Identification of damping and stiffness parameters of cervical and lumbar spines of supine humans under vertical whole-body vibration

Abstract

This work presents a methodology to estimate the unknown damping and stiffness parameters of supine humans at the cervical and lumbar regions while reducing errors presented in the data. Modal parameters (natural frequencies, damping ratios, and eigenvectors) determined from experiments on 11 supine-human subjects exposed to vertical whole-body vibration were used in an inverse modal problem to solve for physical parameters (stiffness and damping). Due to uncertainty in the error level in the modal data, a methodology is presented to reduce the error by correcting the phase of the eigenvectors. Constraints that preserve the inter-connectivity of the physical stiffness and damping matrices were utilized via semi-definite programming. A four-degree-of-freedom human model, as suggested by the experimental modal analysis, was used for computational and analysis purposes. The resulting damping and stiffness parameters of the cervical and lumbar regions produced the right structure of the stiffness and damping matrices and satisfied the equation of motion. Validation analysis on the predicted acceleration response in the time domain of the human model, using the resulting damping and stiffness parameters, demonstrated characteristics very close to those found by the experiments. This work presents new information with many potential applications to the field of biomechanics.