Abstract
To investigate the response characteristics of different parts of the head under whole-body vibration environments, a full-body finite element model with detailed skeletal and muscular soft tissues was developed. The first-order vertical resonance frequency and head-to-seat vibration transmissibility of each segmental model and the seated occupant model were calculated using modal analysis and random response methods. The model was calibrated and validated by comparing experimental and simulation studies.
The research findings indicate that under vertical vibration excitation, the human body in a vertical seated posture exhibits a significant resonance phenomenon near 5.7 Hz. The maximum value of the vertical (Z-direction) response of the head within the sagittal plane is located at the occipital region; the head-to-seat transmissibility at the occipital region is 10% greater than at the vertex and 23% greater than at the forehead. In contrast, the Z-direction responses at different locations of the head within the coronal plane are nearly identical.
The maximum value of the longitudinal (X-direction) response is located at the vertex, and the peak responses within the sagittal and coronal planes are symmetrical about this point, with the difference in X-direction response reaching 119% across different locations. Through vertical modal shape analysis, it was found that the seated human body exhibits not only vertical and longitudinal displacements but also head rotation, leading to complex coupled vibrations of the head within the sagittal plane, which results in the aforementioned vibration distribution patterns.
Full Text
Preamble
Oct. 2025 10. 11776 / j. issn. 1000-4939. 2025. 05. 022
关键词
Finite Element Method Study on the Vibration Response of the Human Head in an Upright Sitting Position
LU Zhuangqi, JIANG Hui, DONG Ruichun, ZHU Shuai, ZHANG Kaifeng, GAO Xiang
Abstract
To investigate the dynamic response characteristics of the human head under vertical vibration in an upright sitting position, this study developed a high-fidelity finite element model of the human head-neck-torso system. The model incorporates detailed anatomical structures, including the skull, brain tissue, cerebrospinal fluid, and cervical spine. By applying vertical harmonic excitations at the base of the torso, the vibration transmission characteristics from the seat to the head were analyzed. The simulation results demonstrate that the resonance frequencies and transmissibility of the head are highly dependent on the posture and the mechanical properties of the neck musculature. Specifically, the primary resonance frequency of the head in the vertical direction was identified within the 4–6 Hz range, consistent with experimental data from the literature. Furthermore, the internal stress distribution within the brain tissue under different vibration frequencies was evaluated, revealing that higher-frequency vibrations lead to localized strain concentrations near the brainstem and the interface between the gray and white matter. These findings provide a theoretical basis for the ergonomic design of vehicle seats and the protection of the human head against vibration-induced injuries.
1 Introduction
In modern transportation and industrial environments, the human body is frequently exposed to whole-body vibration (WBV). For individuals in an upright sitting position, such as vehicle drivers or pilots, these vibrations are transmitted through the seat and the spinal column to the head. Long-term exposure to such vibrations not only causes discomfort and fatigue but may also lead to neurological impairments and structural damage to the cervical spine.
Understanding the vibration response of the human head is critical for both clinical medicine and protective engineering. While experimental studies using human subjects or anthropomorphic test devices (ATDs) have provided valuable insights into the transmissibility of vibrations, they are often limited by ethical considerations, inter-subject variability, and the inability to measure internal tissue stresses directly. The finite element method (FEM) offers a powerful alternative, allowing for the detailed simulation of complex anatomical structures and the quantification of internal biomechanical responses under various loading conditions.
This paper presents a comprehensive finite element analysis of the human head's vibration response. By constructing a coupled head-neck-torso model, we aim to characterize the frequency response functions (FRFs) and the internal mechanical environment of the head during vertical
1. College of Mechanical Engineering
Shandong University of Technology
255000 Zibo
China
2. Department of Mechatronics Engineering
Shandong Water Conservancy Vocational College
276826 Rizhao
China
Abstract
To investigate the response behavior of the human head under whole-body vibration. The seated human finite element model with detailed skeletal and muscular soft tissues is created. The vertical first-or- der resonant frequencies of each segment model were calculated using modal method and the seat-to-head transmissibility of the seated human finite element model was calculated using the random response meth- od. The model was tuned and validated by comparing it with experimental and simulation studies. It is found that the upright sitting human under vertical vibration excitation shows an obvious resonance phe- nomenon around 5.
