竖直坐姿人体头部振动响应的有限元法研究

Finite element method study on the vibration response of the human head in an upright sitting position

摘要

为探究全身振动环境下头部不同部位的响应特点，创建了具有详细骨骼和肌肉软组织的全人体有限元模型，采用模态法与随机响应法计算了各节段模型和坐姿乘员模型的垂向第一阶共振频率与头椅振动传递率，并对比实验和模拟研究，对模型进行了调校与验证。研究发现：在垂向振动激励下竖直坐姿人体在5.7 Hz附近出现明显的共振现象，头部垂向（Z向）响应在矢状面内的最值位于后枕部，后枕部的头椅传递率较头顶处大10%，比额头处大23%，而在冠状面内头部不同位置Z向响应几乎相同；前后向（X向）响应的最值位于头顶处，且矢状面和冠状面内的响应峰值关于此点对称，不同位置X向响应差异达到119%。通过垂向的模态振型分析发现坐姿人体不仅有垂向和前后位移，头部还有转动，导致头部在矢状面内存在复杂的耦合振动，从而出现上述的振动分布规律。

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-order 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 method. 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 phenomenon around 5.7 Hz，and the maximum value of the vertical （Z-direction）response of the head in the sagittal plane is located in the posterior occipital region，where the seat-to-head transmissibility is 10% larger than that at the crown of the head，and 23% larger than that at the forehead. The Z-directional responses of the head in different positions within the coronal plane are almost identical. The maximum value of the fore-and-aft （X-direction）response is located at the top of the head，and the peak response in the sagittal and coronal planes is symmetrical about this point. In addition，the maximum difference of X-directional response at different positions reaches 119%. Finally，the modal vibration analysis in the vertical direction 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，resulting in the above-mentioned vibration distribution pattern. This paper provide reference and theoretical basis for the vibration test，model creation and vibration comfort evaluation of the head of the vehicle's occupant.

关键词

振动响应 / 有限元法 / 竖直坐姿人体 / 模态分析 / 随机响应分析 / 头椅振动传递率

Key words

vibration response / finite element method / upright seated human body / modal analysis / random response analysis / seat-to-head transmissibility

参考文献

[1] COYTE J L， STIRLING D， DU H P， et al. Seated whole-body vibration analysis，technologies，and modeling：a survey[J]. IEEE transactions on systems，man，and cybernetics：systems， 2016， 46（6）： 725-739.

[2] 潘晓勇， 周德林， 何佩珠， 等. 全身振动对机体不良影响的职业流行病学研究[J]. 工业卫生与职业病， 1992， 18（3）： 142-145.

[3] PAN Xiaoyong， ZHOU Delin， HE Peizhu， et al. Occupational epidemiological study-effects of whole-body vibration on human body[J]. Industrial health and occupational diseases， 1992， 18（3）： 142-145（in Chinese）.

[4] ZHANG S G， SHI W K， CHEN Z Y. Modeling and parameter identification of seated human body with the reference vector guided evolutionary algorithm[J]. Advances in mechanical engineering， 2021， 13（ 11）： 1-11.

[5] PADDAN G S， GRIFFIN M J. The transmission of translational seat vibration to the head-I. vertical seat vibration[J]. Journal of biomechanics， 1988， 21（3）： 191-197.

[6] ZHAO Y L， BI F R， KHAYET M， et al. Study of seat-to-head vertical vibration transmissibility of commercial vehicle seat system through response surface method modeling and genetic algorithm[J]. Applied acoustics， 2023， 203： 109216.

[7] YU Z Z， ZHAO Q H， YANG J， et al. Uncoupled spatial biodynamic model for seated humans exposed to vibration-development and validation[J]. International journal of industrial ergonomics， 2021， 85： 103171.

[8] VALENTINI P P， PENNESTRÌ E. An improved three-dimensional multibody model of the human spine for vibrational investigations[J]. Multibody system dynamics， 2016， 36（4）： 363-375.

[9] FRITZ M. Three-dimensional biomechanical model for simulating the response of the human body to vibration stress[J]. Medical and biological engineering and computing， 1998， 36（6）： 686-692.

[10] WANG W P， RAKHEJA S， BOILEAU P É. Effect of back support condition on seat to head transmissibilities of seated occupants under vertical vibration[J]. Journal of low frequency noise，vibration and active control， 2006， 25（4）： 239-259.

[11] RAHMATALLA S， DESHAW J. Effective seat-to-head transmissibility in whole-body vibration：effects of posture and arm position[J]. Journal of sound and vibration， 2011， 330（25）： 6277-6286.

