Fit the Linear Terms in the Model

The purpose of this fitting is to determine the overall shape of the dynamic stiffness and phase angle curves.

  • The results from Initial Design Parameters are used as the starting point.
  • You can observe from the plot below that the model is linear in terms of the parameters k0, k1, k2, c0, c1 and c2. Non-linearity occurs in the parameters p0, p1, p2, q0, q1 and q2. Therefore, p0, p1, p2, q0, q1 and q2 are kept fixed at reasonable values as an optimization is run to determine k0, k1, k2, c0, c1 and c2.
  • Since the model is linear when parameters p0 through q2 are fixed, it does not show any amplitude dependency. Moreover, the equations can be solved using linear methods.
  • The following plot shows the effect of a linear fit:
    Figure 1.