the inverse model, the classification and regression neural networks were trained using the experimental data to accurately determine the input current corresponding to the target damping force. The testing dataset validated the superior performance of the classification-based model over the regression approach. Furthermore, a control strategy incorporating proportional-integral-derivative compensation was introduced to improve the accuracy and robustness of the inverse model. The integration of the classification model with a damping force tracking mechanism enabled precise current prediction and effective force tracking, thereby confirming the effectiveness of the proposed methodology.

Sound field reproduction (SFR) is vital for noise simulation and acoustic comfort optimization in vehicle cabins. This paper reviews three core SFR techniques: Wave Field Synthesis (WFS), Higher-Order Ambisonics (HOA), and Pressure Matching (PM). Their theoretical fundamentals, engineering optimizations, and adaptability to narrow enclosed cabins are analyzed. We compare the three methods in terms of reproduction accuracy, system complexity, and cost. Key challenges in vehicular applications are summarized, including strong reverberation, multi-source coupling, and the mismatch between physical reproduction and subjective perception. Future directions are proposed, such as physics-data hybrid optimization, low-cost lightweight design, and personalized acoustic comfort. This review offers a practical reference for the engineering application of SFR in vehicle cabin acoustic optimization.

Vibration magnitudes and backrest inclination affect apparent masses of the seated human body, yet their interaction remains unexplored. In this study, the in-line fore-aft, lateral, and vertical apparent masses were studied experimentally with a series of vibration magnitudes (0.25, 0.5, and 1.0 ms-2 r.m.s. in three translational directions, respectively) and backrest inclination angles (0°, 10°, and 20°). The peak modulus of the fore-aft apparent mass at the seat pan first decreased from 0° to 10° and then rose from 10° to 20°. Significant interaction between the two factors was found for fore-aft resonance parameters, which may be attributed to pelvic motion modulated by muscle activities. In contrast, lateral and vertical resonance parameters varied monotonically with backrest inclination and no significant interaction was detected. These findings reveal that the interaction between vibration magnitude and backrest inclination should be considered for accurate fore-aft ride comfort assessment.

Overall sitting comfort is related to both static pressure distribution and dynamic human–seat interaction during vibration. This study proposes a simplified finite-element model of the seated human body that could potentially be used to assess overall sitting comfort. The static pressures of the seated human body measured on a rigid seat with different footrest layouts, together with the overall and localised apparent masses of the human body measured in a previous study, were used for model validation. The proposed model contained homogeneous soft tissues of the buttocks and thighs and rigid bodies connected to represent the torso. The tissue geometry was adjusted to match the measured anthropometry. Viscoelastic material was assigned to the tissues, and the properties were identified by fitting the modelled pressures and apparent masses to the measurement results. The proposed model was capable of reproducing static pressures and dynamic forces over the seat for the three sitting postures.

This paper introduces a novel joint framework designed to efficiently verify in-vehicle active noise control (ANC) systems within a reproduced sound field environment. Traditional validation of in-vehicle active noise control (ANC) systems relies on extensive road tests involving real-time control systems integrated into test vehicles. However, the increasing complexity of ANC algorithms and the proliferation of parameters have rendered the optimization process during actual road tests both cumbersome and costly. To address these challenges, a sound field reproduction (SFR) system is proposed to seamlessly bridge real-world acoustic environments with laboratory simulations. By employing a speaker array to accurately reproduce target sound fields, the system facilitates rapid verification and refinement of ANC prototypes. The SFR-ANC framework integrates a frequency-domain pressure matching module with equalization feedback optimization and a time-domain adaptive notch filter module with engine speed modulation. Simulation studies were performed using measured in-vehicle acceleration noise, engine speed data, and acoustic transfer functions obtained in a listening room, and the results verify the effectiveness of the framework in optimizing ANC performance.

This study investigated the vibration-induced discomfort experienced at the second-row seat in multi-purpose vehicles (MPVs) and proposed a deep learning-based prediction model for discomfort. Experiments were conducted on a four-poster test rig to collect time-domain accelerations in three directions at the backrest, seat pan and armrests, with different seat absorber designs and vehicle operating conditions. A Long Short-Term Memory (LSTM) neural network was developed to model the nonlinear relationship between the objective vibration features and subjective discomfort ratings. To increase the sample size and enhance generalisation, a data augmentation strategy was implemented by filtering white noise signals to match the spectral characteristics of the measured accelerations. Results demonstrated that using the three-directional backrest acceleration as input yielded high prediction accuracy; however, expanding input features to include vibrations from other seat components led to degraded performance. This study established a framework for modelling the relationship between seat vibration and occupant discomfort.

