MODAL ANALYSIS OF A HUMAN LUMBAR SPINE BY EULER-BERNOULLI BEAM THEORY

Resumo

Human lumbar spine supports most of loads arising daily activities. Those loads are mainly
dynamic or periodic, therefore, an accurate study of free vibration of this structure can lead to a better
understanding the behavior of the system. In anatomical point of view, there are five lumbar vertebrae
in a human lumbar spine, two adjacent vertebral body are separated from each other by upper end plate,
intervertebral disc and lower end plate. Each part of the column has a unique structure. In this paper, an
analytical approach to study free transverse vibration of a human lumbar spine as a segmental multi-layer
beam by the classical beam Euler-Bernoulli theory is developed. A uniform transverse section of lumbar
spine is considered and the material properties are composed of different mechanic parameters. Free
vibration is analyzed considering different material properties, in order to simulate the aging process.
Continuity and equilibrium conditions are imposed as boundary conditions throughout the junctions of
the segments. Those conditions are in terms of displacement, slope, shear force, and bending moments.