3. Operands#
3.1. Key words MATR_MASS and MATR_RIGI#
♦ MATR_MASS
Real, symmetric assembled matrix of type [matr_asse_depl_r].
♦ MATR_RIGI
Real, symmetric assembled matrix of type [matr_asse_depl_r].
3.2. Keyword ETAT_INIT#
◊ ETAT_INIT
Under this keyword factor, you can enter a periodic solution to initialize the algorithm for calculating non-linear modes.
3.2.1. Operand MODE_LINE#
◊ MODE_LINE
Mode_me structure based on a calculation using the CALC_MODES operator. This keyword is not valid if the MODE_NON_LINEest keyword is present.
3.2.2. Operand MODE_NON_LINE#
◊ MODE_NON_LINE
Table_container structure resulting from a calculation with the MODE_NON_LINE operator. This keyword is not valid if the MODE_LINE keyword is present.
3.2.3. Operand NUME_ORDRE#
◊ NUME_ORDRE
If the keyword MODE_LINE is present then num_ordr indicates the order number of the linear eigenmode from mode_line chosen to initialize the algorithm.
If the keyword MODE_NON_LINE is present then num_order indicates the order number of the periodic solution from resu_in chosen to initialize the algorithm.
3.2.4. Operand DIR_EVOLUTION#
◊ DIR_EVOLUTION
If 1 then we go in the same direction as the first calculated tangent vector.
If -1 then we go in the opposite direction to the first calculated tangent vector.
The value by default is -1.
3.2.5. Operand COEF_AMPL#
◊ COEF_AMPL
ampl is the maximum amplitude given to the periodic solution chosen to initialize the algorithm.
This value is useful when initializing with a linear eigenmode, where the maximum amplitude must be small for the algorithm to converge.
The value by default is 1.
3.3. Keyword CHOC#
◊ CHOC
Under this keyword factor, we enter the configuration and the physical parameters corresponding to the shock nonlinearity that we want to impose.
3.3.1. Operand JEU#
♦ JEU
Play is the distance between the knot and the elastic stop over which this one can come into contact.
3.3.2. Operand RIGI_NOR#
♦ RIGI_NOR
alpha is the stiffness of the elastic stop.
3.3.3. Operand PARA_REGUL#
◊ PARA_REGUL
eta is the parameter for regularizing the law of behavior that governs the relationship between the node and the elastic stop.
The value by default is 0.005.
3.3.4. Operand GROUP_NO#
◊ GROUP_NO
grno is the name of the node group where the nonlinearity is located. Note that grnone must contain only one node.
3.3.5. Operand OBSTACLE#
◊ OBSTACLE
Three possibilities:
“PLAN” which corresponds to a unilateral elastic stop.
“BI_PLAN” which corresponds to a bilateral elastic stop.
“CERCLE” which corresponds to a circular elastic stop.
3.3.6. Operand ORIG_OBST#
◊ ORIG_OBST
This keyword is only available when OBSTACLE = “CERCLE”. It defines the Cartesian coordinates of the center of the circle in the local coordinate system whose origin is the shock node.
3.3.7. Operand NOM_CMP#
◊ NOM_CMP
If OBSTACLE = “PLAN”, or OBSTACLE = “BI_PLAN”, then this keyword indicates on which axis, “DX”, “DY”, or “DZ”, the stop is located.
If OBSTACLE = “CERCLE”, then this keyword indicates in which plane the stop is located.
Oxy plan: (“DX”, “DY”),
Oyz plan: (“DY”, “DZ”),
Oxz Plan: (“DX”, “DZ”)
3.4. Keyword RESOLUTION#
♦ RESOLUTION
Under this keyword factor, we enter the type of algorithm and the associated parameters. The available methods are to be declared under the METHODE operand.
3.4.1. Operand METHODE#
◊ METHODE
Choice of the algorithm for calculating non-linear modes. The only algorithm currently available is” EHMAN “corresponding to the combination of the harmonic balancing method (EH) and the numerical asymptotic method (MAN), as well as a Newton algorithm. The latter makes it possible to ensure the convergence of the algorithm.
3.4.2. Operand NB_HARM_LINE#
♦ NB_HARM_LINE
Hl is the number of harmonics used to develop displacement variables in the form of a Fourier series.
3.4.3. Operand NB_HARM_NONL#
◊ NB_HARM_NONL
Hnl is the number of harmonics used to develop in the form of a Fourier series the functions representative of the laws of behavior that govern the relationship between the node and the elastic stop. The following condition Hnl>Hl must be met.
The default is 201.
3.4.4. Operand NB_BRANCHE#
♦ NB_BRANCHE
nbra is the number of branches calculated by MAN.
3.4.5. Operand NB_PAS_MAN#
♦ NB_PAS_MAN
npas is the discretization step for branches calculated by MAN.
3.4.6. Operand NB_ORDRE_MAN#
◊ NB_ORDRE_MAN
nordre is the number of branch discretizations calculated by MAN.
The value by default is 20.
3.4.7. Operand PREC_MAN#
◊ PREC_MAN
eps_man is the tolerance for algorithm MAN.
The value by default is 1.E-9.
3.4.8. Operand PREC_NEWTON#
◊ PREC_NEWTON
eps_newtest the tolerance of the Newton algorithm.
The value by default is 1.E-8.
3.4.9. Operand ITER_NEWTON_MAXI#
◊ PREC_NEWTON
iter_newtest the maximum number of iterations of the Newton algorithm.
The value by default is 15.
3.4.10. Operand CRIT_ORDR_BIFURCATION#
◊ CRIT_ORDR_BIFURCATION
crit_bif is the number of coefficients in the entire series from MAN. The bifurcation analysis is carried out on these points.
The value by default is 3.
3.4.11. Operand RESI_RELA_BIFURCATION#
◊ RESI_RELA_BIFURCATION
eps_bif is the tolerance of the criterion that makes it possible to decide whether or not a bifurcation is present.
The value by default is 1.E-4.
3.5. Keyword SOLVEUR#
◊ SOLVEUR
The syntax of this keyword common to several commands is described in the document [:external:ref:`U4.50.01 <U4.50.01>`].
3.6. Keyword INFO#
◊ INFO
Integer used to specify the printing level in the file MESSAGE.
If INFO =1, only the calculated branch number is reported.
If INFO =2, the relative error of the last point in the branch is also displayed. As well as the error for each eventual Newton's iteration. And finally, the energy and frequency of the first and last points in the branch.