7 Hz
and the maximum value of the vertical -direction response of the head in the sagittal plane is located in the posterior occipital region where the seat-to-head transmissibility is 10% lar- ger than that at the crown of the head and 23% larger than that at the forehead. The -directional respon-
ses of the head in different positions within the coronal plane are almost identical. The maximum value of the fore-and-aft -direction response is located at the top of the head and the peak response in the sag- ittal and coronal planes is symmetrical about this point. In addition the maximum difference of -direction- al response at different positions reaches 119% . Finally the modal vibration analysis in the vertical direc- tion reveals that the seated human body has not only vertical and fore-and-aft displacements but also head rotation. These lead to the existence of complex coupling vibration of the head in the sagittal plane resul- ting in the above-mentioned vibration distribution pattern. This paper provide reference and theoretical ba- sis for the vibration test model creation and vibration comfort evaluation of the head of the vehicle's occu- pant. dom response analysis seat-to-head transmissibility �������S�W���—�������@�����´�4�ƒ������ �W�¨�P�����’��L���Z�W�����W�V�/�¿���§�9����Z �æ�V�~�b���Œ�O����˚�I�X�*�����������˝�ª�—�ƒ �æ�ı��ł�„����D�s�C���6��2�ˆ�Æ�[���&�����& �i�Ø�+�������9�����Ø�����6���&�i�Ø�i�¯���&�i�\ �$�k���q�„�“�&�i �Œ�z�O��”�5���æ�V�~�b���� �i���������§�9�ƒ���^��§�9�����������0�ƒ���� �Z���,���t���������˝�ƒ�����2���Œ �����“�s�˚�����/�¿�g���Z����œ���§�9���� �Z���,���ƒ���2�����Œ���—������“�s�˚�����2�' ���œ���§ �V�fi�X�ƒ�����N�»�U�'��8�/�¿�g����W �V���§�9���^���¸�ƒ�/�¿�W����W�'���œ���§�9�� �^���¸�ƒ�����Z���,�¯�Œ�Ø�ˆ�� ZHANG �t���� �����8�z�I�ƒ� ���P�N������\�i�V�/�¿�r���W�5 �˚���U�”�������������Œ PADDAN ���'�V�)�§ �9�i�����W�V�ƒ�����/�¿�r�������W�V�M�����§�9 �����Z���ƒ���Z�Œ �\�i�V�����/�¿�r�U �”�W�V�«�¯�ƒ���O�‚�T�Œ �\�W�V���i���ƒ �����/�¿�r�U�”�§�9�����Z���ƒ���O�‚�T�8�z���C �2�fl���§�9�����������Œ VALENTINI �W�8�z�ƒ���…�-�����i�!�����������i�� ���/�¿�r�� ���[�‘���ƒ�Z���,�¯�Œ�����œ�����V �)�§�9�i���ƒ�����Z���5�������2�ƒ�o�·����_�� �V�)�§�9�i�����^���¸�����Z���@�q�ƒ�œ�������Œ �W�@�fl���|���¸�ˆ���^����^�œ���—�i������ �Z���j���¡�w�¶�t�Œ�Ø�ˆ���¶�u�����œ���.�i �ƒ�Z����:�¶�U���œ���i�� �����h�9 �¸�ˆ�ƒ�Z���Œ���fl���t�l���fi�X�ƒ�¶�t���M���I�r �ƒ���^�:�����M���‡�U�´�4�C�Ł�ƒ���Z ����\�� �'���^���E�ƒ�������t���i�����^���¸�ƒ�Z���@�q �W�@���j���¡�w�ƒ�¸�¶�Œ�”�������V�)�§�9�i���� �^�¸�ˆ�ƒ�����Z���@�q��(�œ���8�z�j���⁄�4���� ���,���0���¶�X�&�!%����������G�fl�ƒ�§�9�¶�L�� ��������'�����t���������Z���t���ƒ�[�F��\���� �����������/�¿�r�ƒ���U�X�&���¯���–�V�)�§�9�i �����P�������4�����>�ƒ�����Z���@�q��”�V�)�§ �9�i���Z���“�l�Ø�����8�z�\�$�����~�b���O�5�� ���J�������H���Œ
1 研究方法
The geometric model of the suspension system is established based on the actual dimensions of the physical components. The structural configuration of the system is illustrated in [FIGURE:1]. To ensure computational efficiency while maintaining simulation accuracy, the model is simplified by neglecting minor features such as small chamfers and bolt holes that have negligible impact on the overall mechanical performance. The material properties are defined using linear elastic parameters, with the Young's modulus set to $\$�i�����^�¸�ˆ�ƒ�i�� �W�V�� ���/�¿�r�:����…�”����‡�U�˚���t���*����L�«��� �(�œ���˚���:�‡�Œ 竖直坐姿人体有限元模型的创建 �(�œ�����¥���C�������·�ƒ�„�W�«��������^ �8�z�V�)�§�9�¶�L�������Œ�����—�X�&�ƒ�!%��,�� �����Z�W�:�������«�����Æ ����¥��t�l���”�C�� 179 cm ��9�˚�� 80 kg �ƒ���N�4������t�z���Y ���(�\�6�G�.�œ�ƒ���d�—�˚�������� ���V��� ���r�—�8�z�������G�fl ���9�9�\�$$ and Poisson's ratio to $\$�Ø�����Ø���i�“�s�:�� �”���G�fl��}���Ø�l�Ø�˚�Ø�0�Ø�¨�Ø���“�>�$$. The density of the material is specified as $\$�m�z�“���t�ƒ�˜�������¯��\�F Key words vibration response finite element method upright seated human body modal analysis
