4. B modeling#
4.1. Characteristics of modeling#
The discrete element modeling is the same as in § 3.1. The only difference lies in the way in which the second mode is specified for all analyses on a truncated modal basis: the second mode is specified explicitly by imposing on the nodes \(\mathit{NO2}\), \(\mathit{NO}3\) and \(\mathit{NO}4\) a displacement \(\mathit{DX}\) corresponding to the reference modal deformation of § 2. This is representative of situations where certain modes are the result of experimental reconstruction and specified by imposed displacements.
4.2. Characteristics of the mesh#
Same as § 3.2.
4.3. Tested sizes and results#
The tested quantities, reference values and tolerances are the same as in § 3.3. This makes it possible to ensure that the various static correction methods work in the same way with (i) a fully calculated modal base or (ii) a modal base in which certain modes have been given by imposed displacements.
The results obtained are summarized in the table below:
Values for the relative displacement of node \(\mathrm{NO4}\) at time \(t=\mathrm{19,4}s\) (m):
modal basis |
Reference |
Tolerance |
truncated base |
-0.011301 |
|
full base |
-0.011301 |
1.e -04% |
static correction*a posteriori* |
-0.011301 |
|
static correction*a priori*, pseudo-mode, with re-orthogonalization |
-0.011301 |
1.e -04% |
static correction*a priori*, static force-imposed modes, with re-orthogonalization |
-0.011301 |
1.e -04% |
static correction*a priori*, pseudo-mode, static force-imposed modes, with re-orthogonalization |
-0.011301 |
1.e -04% |
Values for the relative displacement of node \(\mathrm{NO2}\) at time \(t=\mathrm{19,4}s\) (m):
modal basis |
Reference |
Tolerance |
truncated base |
7.33162E-04 |
|
full base |
7.33162E-04 |
1.0E -04% |
static correction*a posteriori* |
7.33162E-04 |
|
static correction*a priori*, pseudo-mode, with re-orthogonalization |
7.33162E-04 |
1.0E -04% |
static correction*a priori*, static force-imposed modes, with re-orthogonalization |
7.33162E-04 |
1.0E -04% |
static correction*a priori*, pseudo-mode, static force-imposed modes, with re-orthogonalization |
7.33162E-04 |
1.e -04% |