Transfer of the external loading such as shock or vibration to whole body could cause harmful or beneficial effects, depending on its nature. Two contradicting effects were investigated with macro and micro scale. In macro scale, the vibration absorbing capability of the human foot and ankle system (FAS) was investigated as the starting point of the whole body vibration using experimental method (transmissibility and phase delay measurement) and a model development. For biological cells, Finite Element modeling was utilized for modal analysis of an adherent cell in micro scale.
Vibration transfer characteristics of the FAS have been studied under vertical sinusoidal vibration (10-50 Hz with 5 Hz increments and 17.9 m/s² (peak to peak)) as a function of the external mass and foot and ankle postures. The results showed that the FAS played an important role in vibration transmission since the transmissibility of the FAS was dominant in lower leg. It was also found that the applied mass made the system stiffer and less damping, and the increase of the applied mass led to the increase of the resonant frequency from 20 to 30-40 Hz. This result explains that the overweight or obese persons can get more vibration transmission to the whole body when they are exposed to higher frequency (30-40 Hz). Furthermore, it supports that the resonant frequency of overweight or obese persons is similar to a major frequency range of heel strike, and overweight and obesity could be a potential injurious effect.
As the beginning step of a model development, system identification based on black box models (linear polynomial structures and state-space models) was utilized for understanding the transfer function on the basis of the acceleration measurement data of the foot and ankle exposed to vertical excitation. The identification of black box models showed good estimation results (60-98 %). The fitting error of the lower frequency (10 and 15 Hz regardless of the applied mass conditions) was observed because of nonlinear behavior of the viscoelastic material of the foot and ankle system. The identified statespace model gave the guide for order selection (2-8) of the grey box model in the next step.
The dynamic model of the foot and ankle exposed to vertical vibrations has been developed by deriving analytical dynamic equations that include viscoelastic material properties. Using parameter sensitivity analysis with respect to the states, complex derived equations were simplified as a two degrees of freedom model with linear spring and nonlinear damping at the fat pad and talocrural joint. Unknown parameters of the dynamic model were estimated by the parameter estimation method (optimization algorithm) by fitting the experimental data. The estimated parameters demonstrated that the fat pad dissipated more energy of the applied vibration than the talocrural joint and the applied mass and frequency increase affected the stiffness increase at the ankle joint and fat pad. The derived model is expected to be utilized for estimating some other frequencies and loading conditions.
An adherent single cell was modeled as a simple dome to extract the natural frequency and mode shapes of a cell in the culturing environment using Finite Element modal analysis. Simulation results showed that the adhered cell shape did not affect the modal analysis results. However the natural frequency was increased proportionally to the increase in Young’s modulus. It is supposed that the natural frequency of cells (18-25 Hz) is closely related to the optimal vibration range (20-60 Hz) for bone growth.