[12] MANDAPURAM S， RAKHEJA S， BOILEAU P É， et al. Apparent mass and head vibration transmission responses of seated body to three translational axis vibration[J]. International journal of industrial ergonomics， 2012， 42（3）： 268-277.

[13] SMITH S D， SMITH J A. Head and helmet biodynamics and tracking performance in vibration environments[J]. Aviation，space，and environmental medicine， 2006， 77（4）： 388-397.

[14] RAKHEJA S， DEWANGAN K N， DONG R G， et al. Whole-body vibration biodynamics-a critical review：experimental biodynamics[J]. International journal of vehicle performance， 2020， 6（ 1）： 1-51.

[15] 郭云强， 刘忠， 杨先海， 等. 坐姿人体动态特性的有限元法研究[J]. 应用力学学报， 2023， 40（6）： 1445-1452.

[16] 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（6）： 1445-1452（in Chinese）.

[17] KONG W Z， GOEL V K. Ability of the finite element models to predict response of the human spine to sinusoidal vertical vibration[J]. Spine， 2003， 28（17）： 1961-1967.

[18] LITTLE J P， ADAM C J. Effects of surgical joint destabilization on load sharing between ligamentous structures in the thoracic spine：a finite element investigation[J]. Clinical biomechanics， 2011， 26（9）： 895-903.

[19] 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[J]. Journal of sound and vibration， 2019， 438： 543-554.

[20] GRUJICIC M， PANDURANGAN B， ARAKERE G， et al. Seat-cushion and soft-tissue material modeling and a finite element investigation of the seating comfort for passenger-vehicle occupants[J]. Materials & design， 2009， 30（10）： 4273-4285.

[21] 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 technology， 2003， 9（3）： 274-283.

[22] HOOF J， MARKWIJK R， VERVER M， et al. Numerical prediction of seating position in car seats[J]. SAE international journal of materials and manufacturing， 2004， 113（5）： 881-885.

[23] DONG R C， GUO L X. Human body modeling method to simulate the biodynamic characteristics of spine in vivo with different sitting postures[J]. International journal for numerical methods in biomedical engineering， 2017， 33（11）： 15-50.

[24] GARCÍA J M， DOBLARÉ M， SERAL B， et al. Three-dimensional finite element analysis of several internal and external pelvis fixations[J]. Journal of biomechanical engineering， 2000， 122（5）： 516-522.

[25] MAO N F， SHI J， HE D W， et al. Effect of lordosis angle change after lumbar/lumbosacral fusion on sacrum angular displacement：a finite element study[J]. European spine journal， 2014， 23（11）： 2369-2374.

[26] 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[J]. Journal of sound and vibration， 2019， 459： 114846.

[27] WU J， QIU Y， SUN C. Modelling and analysis of coupled vibration of human body in the sagittal and coronal planes exposed to vertical，lateral and roll vibrations and the comparison with modal test[J]. Mechanical systems and signal processing， 2022， 166： 108439.

[28] 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[J]. IEEE access， 2020， 8： 125046-125055.

[29] LIU C， QIU Y， GRIFFIN M J. 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[J]. Ergonomics， 2015， 58（7）： 1207-1219.

[30] KITAZAKI S， GRIFFIN M J. Resonance behaviour of the seated human body and effects of posture[J]. Journal of biomechanics， 1998， 31（2）： 143-149.

[31] GAO K Z， LI C Y， XIAO Y， et al. Finite element modeling and parameter identification of the seated human body exposed to vertical vibration[J]. Biomechanics and modeling in mechanobiology， 2021， 20（5）： 1789-1803.

[32] LIN Z F， ZHANG J H， LI M， et al. Biodynamic response of seated human body to roll vibration：effect of armrest support[J]. Journal of sound and vibration， 2022， 529： 116939.

[33] HINZ B， SEIDEL H， BRĂUER D， et al. Bidimensional accelerations of lumbar vertebrae and estimation of internal spinal load during sinusoidal vertical whole-body vibration：a pilot study[J]. Clinical biomechanics， 1988， 3（4）： 241-248.

[34] 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（10）： 101002.

[35] BOYNTON A M， TRUONG T E， LUTTMER N G， et al. Axial muscle activation provides stabilization against perturbations while running[J]. Human movement science， 2023， 89： 103096.

基金资助

国家自然科学基金资助项目(52005305)

山东省自然科学基金资助项目(ZR2019BEE071)

山东省自然科学基金资助项目(ZR2021QE203)

中国博士后科学基金资助项目(2019M652443)