Traction induction motors (TIMs) are widely used in electrically powered railway vehicles. TIMs can generate significant noise during operation, which has become one of the primary noise sources for railway vehicles. In this paper, a purposely designed experiment was conducted to characterize the acoustic performance of a TIM based on the comparison of speed up and power off conditions. It was found that aerodynamic noise was dominant at speeds higher than 3000 r/min (3000 rotations per minute) and the main component of the aerodynamic noise was the 48th order (48 times the rotation frequency), which was related to the 48 conductors in the air-gap. To simulate the aerodynamic noise of the TIM, a computational fluid dynamics model was developed to calculate the flow field of the TIM. Lighthill acoustic analogy was then applied to calculate the noise due to the acoustic sources induced by the flow. Compared to the method with Ffowcs Williams–Hawkings acoustic analogy, the proposed method improved the accuracy in predicting the aerodynamic noise, and allowed to quantify the contribution to the aerodynamic noise of TIMs from a variety of acoustic excitation sources. The results showed that the excitation sources adjacent to the rotational air gap contributed the most to the motor’s aerodynamic noise. The proposed method was proven to be an efficient approach for optimal design of the TIM aerodynamic noise by identifying the main excitation sources and offered valuable insights for prediction of aerodynamic noise of other types of induction motors.

The human body is routinely exposed to various vibration, most of which exhibit non-stationary characteristics. This study carried out experimental research to investigate the biodynamic response, apparent mass, of seated human body under non-stationary vibration. Experimental protocols included two kinds of non-stationary vibrations, vibrations with gradually decreasing intensities and combinations of two steady vibrations. Responses under conventional steady-state vibrations were also measured as the references. The experiments revealed the time-varying vibration profiles influenced the human response. However, the nonlinearity in terms of time was not significant. Notably, the gradually changing vibration weakened the intensity-dependent nonlinearity which is the most conventional nonlinearity of the human body. Conversely, the sudden change can hardly affect the dynamic characteristics. When subjects were exposed to a combination of two steady-state vibration, it was like that they responded to separate steady-state vibrations. The transient vibration histories do not significantly affect immediate biomechanical responses after an abrupt vibration transitions. As for the environment without such abrupt change on the vibration intensity, the linear assumption for the human body may be acceptable for the discomfort evaluation and biodynamic modelling. This conclusion holds relevance for ergonomic assessments and vibration exposure standards.

Polyurethane foam is widely used as a primary filling material in car seats. While it provides good damping and energy absorption, the mechanical properties are complex but play a vital role in vibration attenuation and vehicle ride comfort. This study proposes a comprehensive experimental and analytical method to characterize the visco-hyperelastic properties of seat-grade polyurethane foam. Quasi-static and dynamic compression tests were conducted on foam blocks to obtain load–deflection curves and dynamic stiffness. A visco-hyperelastic material model was developed, where the hyperelastic response was derived via the hereditary integral and difference-stress method, and viscoelastic behavior was captured using a Prony series fitted to dynamic stiffness data. The model was validated using finite element simulations, showing good agreement with experimental results in both static and dynamic conditions. The proposed method enables accurate characterization of the visco-hyperelastic material properties of seat-grade polyurethane foam.

A numerical method combining the vehicle-crossing multi-body dynamic model and the wheel-crossing three-dimensional explicit finite element dynamic model is developed to simulate the dynamic interaction between the wheel and one type of assembled crossing. Using the real parameters of the wagon vehicle and the assembled crossing model, the dynamic force calculation results of the vehicle-crossing multibody dynamic model are applied to the wheel-crossing explicit finite element dynamic model as a dynamic load, the advantage is that it takes into account both the influence of vehicle dynamics and the elastic-plastic material characteristics of the crossing on the whole and local stress response of the crossing, and the obtained local stress state can be used to predict the long-term behavior of the crossing in detail, such as fatigue damage. The acceleration of this type of assembled crossing is measured on the Chinese railway, and the calculated results are compared and analyzed with the vehicle-crossing multi-body dynamics model. The stress response of the assembled crossing when the vehicle passes through under the condition of heavy load is discussed.

