A new method to study free transverse vibration of the human lumbar spine as segmental multi-layer Timoshenko and Euler–Bernoulli beams

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.