3. Operands#
3.1. Keyword ENER_SOL#
This key word factor used only once is used to enter the data necessary to calculate the potential energy in the ground by degree of freedom for all the frequencies of a mode_meca concept.
3.1.1. Operand METHODE#
This operand makes it possible to define the method for calculating the energy in the ground by frequency.
With the value “DEPL”, the energy is calculated from the averaged displacements over the nodes of the raft for each mode: \(E\mathrm{=}\frac{1}{2}\mathrm{\sum }_{i\mathrm{=}\mathrm{1,6}}{k}_{i}{U}_{i}^{2}{(\mathit{fr})}_{i}\), where the \({k}_{i}\) represent the 6 components KX, KY, KZ, KRX, KRY and KRZ, of the overall stiffness of ground springs (cf. [§3.1.3]).
With the value “RIGI_PARASOL”, we calculate the energy from the efforts averaged on the nodes of the raft for each mode: \(E\mathrm{=}\frac{1}{2}\mathrm{\sum }_{i\mathrm{=}\mathrm{1,6}}\frac{{F}_{i}^{2}}{{k}_{i}}{(\mathit{fr})}_{i}\).
The nodal forces with this method are determined from the stiffness values distributed to the nodes under the slab as per option RIGI_PARASOL of the AFFE_CARA_ELEM [U4.42.01] command.
3.1.2. Operand MODE_MECA#
Allows you to introduce the mode_meca concept containing the frequencies for calculating potential energy.
3.1.3. Operands KX/KY/KZ/KRX/KRY/KRZ#
Represent the values of the components of the overall stiffness of ground springs.
Involved in the calculation of terms \({k}_{i}\mathrm{.}{U}_{i}^{2},i\mathrm{=}\mathrm{1,}\mathit{NCmp}\),
\(\mathrm{NCmp}\) is the number of components (3 or 6) determined by the presence or absence of the operands KRX, KRY, KRZ used (if they are) necessarily used together. \(\mathrm{NCmp}\) and the number of ddls carried by the nodes of the raft may be different.
In the particular case of an embedded structure, the various components of the stiffness of the ground springs are indicated as being equal to zero so as to cancel out the energy associated with the ground. These values are compatible with the default value “DEPL” for the METHODE operand.
3.1.4. Operand GROUP_NO_RADIER#
This operand is linked to the value “DEPL” of the METHODE operand.
List of groups of nodes constituting the base of the structure placed on the ground. The averaged displacement at these nodes \(U\) of components \({U}_{i}\) is then calculated for each calculated mode of frequency \(\mathrm{fr}\) in order to be able to determine the energy in the ground by ddl and by frequency: \(\frac{1}{2}{k}_{i}\mathrm{.}{U}_{i}^{2}(\mathrm{fr})\).
3.1.5. Operand GROUP_MA_RADIER#
This operand is linked to the value “RIGI_PARASOL” of the METHODE operand.
List of groups of meshes constituting the base of the structure placed on the ground. Allows you to calculate the average effort at the nodes of these cells \(F\) of components \({F}_{i}\) for each calculated mode of frequency \(\mathrm{fr}\) in order to determine the energy in the ground by ddl and by frequency: \(\frac{1}{2}\frac{{F}_{i}^{2}}{{k}_{i}}(\mathrm{fr})\).
3.1.6. Operand FONC_GROUP/COEF_GROUP/GROUP_NO_CENTRE/COOR_CENTRE#
These operands are also linked to the value “RIGI_PARASOL” of the METHODE operand.
These are the same as in option RIGI_PARASOL of the AFFE_CARA_ELEM [U4.42.01] command. They also make it possible to obtain the stiffness values distributed at the nodes under the slab used to determine the nodal forces by mode and then their mean \(F\) of component \({F}_{i}\).
An operand chosen from FONC_GROUP/COEF_GROUP makes it possible to determine the weightings, functions of the abscissa or real, of each of the groups of cells constituting the slab. The formulas remain at the user’s choice. By default, the distribution function is considered to be constant and unitary, i.e. each surface is affected by the same weight [bib2].
Therefore, as many terms are needed in the corresponding list as in the list of mesh groups given by operand GROUP_MA_RADIER.
An operand chosen from GROUP_NO_CENTRE/COOR_CENTRE makes it possible to provide either the central node of the deregister by a group of nodes of a single node, or directly the coordinates locating the central node.
3.2. Keyword AMOR_INTERNE#
Used only once at the same time as the ENER_SOL keyword.
The contribution to the reduced damping of each mode is established from the distribution of potential energy in the structure for the mode in question. This distribution is obtained using the POST_ELEM [U4.81.22] command from the mode_meca type concept (cf. [§3.1.1]) which produces a table.
The input parameters in this table are names of mesh groups, defined by the user based on the material damping distributions in the structure.
3.2.1. Operand ENER_POT#
Name of the potential energy table produced by command POST_ELEM [U4.81.22].
The required parameters of the table are:
Settings |
Type |
Description |
NUME_ORDRE |
I |
Order number |
FREQ |
R |
Frequency at order number NUME_ORDRE |
LIEU |
K8 |
Associated geometric entity: it can be the whole structure, a set of cells, or groups of cells |
POUR_CENT |
R |
Rate of potential energy compared to total energy |
For more information on the meaning of the parameters, the reader is invited to consult the documentation for the POST_ELEM [U4.81.22] command.
