Secant Stiffness Proportional Damping
The SecantStiffnessProportional
class implements a damping model that is proportional to the secant stiffness of the structure.
Mathematical Formulation
The damping force is calculated as:
Where: - \(f_{damping}\) is the damping force - \(K_{secant}\) is the secant stiffness matrix - \(\dot{u}\) is the velocity vector
Parameters
dampingFactor
: Coefficient used in the secant stiffness-proportional damping (float between 0 and 1) [required]Ta
: Time when the damping is activated (float) [optional]Td
: Time when the damping is deactivated (float) [optional]tsTagScaleFactorVsTime
: Time series tag identifying the scale factor of the damping versus time (int) [optional]
Usage
from femora.components.Damping import DampingManager
damping_manager = DampingManager()
secstiff_damping = damping_manager.create_damping(
'secant stiffness proportional',
dampingFactor=0.03 # 3% damping proportional to secant stiffness
)
Advanced Usage
With time-dependent activation:
secstiff_damping = damping_manager.create_damping(
'secant stiffness proportional',
dampingFactor=0.03,
Ta=2.0, # Activate at 2 seconds
Td=15.0 # Deactivate at 15 seconds
)
Notes
This damping model is especially useful for nonlinear analyses
The secant stiffness is recalculated at each time step, making this model more computationally intensive but potentially more accurate for nonlinear systems