Finite Element Modeling and Vibration Analysis of the First Lumbar Vertebra

This research deals with finite element (FE) modeling and vibration analysis of the first lumbar vertebra. Since the material and geometrical properties of the human organs can be affected by age, gender, or some diseases, the effect of uncertainty in the material and geometric properties of the FE model of the L۱ vertebra on its vibration behavior is studied numerically. To do so, the Young’s modulus, the density, and the Poisson’s ratio of the cortical and trabecular bones as well as those of the posterior bony portion together with the thickness of the cortical bone are considered as the design variables. Then, the effect of the uncertainty in these design variables on the modal parameters the FE model are investigated. Based on the obtained results, the density of the posterior bony of the L۱ vertebra has a significantly higher influence on the modal parameters compared to other density parameters. Therefore, when modeling the vibration behavior of the spine, it is important to model the posterior bony as it has different material properties with different influences on modal parameters compared to those of cortical and trabecular bones. Also, the Young’s modulus of different parts of the FE model has significant influences on the modal parameters. Moreover, it is observed that the variations in the Poisson’s ratios do not affect the natural frequencies considerably, but they slightly change the mode shapes. The thickness of the cortical bones also influences both natural frequencies and mode shapes.

کلیدواژه ها:

Lumbar vertebra ، Finite element method ، Vibration analysis ، Sensitivity analysis