Defining structural damping ratio #1003
rahultarale
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To calculate the damping matrix
where:
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$r$ corresponds to the$r^\text{th}$ degree of freedom, with$r = 1, 2, 3, ..., n_{\text{dofs}}$ ; -
$\xi_r$ is the damping ratio the$r^\text{th}$ mode; -
$\omega_r$ is the natural frequency of the$r^\text{th}$ mode; -
$M_{r,r}$ is the mass matrix element corresponding to the$r^{\text{th}}$ mode.
In ROSS, the damping matrix can be implemented with the following script:
import scipy as sp
import numpy as np
import ross as rs
# Initialize the rotor system
rotor = ...
n = rotor.ndof
# Define the damping ratios for each mode
# Make sure the number of ratios matches the system's degrees of freedom (n)
damping_ratio = [...]
# Retrieve the mass matrix for the rotor system
M = rotor.M(0)
# Retrieve the stiffness matrix removing the cross-coupled coefficients
# of bearing stiffness matrix
K_aux = rotor.K(0)
for elm in rotor.bearing_elements:
dofs = list(elm.dof_global_index.values())
# If 4 dof model:
K_aux[np.ix_(dofs, dofs)] -= elm.K(0) * [[0, 1], [1, 0]]
# If 6 dof model:
# K_aux[np.ix_(dofs, dofs)] -= elm.K(0) * [[0, 1, 0], [1, 0, 0], [0, 0, 0]]
# Calculate the natural frequencies
evals, evectors = sp.linalg.eigh(K_aux, M)
wn = np.sqrt(evals)
# Initialize the damping matrix
C = np.zeros((n, n))
# Populate the diagonal elements of the damping matrix
for r in range(n):
C[r, r] = 2 * damping_ratio[r] * wn[r] * M[r, r]
# Replace the rotor's damping matrix method with the custom one defined above
rotor.C = lambda frequency: C
# Run the unbalance response analysis
unbalance = rotor.run_unbalance_response(...)Beta Was this translation helpful? Give feedback.
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please help me to understand how to apply structural damping ratio while performing unbalance response analysis.
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