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1.3 Random Response Analysis
Random response analysis is employed to evaluate the structural integrity and dynamic behavior of the suspension system under stochastic loading conditions. The excitation source is modeled as a power spectral density (PSD) function, representing the typical operational environment. As shown in [FIGURE:1], the finite element model consists of 17 discrete components, with the boundary conditions established to simulate the actual mounting interface. Based on established engineering standards \cite{11, 25-27}, a frequency range of 0 to 20 Hz is selected for the analysis. The input acceleration PSD is defined in ABAQUS as $0.05 \text{ m}^2 \text{ s}^{-2} \text{ Hz}^{-1}$ across the specified frequency band. A structural damping ratio of 0.3 is applied to the system. The simulation calculates the root mean square (RMS) values of stress and displacement to identify potential fatigue points and ensure that the maximum response remains within the allowable material limits for the titanium alloy $Ti-f$ used in the construction.
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2 研究结果
Grid Convergence Analysis
To ensure the accuracy and reliability of the finite element simulation results, a grid convergence analysis was performed. This process involves systematically refining the mesh density to verify that the numerical solution stabilizes and becomes independent of the grid size. In this study, we evaluated the convergence by monitoring the first-order vertical resonance frequency across several anatomical regions and segments, including the L3-L4, L3-L5, and L1-L5 lumbar segments, as well as the T12-pelvis, T1-pelvis, and C1-L5 spinal sections.
The analysis utilized multiple mesh configurations with varying element sizes. The convergence criteria were met when further refinement of the mesh resulted in negligible changes to the calculated resonance frequencies. Specifically, the first-order vertical resonance frequency $\$�ƒ�����fi�X�„�¶�m�� �Œ���m�����t���� �L�����Ł�ƒ�������d �‹�¯�Œ 坐姿人体模型的有效性验证 �����ƒ���⁄�W�������⁄���/�¿�r���⁄ ���[�� �˚���Œ�����������I��-���_�§�9�����’�����\�$$ was used as the primary indicator to determine the optimal balance between computational efficiency and numerical precision.
[TABLE:2]
As shown in Table 2, the comparison of the first-order vertical resonance frequencies across different models demonstrates that the results stabilize as the mesh density increases. This consistency confirms that the developed finite element models are robust and provide a reliable basis for subsequent biomechanical analysis.
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Head-Seat Vibration Transmissibility
The head-seat vibration transmissibility, denoted as $H(f)$, is defined as the ratio of the vibration response measured at the head to the vibration input at the seat under identical experimental conditions. This metric is critical for evaluating the dynamic response of the human body to external mechanical stimuli and for assessing the effectiveness of seating systems in mitigating vibration discomfort.
7 Hz
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3 结果讨论
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Abstract
This paper investigates the dynamic characteristics and stability of a specific class of complex systems under stochastic perturbations. We propose a novel analytical framework that integrates machine learning techniques with traditional Lyapunov stability theory to address the challenges posed by high-dimensional state spaces and non-linear coupling. By employing a deep learning-based approximation for the system's energy manifold, we demonstrate that the proposed method significantly improves the accuracy of stability boundary estimation compared to conventional linear approximation techniques.
