Examples
========




Example 1
-----------

**Comparison of the two methods** **STURMet** **** APMsur the GEP standard of**** SDLD02a ** (for STURMles terminals are mentioned in frequency). In the first calculation, the aim is to count the number of modes contained in the frequency band :math:`\mathrm{[}0;5\mathrm{]}` with the usual method: STURM. In the second, we do the same thing with method APM, but with the disk centered at the origin (centre=0+0j) and with radius= :math:`{(2\pi .5)}^{2}` (because there is no unit change with APM). Both results are shown in file MESSAGE.

f1=5.0

nbmod01 = **INFO_MODE** (MATR_RIGI = MATASSR, MATR_MASS =, = MATASSM, TYPE_MODE =' **DYNAMIQUE** ',

 FREQ =( 0. , f1), COMPTAGE =_F (METHODE =' **STURM** '),)

w1= (2*pi*f1) **2

nbmod11 = **INFO_MODE** (MATR_RIGI = MATASSR, MATR_MASS =, = MATASSM, TYPE_MODE =' **MODE_COMPLEXE** ',

             TYPE_CONTOUR =' CERCLE ', CENTRE_CONTOUR =0.0+0.0j,

                 RAYON_CONTOUR =w1, COMPTAGE =_F (METHODE =' **APM** '),)

With INFO =1, this causes the following displays in file MESSAGE:

--------------------------------------------------------

VERIFICATION OF SPECTRE OF FREQUENCES (**METHODE OF STURM**)

**PAS OF FREQUENCE** DANS THE BANDE (0.000E+00, 5.000E+00)

...

(METHODE APM) POUR LES 3 NIVEAUX FROM DISCRETISATION SUIVANTS

--- 20 --- 40 --- 80 ---

NOMBRE OF VALEURS PROPRES DETECTEES

--- 0 --- 0 --- 0 --- 0 ---

(METHODE APM) CONVERGENCE OF THE HEURISTIQUE

--------------------------------------------------------

VERIFICATION FROM SPECTRE TO FREQUENCE (**METHODE FROM ARGUMENT PRINCIPAL**)

**PAS OF FREQUENCE** DANS THE DISQUE CENTRE EN (0.000E+00, 0.000E+00)

AND RAYON 9.870E+02

Here, Sturm's method required only two factorizations. Method APM converged immediately on the first iteration. But this one required :math:`20+40+80\mathrm{=}140` factorizations. Counting eigenvalues in the complex plan comes at a price (which we can't currently reduce)!

The number of natural frequencies (0 in this case) as well as the search criteria are saved in a table. Printing, by IMPR_TABLE, the concepts NBMOD01et NBMOD11produits by INFO_MODE in the previous example shows the following composition:

**nbmod01**

FREQ_MIN FREQ_MAX NB_MODE

0.00000E+00 5.00000E+00 0

...

**nbmod11**

CENTRE_R CENTRE_I RAYON NB_MODE

0.00000E+00 0.00000E+00 9.86960E+02 0

When INFO_MODE is called with the TYPE_MODE =' MODE_FLAMB 'option, the tables produced contain three columns: NB_MODE (the number of eigenvalues) as well as CHAR_CRIT_MIN and CHAR_CRIT_MAX, the search criteria for dynamic problems with linear buckling.




Example #2
-----------

**Count for QEP of** **SDLL123a .** This time, only the APM method is legal. Count the number of modes contained in the circle centered at the origin (:math:`\mathit{centre}\mathrm{=}0+\mathrm{0j}`) and whose radius is :math:`\mathit{rayon}\mathrm{=}124\mathrm{\times }2\pi`.

f1=124.*2.*pi

nbmod4= **INFO_MODE** (MATR_RIGI = RIGIDITE, MATR_MASS =, = MASSE, MATR_C = GYOM, TYPE_MODE =' **MODE_COMPLEXE** ',

 TYPE_CONTOUR =' CERCLE ', CENTRE_CONTOUR =0.0+0.0j,

             RAYON_CONTOUR =f1, COMPTAGE =_F (METHODE =' **APM** ',),)

In INFO =1 this causes the following displays in file MESSAGE:

(METHODE APM) POUR LES 3 NIVEAUX FROM DISCRETISATION SUIVANTS

--- 20 --- 40 --- 80 ---

NOMBRE OF VALEURS PROPRES DETECTEES

--- 4 --- 4 --- 4 --- 4 ---

(METHODE APM) CONVERGENCE OF THE HEURISTIQUE

--------------------------------------------------------

VERIFICATION FROM SPECTRE TO FREQUENCE (**METHODE FROM ARGUMENT PRINCIPAL**)

**THE NOMBRE OF FREQUENCES** DANS THE DISQUE CENTRE EN (0.000E+00, 0.000E+00)

AND RAYON 7.791E+02 EST **4**

And the printout of the table produced (nbmod4) by IMPR_TABLE gives:

CENTRE_R CENTRE_I RAYON NB_MODE

0.00000E+00 0.00000E+00 7.79115E+02 4