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 | CSME 2025/10 Volume 46 No.5
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                            541-548
 
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            | Vertical Modal Characteristics of the Human Lumbar Spine Under Compressive Follower Preload: A Finite Element Study 
 Wei Fan a, Hao Dong b, Dong-Mei Chen c, Huai-Ming Sui c and Li-Xin Guo d
 aAssociate Professor, School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China
 bSenior Engineer, CRRC Dalian Co. Ltd., Dalian 116022, China.
 cSenior Engineer, Yangzhou Fengming Photoelectric New Material Co. Ltd., Yangzhou 225117, China.
 dProfessor, School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China.
 
 
 
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            | Abstract: 
                The vibrational stimuli, particularly when it approximates the resonant frequency of human spine, can subject the spine to significant forces, heightening the risks of damage and potentially causing devastating consequences. Although numerous biomechanical inquiries have delved into the resonant frequency and its corresponding mode shape of the human lumbar spine, the majority overlooked the influence of physiological compressive loading stemming from muscular contractions. Consequently, this research aimed to scrutinize the modal characteristics of the entire human lumbar spine under the influence of this loading. Initially, a computed tomography-based, 3-dimensional ligamentous finite element model of the human T12–pelvis spinal segment was created and validated. Subsequently, modal analysis was conducted on this model, incorporating varying levels of compressive preload applied via a follower load method, to determine its resonant frequency and corresponding mode shape in the vertical plane. The results showed that the T12–pelvis model exhibited a vertical resonant frequency of 6.49 Hz under no preload. Furthermore, the observed vertical mode shape showcased the lumbar spine engaging in not just vertical motion, but also anterior-posterior and rotational motions. Additionally, it was found that the modal responses were preload-dependent. As the preload increased, the vertical resonant frequency increased, whereas the vertical displacement of the vertebrae decreased. The present findings have the potential to enhance our comprehension of vibrational responses in the human lumbar spine, thus offering crucial insights in reducing injuries and discomfort among individuals exposed to vibration environment. 
 
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            | Keywords:  lumbar spine, modal characteristics, compressive follower preload, finite element. | 
        
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            | ©
                2025
                 CSME , ISSN 0257-9731 
 
 
 
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