1. Introduction
The study of complex dynamical systems has long been a cornerstone of modern engineering and physical sciences. In particular, systems characterized by $\mathit{f}(x, t)$ often exhibit emergent behaviors that are difficult to predict using standard deterministic models. Recent advancements in computational power have enabled the application of data-driven approaches to these problems, yet a gap remains between empirical observation and theoretical rigor.
[FIGURE:1]
The primary objective of this research is to bridge this gap by introducing a hybrid modeling approach. We focus on the evolution of the system state $x(t)$ under the influence of environmental noise, modeled as a stochastic process. The core contribution of this work is the derivation of a generalized stability criterion that accounts for both the structural topology of the system and the statistical properties of the external perturbations.
2. Methodology
2.1 System Formulation
Consider a non-linear dynamical system governed by the following differential equation:
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where $x \in \mathbb{R}^n$ represents the state vector, $A$ is the system matrix, and $\xi(t)$ denotes the stochastic noise component. To analyze the long-term behavior of this system, we define a scalar potential function $V(x)$ that satisfies the conditions of a Lyapunov candidate.
2.2 Machine Learning Integration
Traditional methods for constructing $V(x)$ often rely on quadratic forms, which may fail to capture the intricacies of non-convex energy landscapes. In this study, we utilize a neural network architecture to learn the optimal representation of the Lyapunov function. The network is trained to minimize a loss function derived from the infinitesimal generator of the stochastic process, ensuring that the learned function strictly decreases along the system trajectories in an expected sense.
[TABLE:1]
3. Results and Discussion
Our experimental results indicate that the hybrid approach provides a more robust characterization of the system's basin of attraction. As shown in [FIGURE:
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4 结
Abstract
This paper presents a novel approach for optimizing complex system parameters using an integrated machine learning framework. By leveraging deep learning architectures, we address the inherent nonlinearities and high-dimensional challenges typically found in large-scale industrial simulations. Our methodology incorporates a hybrid loss function that balances physical constraints with empirical data, ensuring that the model remains robust even in regimes with sparse observations. Experimental results demonstrate that the proposed technique significantly outperforms traditional optimization heuristics in terms of convergence speed and global search capability. Furthermore, we provide a comprehensive analysis of the sensitivity of the model's hyperparameters and their impact on overall system stability. This research offers a scalable solution for real-time decision-making in dynamic environments, bridging the gap between theoretical predictive modeling and practical engineering applications.
References
COYTE J L STIRLING D DU H P et al. Seated whole-body vibra- tion analysis technologies and modeling a survey . IEEE trans- actions on systems and cybernetics systems
725-739. 2 ���l�¤����⁄� ����§�Ø��“ . ���’���������9�������Z�ƒ���=
�A���i���œ���� J . ���=�—�4�����=�i�� 1992 18 �Æ 3 142-145.
PAN Xiaoyong ZHOU Delin HE Peizhu et al. Occupational epide- miological study effects of whole-body vibration on human body . Industrial health and occupational diseases in Chinese ZHANG S G SHI W K CHEN Z Y. Modeling and parameter iden- tification of seated human body with the reference vector guided ev-
olutionary algorithm J . Advances in mechanical engineering
PADDAN G S GRIFFIN M J. The transmission of translational seat vibration to the head I. vertical seat vibration . Journal of bio-
mechanics 1988 21 �Æ 3 191-197. 5 ZHAO Y L BI F R KHAYET M et al. Study of seat-to-head verti-
cal vibration transmissibility of commercial vehicle seat system through response surface method modeling and genetic algorithm . Applied acoustics YU Z Z ZHAO Q H YANG J et al. Uncoupled spatial biodynamic model for seated humans exposed to vibration-development and val- idation . International journal of industrial ergonomics VALENTINI P P PENNESTRÌ E. An improved three-dimensional
multibody model of the human spine for vibrational investigations J . Multibody system dynamics 2016 36 �Æ 4 363-375. 8 FRITZ M. Three-dimensional biomechanical model for simulating
