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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.
Highlights
The motion of the cervical and lumbar spines of humans is to some extent determined by the collective physical properties of the intervertebral discs, facet joints, ligaments, surrounding tissues, and muscles
Different methods were proposed in the literature to predict the damping, mostly proportional damping, and stiffness parameters of humans under whole-body vibration using human modeling
The method developed in this work solves for the unknown damping and stiffness parameters at the cervical and lumbar areas of supine humans under vertical whole-body vibration using modal data that may inherit some errors
Summary
The motion of the cervical and lumbar spines of humans is to some extent determined by the collective physical properties of the intervertebral discs, facet joints, ligaments, surrounding tissues, and muscles. Different methods were proposed in the literature to predict the damping, mostly proportional damping, and stiffness parameters of humans under whole-body vibration using human modeling In these approaches, the unidentified stiffness and damping parameters of multi-mass-spring,[5,6,7,8] rigid bodies connected by viscoelastic elements and muscle groups,[9,10] or finite element[11,12,13] models, are predicted using optimization schemes. The method developed in this work solves for the unknown damping and stiffness parameters at the cervical and lumbar areas of supine humans under vertical whole-body vibration using modal data that may inherit some errors. In this process, experimental motion data were first collected from human subjects and their modal parameters were identified. An eigenvector correction algorithm was introduced to reduce the error in the modal data and to ensure the right inter-connectivity structure in the stiffness and damping matrices that satisfy the equation of motion
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