Manual pages | Cast3M

$$$$ VIBC     NOTICE  BP208322  12/10/03    21:15:34     7517           
                                             DATE     12/10/03
                                             
  Operateur VIBC                           Voir aussi :
    --------------   
    --------------------
    | 1ere possibilite |
    --------------------
    
      BAS2 = VIBC 'MODES' MASS1 RIG1 (AMOR1) (BAS1);



    Description :
    _____________

    The VIBC operator searches for the complex eigenvalues and eigen
 vectors of the general equation of motion :
                         M X'' + C X' + K X = 0
 where the mass, stiffness and damping have previously been expressed
 relatively to a real eigen modes basis.
 The algorithm used is the QZ.
 
    Contents :
    __________

    MASS1        : mass matrix, expressed relatively to a real eigen
                   modes basis. (RIGIDITE type, MASSE subtype)

    RIG1         : stiffness matrix, expressed relatively to a real 
                   eigen modes basis. (RIGIDITE type, RIGIDITE subtype)

    AMOR1        : damping matrix, expressed relatively to a real eigen 
                   modes basis. (RIGIDITE type, AMORTISSEMENT subtype)

   These three matrices must be expressed :
       - on a geometrical support made of one element composed of  
         POINT_REPERE points
       - with the components : ALFA
       - with the dual components : FALF
   If matrix subtypes correspond to MASSE, RIGIDITE and AMORTISSEMENT 
 (in case it is specified), matrices are sorted and so order is 
unimportant. Else, they are processed in the order of their input.

    BAS1         : real eigen modes basis which above matrices are 
                   relatively expressed to (TABLE type, BASEMODA 
                   subtype)

    BAS2         : generated object containing the complex eigen 
                   values and eigen modes (TABLE type, BASEMODA subtype)

REMARK :   BAS2 structure (TABLE type object)
_______     

           
           BAS2.'SOUSTYPE' = 'BASE_MODALE'
           BAS2.'MODES' = TAB2  
           BAS2.'CONVERGENCE' = LOGIQ1  

           TAB2.'SOUSTYPE' = 'BASE_DE_MODES'
           TAB2.'MAILLAGE' = MAIL1
           TAB2.IMOD = TAB3 (objet de type TABLE)

           TAB3.'SOUSTYPE' = 'MODE_COMPLEXE'
           TAB3.'POINT_REPERE' = PT1
           TAB3.'NUMERO_MODE' = NUMOD
           TAB3.'FREQUENCE_REELLE' = FLOT1
           TAB3.'FREQUENCE_IMAGINAIRE' = FLOT2
           TAB3.'DEFORMEE_MODALE_REELLE' = CH1
           TAB3.'DEFORMEE_MODALE_IMAGINAIRE' = CH2


      MAIL1 : modes geometrical support (MAILLAGE type)

      IMOD  : number ranging from 1 to the number of calculated modes
              (ENTIER)

      PT1   : point used to identify the mode (POINT)

      NUMOD : numero du mode (ENTIER)

      FLOT1 : real part of the eigen frequency value (FLOTTANT)
      FLOT2 : imaginary part of the eigen frequency value (FLOTTANT)

      CH1   : real part of the eigen vector (CHPOINT)
      CH2   : imaginary part of the eigen vector (CHPOINT)
      
      LOGIQ1 : logical indicating if VIBC converged


    --------------------
    | 2eme possibilite |
    --------------------

    Option 'BALOU'

      CHPO1 CHPO2 = VIBC 'BALOU' MASS1 RIG1 (AMOR1) BAS1 FPROJ OMEGA ;


    Option 'BALOU' :

    Description :
    _____________

          BEWARE ! The 'BALOU' option of the VIBC operator can only be
    use with the "ROTOR sous CASTEM 2000" code. Then, it allows to search
    the complex solutions of the general equation of motion in the case
    of an mass unbalance excitation F :

                        M X'' + C X' + K X = F     (1)

    Considering the expression of F is :
           F = Fs * SIN(OMEGA*t) + Fc * COS(OMEGA*t) 
    solutions of this equation are sought as :
           X = Xs * SIN(OMEGA*t) + Xc * COS(OMEGA*t)
 
    So, equation (1) can be written as :

                 | K-OMEGA^2  -OMEGA*C | | Xs |   | Fs |
                 |                     | |    | = |    |
                 |  OMEGA*C  K-OMEGA^2 | | Xc |   | Fc |

    and be solved thanks to the operator RESOU (solve KU=F)


    Contents :
    __________

    MASS1        : mass matrix, expressed relatively to a real eigen
                   modes basis. (RIGIDITE type, MASSE subtype)

    RIG1         : stiffness matrix, expressed relatively to a real 
                   eigen modes basis. (RIGIDITE type, RIGIDITE subtype)

    AMOR1        : damping matrix, expressed relatively to a real eigen 
                   modes basis. (RIGIDITE type, AMORTISSEMENT subtype)

    These three matrices must be expressed :
       - on a geometrical support made of one element composed of  
         POINT_REPERE points
       - with the components : ALFA
       - with the dual components : FALF

    BAS1         : real eigen modes basis which above matrices are 
                   relatively expressed to (TABLE type, BASEMODA 
                   subtype)

    FPROJ        : mass unbalance force, expressed relatively to a real
                   eigen modes basis. (CHAMPOIN type, of components ALFA
                   and dual components FALF)  
              
    The FPROJ vector must be obtain by the following way :
      - separation from components SIN(OMEGA*t) and COS(OMEGA*t) in
        two CHAMPOIN
      - projection of those two CHAMPOIN on the N real eigen modes basis
        BAS1 (PJBA operator)
      - combination of those two CHAMPOIN to obtain a 2*N vector

    OMEGA        : whirl speed of the rotor, in rad/s

    CHPO1 CHPO2  : generated object containing the values of the
                   displacment vectors 
                   CHPO1 deals with COS(OMEGA*t) component  
                    (real component)
                   CHPO2 deals with SIN(OMEGA*t) component
                    (imaginary component)
                   Those CHAMPOIN are expressed in the physical mesh of
                   the real eigen modes basis BAS1

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