Rayleigh Damping
The RayleighDamping
class implements classical Rayleigh damping, which defines the damping matrix as a linear combination of the mass and stiffness matrices.
Mathematical Formulation
The Rayleigh damping matrix is defined as:
Where:
\(C\) is the damping matrix
\(M\) is the mass matrix
\(K\) is the stiffness matrix
\(K_{init}\) is the initial stiffness matrix
\(K_{comm}\) is the committed (last converged) stiffness matrix
\(\alpha_M\), \(\beta_K\), \(\beta_{KInit}\), \(\beta_{KComm}\) are the proportionality factors
Parameters
alphaM
: Factor applied to the mass matrix (default: 0.0)betaK
: Factor applied to the stiffness matrix (default: 0.0)betaKInit
: Factor applied to the initial stiffness matrix (default: 0.0)betaKComm
: Factor applied to the committed stiffness matrix (default: 0.0)
Usage
from femora.components.Damping import DampingManager
damping_manager = DampingManager()
rayleigh_damping = damping_manager.create_damping(
'rayleigh',
alphaM=0.05,
betaK=0.001,
betaKInit=0.0,
betaKComm=0.0
)
Notes
At least one of the proportionality factors must be greater than zero
All factors must be between 0 and 1
The usage of Rayleigh damping may provide incorrect results when used with non-linear time history analysis using concentrated plasticity models