Frequency Domain Analysis

The options in a frequency domain analysis are:

• Number of Iterations
• Effective Shear Strain Ratio (SSR)
• Complex Shear Modulus Formulation
  • Frequency Independent
  • Frequency Dependent
  • Simplified

Number of Iterations

This option determines the number of iterations in performing an equivalent linear analysis. Check whether the solution has converged and the selected iteration number is sufficient by viewing the Check Convergence tab after running the analysis.

Effective Shear Strain Ratio (SSR)

When performing an equivalent linear analysis, the effective strain needs to be defined. An effective shear strain, calculated as a percentage of the maximum strain, is used to obtain new estimates of shear modulus and damping ratio. The default and recommended value is 0.65 (65%). The following equation relates this value to earthquake magnitude.

Complex Shear Modulus

RSSeismic allows a choice among three types of complex shear modulus formulae in performing frequency domain analysis:

• Frequency Independent Complex Shear Modulus (Kramer, 1996)
  The frequency independent shear modulus results in frequency independent damping, and is thus recommended to be used in the analysis. This is the same modulus used in SHAKE91.
  𝐺∗=𝐺 (1+ 𝑖2𝜉)
• Frequency Dependent Complex Shear modulus (Udaka, 1975)
  The frequency dependent shear modulus results in frequency dependent damping, and should thus be used with caution.
  
  
• Simplified Complex Shear modulus (Kramer, 1996)
  This is a simplified form of frequency independent shear modulus defined as:
  𝐺∗=𝐺 (1−𝜉²+ 𝑖2𝜉)