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.