The aim of this study is to propose a method for studying the free transverse vibration of the human lumbar spine using Timoshenko and Euler–Bernoulli beam theories. The cross section of the lumber spine is assumed to be uniform, and the material properties are different for the vertebral bodies, endplates, and intervertebral discs. To derive equations with biomedical approach, they were developed with n segments of the lumbar spine including vertebrae, intervertebral discs, and endplates. Three first natural frequencies and mode shapes of system were computed and then validated with a finite element analyzer. Due to good agreements between the results, it was concluded that the proposed method offered acceptable results; therefore, it can be applied to the entire spine from the neck region to the tailbone and pelvis ones.

中文翻译：

---

研究多层腰椎Timoshenko和Euler–Bernoulli梁作为腰椎自由横向振动的一种新方法

这项研究的目的是提出一种使用Timoshenko和Euler-Bernoulli束理论研究人腰椎自由横向振动的方法。腰椎的横截面被认为是均匀的，并且椎体，端板和椎间盘的材料特性是不同的。为了通过生物医学方法推导方程式，将它们开发为包含脊椎，椎间盘和终板的n个腰椎节段。计算了系统的三个第一自然频率和模式形状，然后使用有限元分析仪进行了验证。由于结果之间达成了良好的协议，因此得出结论，所提出的方法提供了可接受的结果；因此，它可以应用于从颈部到尾骨和骨盆的整个脊柱。