PSI - Issue 6

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

213



 0

r

u X

Y

0 , X v X i C 

Y

, Y w Z 

cos

sin

sin

cos

 

























Finally, we obtain:

AB C

i

i

i

i

i

C

0

0

0

0

0



 sin ,0 

r

X

Y

Y

X

cos

, sin 

cos



















BC

i

i

i

i

0

0

0

0

  i C R R ;

  iC C M M ;

i iC BC r R M  

i

j

k

M

X

Y

Y

X

cos

sin

cos

sin

0

























iC

i

i

i

i

0

0

0

0

X R

R

R

ix

iy

iz

 i Y







R j X  

Y

 ix iz R

cos

sin

cos

sin

   



























i

i

iz

i

i

0

0

0

0











k X

Y

iy R Y 

X

R

cos

sin

cos

sin

























i

i

i

i

0

0

0

0

2.4. Third group of equations

The second group of equations describes the relationship between the devices internal forces (or bearings internal forces) and the PS attachment points displacements. The internal force R i in the bar AB is determined in the following way:   AB AA i r r r      , i i k r R    ,   AB AA i i r k r        

r r

AB AB

AB AB

r R R r

  B A B A B X X Y Y Z , ,    , r AA   The length of the rod of the bearing when t ≠ 0 is AB r   0 0,0, Z

2 2 2 iz iy r

r r l   

i

ix

The deformation of the rod is 0 l Z l i i     The reaction components are

r

i iy

i ix

i iz

i l R k l r     l R k l r     The total reactions relatively to the center of mass are:   i C R R ;   ix x R R ;   iy y R R ;   iz z R R ix , i iy l R k l     , i iz

The moment of one reaction relatively to C is:

i iC BC r R M   The total moment of all bearing reactions, constituting the relatively to C is:   iC C M M