PSI - Issue 6

Yu. L. Rutman et al. / Procedia Structural Integrity 6 (2017) 208–215 Author name / Structural Integrity Procedia 00 (2017) 000–000

212

(8)

2 mu R mv P     

t ma x

( )

   

C

x

x

x

1

(9)

2 mv R mu P     

ma t y

( )

   

C

y

z

y

y

1

(10)

1 z C        mw R mg P z z

t ma

( )

z

(11)

 

I M M I t         

z z

c z

pz

z

z

2

(12)

c x x x I M M

    

2 

px

x

(13)

c y y y I M M

    

2 

py

y

Where

( iC C M M M M M    , cz cy cx

  iz z R R ;

  ix x R R ;

  iy y R R ;

)

i iC BC r R M   BC r – vector BC

Initial conditions:   0 v u  

  0   C C w 

  0 0 

C

  0   C C v u

  0 0

nk mg

 

w

 0

C

where n is the number of bearings of the SIS. 2.3. Second group of equations

The first group of equations describes the relationship between the PS generalized coordinates and the displacements of the PS attachment points to pendulum devices or SI bearings. Wherein, PS (superstructure) is assumed to be an absolutely rigid body, i.e. its dynamics is described by six coordinates. The displacement of center of mass C : U c , V c , W c . The coordinates of node B on the fixed coordinate system: when 0  t : node B  node A     0 , , X Y Z A A   when 0  t : node B    0 , cos sin , sin cos w Z Y v X Y u X C A C A A C A                  ; i A A X X X 0    ;

i A A Y Y Y 0    ;

0 Z Z A  