In the feedforward active road noise control (ARNC) system, the noise reduction performance relies on the correlation between the reference signals and the target noise signals. To achieve better noise reduction performance, the operational transfer path analysis (OTPA) model with singular value decomposition was proposed to separate the road noise component from the target noise. Combined with OTPA and multi-coherence sorting method (MCSM), simulation analysis and real vehicle tests under various speeds both showed that the system with optimized reference sensor set had better road noise reduction performance, especially at the peak frequencies. To further improve noise reduction performance and reduce computational load, a selective subband adaptive filtering (SSAF) algorithm was proposed to build an active road noise control model with optimized reference sensor set. Simulation results, employing real vehicle test data, showed that the proposed method further improved the noise reduction performance and effectively reduced the amount of computational load.

Transmissibility is used to assess dynamic responses of the occupant-seat system, and most studies have exclusively assessed the transmissibility from the floor to the cushion or the backrest surface with the human body. In this investigation, the vertical vibration transmitted from the floor to six specific locations both on the seat surface and the frame when the seat was fixed on three positions on the track was examined utilizing an SAE J826 manikin and 12 male adults (0.25 to 20 Hz) for a duration of 120 seconds at three vibration amplitudes. The transmissibility from the floor to the headrest frame, the cushion surface, the headrest surface, the seat back frame, and the seat back surface all exhibited a principal peak frequency within 4-5 Hz. With the exception of the cushion frame, the principal peak frequency and the peak transmissibility in transmissibilities to all positions decreased with increasing vibration amplitude, indicating the non-linearity within the occupant-seat system. It was also found modifying seat track positions minimally affected the seat transmissibility to either the surface or the frame of the seat. Polyurethane foam amplified vibration at peak frequency, simultaneously enhancing static sitting comfort and reducing the vertical vibration transmission above peak frequency.

In this paper, modal properties of the seated human body were identified from measured transmissibilities to the head, chest, lumbar spine L3, pelvis, hips and thighs with single-axis translational vibration; how they were affected by vibration direction and magnitude was quantitatively compared for the first time. To this end, eight subjects were exposed to fore-aft, lateral and vertical single-axis vibrations with three magnitudes at 0.4, 0.8 and 1.2 m/s2 r.m.s., respectively. Three and five vibration modes were identified with fore-aft vibration and with vertical vibration in the sagittal plane, respectively, while three modes identified with lateral vibration were in the coronal plane. As the vibration magnitude increased from 0.4 to 1.2 m/s2 r.m.s., the modal frequencies of the modes at 1.2, 2.2, 2.9 and 6.2 Hz, which contained the pitch, lateral movements, fore-aft movements and vertical movements of the upper body, respectively, were reduced to 1.0, 1.8, 2.3 and 5.8 Hz significantly, and the damping ratios of the modes identified at 0.8, 5.2 and 10.9 Hz were changed. High similarity was observed between the modal shapes identified with different vibration magnitudes.

Seat transmissibility is associated with both seating dynamics and biodynamics. The aim of this experiment was to investigate how seat transmissibilities are affected by the horizontal excitation variations as well as the presence of the vertical excitation. Twelve participants were evaluated for the seat transmissibilities during the horizontal random excitation at three amplitudes with and without additional vertical excitation. The primary resonant frequencies of the vertical cross-axis and horizontal in-line seat transmissibilities reduced with an increase in the horizontal excitation. The seat transmissibility acquired from single-axis excitation exhibited the same resonant behaviour as those obtained from dual-axis excitation. The nonlinearity of the seat transmissibility with dual-axis excitation suggests coupled modes are induced by the cross-axis effect.

Lack of the biodynamic data of lightweight and heavyweight human bodies in seating posture becomes an impediment to developing dynamic dummies and relevant standards for improving vehicle ride comfort and reducing health risks caused by vibration. To acquire missing data and gain an understanding of relevant biodynamic responses, the vertical apparent masses of seated subjects in lightweight and heavyweight groups as well as the mediumweight group (targeted mass 55 kg, 98-115 kg, and 75 kg) were experimentally measured and studied under 9 vibration magnitudes (0.25, 0.315, 0.4, 0.5, 0.63, 0.8, 1.0, 1.25 and 1.6 ms-2 r.m.s. with a common ratio of ca. 1.25) without and with the support of an upright backrest. Each group had twelve subjects. With an increase in the vibration magnitude from 0.25 to 1.6 ms-2 r.m.s., the resonance frequency of the vertical apparent mass showed a decreasing trend. This was observed with all three bodyweight groups and two backrest conditions. Results of pairwise Wilcoxon signed-rank tests showed that, when the vibration magnitude increased by a factor of ca. 1.25, its effect on the resonance frequency was statistically insignificant in most cases. The results provided data on the vertical apparent mass for the heavyweight subjects that have not been reported and augmented the database of those for the lightweight subjects.