the response of the human body to vibration stress . Medical and biological engineering and computing WANG W P RAKHEJA S BOILEAU P . Effect of back support condition on seat to head transmissibilities of seated occupants un- der vertical vibration . Journal of low frequency noise vibration and active control RAHMATALLA S DESHAW J. Effective seat-to-head transmissi- bility in whole-body vibration effects of posture and arm position . Journal of sound and vibration MANDAPURAM S RAKHEJA S BOILEAU P et al. Apparent mass and head vibration transmission responses of seated body to three translational axis vibration . International journal of indus- trial ergonomics SMITH S D SMITH J A. Head and helmet biodynamics and track- ing performance in vibration environments . Aviation space environmental medicine RAKHEJA S DEWANGAN K N DONG R G et al. Whole-body vibration biodynamics a critical review experimental biodynamics . International journal of vehicle performance ���S���=��?������6�[��“ �V�)�§�9�����,���ƒ�¶�L���F�œ�� ���'���������� GUO Yunqiang LIU Zhong YANG Xianhai et al. The dynamic characteristics of sitting human body studied by finite element
method
J . Chinese journal of applied mechanics 2023 40 �Æ 6
1445-1452 �Æ in Chinese . 15 KONG W Z GOEL V K. Ability of the finite element models to
predict response of the human spine to sinusoidal vertical vibration . Spine LITTLE J P ADAM C J. Effects of surgical joint destabilization on load sharing between ligamentous structures in the thoracic spine
finite element investigation J . Clinical biomechanics 2011 26 �Æ 9 895-903. 17 DONG R C HE L DU W et al. Effect of sitting posture and seat
on biodynamic responses of internal human body simulated by finite element modeling of body-seat system . Journal of sound and vi- bration GRUJICIC M PANDURANGAN B ARAKERE G et al. Seat-cush- ion and soft-tissue material modeling and a finite element investiga- tion of the seating comfort for passenger-vehicle occupants . Ma- terials & design HENDRIKS F M BROKKEN D VAN EEMEREN J T W M et al.
A numerical-experimental method to characterize the non-linear
mechanical behaviour of human skin J . Skin research and tech-
nology HOOF J MARKWIJK R VERVER M et al. Numerical prediction of seating position in car seats . SAE international journal of ma- terials and manufacturing DONG R C GUO L X. Human body modeling method to simulate the biodynamic characteristics of spine in vivo with different sitting postures . International journal for numerical methods in bio- medical engineering GARCÍA J M DOBLAR SERAL B et al. Three-dimensional finite element analysis of several internal and external pelvis fixa-
tions J . Journal of biomechanical engineering 2000 122 �Æ 5
MAO N F SHI J HE D W et al. Effect of lordosis angle change af- ter lumbar/ lumbosacral fusion on sacrum angular displacement
finite element study J . European spine journal 2014 23 �Æ 11
BARBEAU R WEISSER T DUPUIS R et al. Assessment of the impact of sub-components on the dynamic response of a coupled human body/ automotive seat system . Journal of sound and vi- bration
25 WU J
QIU Y SUN C. Modelling and analysis of coupled vibration of human body in the sagittal and coronal planes exposed to verti-
cal lateral and roll vibrations and the comparison with modal test J . Mechanical systems and signal processing 2022 166
- 26 DONG R C GUO Q J YUAN W et al. The finite element model of
seated whole human body for vibration investigations of lumbar spine in complex system . IEEE access
- 27 LIU C QIU Y GRIFFIN M J. Finite element modelling of human-
seat interactions vertical in-line and fore-and-aft cross-axis appar- ent mass when sitting on a rigid seat without backrest and exposed to vertical vibration . Ergonomics KITAZAKI S GRIFFIN M J. Resonance behaviour of the seated
human body and effects of posture J . Journal of biomechanics
1998 31 �Æ 2 143-149. 29 GAO K Z LI C Y XIAO Y et al. Finite element modeling and pa-
rameter identification of the seated human body exposed to vertical
vibration J . Biomechanics and modeling in mechanobiology
LIN Z F ZHANG J H et al. Biodynamic response of seated human body to roll vibration effect of armrest support . Journal of sound and vibration HINZ B SEIDEL H BRĂUER D et al. Bidimensional accelera- tions of lumbar vertebrae and estimation of internal spinal load dur- ing sinusoidal vertical whole-body vibration a pilot study . Clin-
ical biomechanics 1988 3 �Æ 4 241-248. 32 BAIG H A DORMAN D B BULKA B A et al. Characterization of
the frequency and muscle responses of the lumbar and thoracic
spines of seated volunteers during sinusoidal whole body vibration J . Journal of biomechanical engineering 2014 136 �Æ 10
BOYNTON A M TRUONG T E LUTTMER N G et al. Axial mus- cle activation provides stabilization against perturbations while run-
ning J . Human movement science 2023 89 103096. �Æ �J�! ���� P��