5. C modeling#
Modeling C is purely functional: it is used to validate the damping input in the form of a diagonal damping matrix.
We use calculation \(n°4\) from modeling A (multi-support calculation decorrelated by the “CQC” method).
The reference values are obviously the same:
absolute displacements: \(\mathrm{DEPL}\)
NOEUD |
Reference |
Tolerance \((\text{\%})\) |
\(\mathrm{NO2}\) |
|
|
\(\mathrm{NO3}\) |
|
|
Note:
This test was chosen because it has clear reference values and because the system is characterized by two natural modes. We can therefore perfectly determine the Rayleigh damping matrix from the reduced damping \(\xi\) of the two natural modes and their natural pulsations ( \({\omega }_{1}\) and \({\omega }_{2}\) ) :
\(C=\alpha K+\beta M\) with \(\alpha =\frac{2\xi }{{\omega }_{1}+{\omega }_{2}}\) and \(\beta =\frac{2\xi {\omega }_{1}{\omega }_{2}}{{\omega }_{1}+{\omega }_{2}}\)
Before the projection of the structural matrices (and the damping matrix in particular) care was taken to specify (in the generalized numbering) that the matrices were diagonal. This is necessary to stay within the traditional amortization framework to COMB_SISM_MODA L is restricted to.