3.2.2. Operand GROUP_MA#
The list of cell group names from which we will point to in the table defined by ENER_POT (cf. [§3.2.1]).
It is imperative that this list contains all the cell groups that make up the structure and that they have had their energy calculated in the table defined by ENER_POT. It will be considered that for each mode the sum of the energies passing through the previous groups of cells will be equal to the total energy minus that passing through the ground springs and distributed using the keyword ENER_SOL.
If the user indicates a name for a group of elements whose energy has not been calculated in the table defined by ENER_POT, he will have an alarm but no stop. It is therefore up to him to check the conformity of the mesh groups in the table and those in the list in the keyword AMOR_INTERNE.
Finally, for the calculation of the list of modal dampenings according to the RCC -G rule to make sense, so that in particular the energy passing through the ground springs is not negative (which would mean that the potential energy rate of all the groups of cells constituting the structure could exceed 100%), it is strongly recommended to impose a solid connection condition on the list of groups of nodes constituting the base of the structure placed on the ground.
To properly calculate the potential energy rate of the constituent cell groups, it is imperative to have the total energy of the entire model. And for this, beforehand it is mandatory that in the table defined by ENER_POT, we have calculated the potential energy by the operator POST_ELEM for the entity TOUT =” OUI “. If not, a stop message is sent.
3.2.3. Operand AMOR_REDUIT#
The list of real material depreciation values corresponding, term for term, to the list of cell group names defined by GROUP_MA (see [§3.2.2]).
3.3. Keyword AMOR_SOL#
Used only once at the same time as the ENER_SOL keyword.
It makes it possible to determine the contribution of geometric damping due to the reflection of elastic waves. These directional damping values are obtained by interpolating for each calculated natural frequency the geometric damping functions \(\frac{\text{Im}(K(\omega ))}{2\text{Re}(K(\omega ))}\) (cf. § [3.3.1]) where \(K(\omega )\) is the complex impedance of the ground determined using one of the software MISS3D, CLASSI or PARASOL:
\(\mathrm{amor}({\omega }_{i})=\left[{\omega }_{i},\frac{\text{Im}(K({\omega }_{i}))}{2\text{Re}(K({\omega }_{i}))}\right]\)
3.3.1. Operand FONC_AMOR_GEO#
Define the list of geometric damping frequency functions, one per degree of freedom (3 or 6).
In the context of a structure on an embedded base, this function must be specified even if it does not have any particular meaning. We can take the constant function equal to zero for example.
3.3.2. Operand AMOR_REDUIT#
Correction in the calculation of geometric damping due to the reduced material damping of the ground.
Note:
The reduced damping value is required if ground impedance is produced by PARASOL. The full value of the reduced material damping of the ground is then affected. If**the impedance of the ground is produced by MISS3D, this value is only necessary if the ground is homogeneous (see operand*HOMOGENE [:ref:`§3.3.3 <§3.3.3>`]) and in this case the half-value of the reduced material damping of the ground is introduced. *
3.3.3. Operand HOMOGENE#
If the ground is homogeneous (“OUI”), the calculation of the geometric damping is weighted by the factor 0.5. So in the case where the impedance of the ground is produced by MISS3D and only if the ground is homogeneous (“OUI”), we must introduce for the operand AMOR_REDUIT (cf. [§3.3.2]) the half-value of the reduced material damping of the ground. Nothing is introduced when the impedance of the ground is produced by MISS3D if the ground is not homogeneous (“NON”).
3.3.4. Operand SEUIL#
Value defined in RCC -G [bib1] (0.3 by default) for the threshold beyond which modal damping is possibly truncated. This threshold operates after any previous corrections.
3.4. Keyword AMOR_RAYLEIGH#
Used only once excluding the ENER_SOL keyword. This keyword makes it possible to calculate a list of modal dampers by calculated frequency of a mode_meca concept. This list depends both on the values of the frequencies in mode \({\mathrm{freq}}_{i}\) and on the coefficients used in the Rayleigh damping expression.
3.4.1. Operand MODE_MECA#
Allows you to introduce the mode_meca concept containing the frequencies from which modal damping will be calculated.
3.4.2. Operands AMOR_ALPHA/AMOR_BETA#
Represent respectively the values of the components \(\mathrm{\alpha }\) and \(\mathrm{\beta }\) involved in the expression of Rayleigh damping using the stiffness and mass operators: \(C=\alpha K+\beta M\).
So for each calculated frequency \({\mathrm{freq}}_{i}\) of the mode_meca \(\mathrm{mod}\) concept associated with a pulsation \({\omega }_{i}=2\pi {\mathrm{freq}}_{i}\), an equivalent modal damping is obtained:
\({\xi }_{i}=\frac{1}{2}(\alpha {\omega }_{i}+\frac{\beta }{{\omega }_{i}})\)
3.4.3. Operands CORR_AMOR_NEGATIF/COEF_CORR_AMOR#
The CORR_AMOR_NEGATIF keyword automatically checks whether there are negative values in the list of damping coefficients generated by the operator.
If this keyword is set to “NON” (value by default), then if negative or zero damping is detected, the execution stops in error, with a message indicating the value in question.
If the keyword is set to “IGNORE”, we act as before except that the error is transformed into a simple alarm.
Finally, if the keyword is equal to “OUI”, then the negative or zero values are replaced by a strictly positive arbitrary value (and less than 1) defined by the user with the COEF_CORR_AMOR keyword.