PSI - Issue 6

Author name / Structural Integrity Procedia 00 (2017) 000–000

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

210

Fig. 2. Idealized system: protected object – SI device

2.1. Adopted assumptions:

 The upper plane is fixed  The lower plane has mass and moments of inertia (PS):      z y x I I I ,  X, Y, Z – is the fixed coordinate system centered at the point  X’, Y’, Z’ – is a movable coordinate system centered at the point  A’ – projection of A when t=0  B – current position of A’ when z ≠ 0  The bar AB at the node A has a spring of rigidity k

 Displacements of the center of mass C on the Cartesian coordinates X, Y, Z are U c , V c , W c  Angles of rotation of the PS (bottom plane) relatively to the coordinates X, Y, Z are φ x , φ y , φ z  Internal forces and moments relatively to C of each bearing are

( , , x y z i R R R R 

)

and

( R i M M M M  

)

, , i c y ic z i c x

2.2. First group of equations. Equations of motion Taking into account the motion of center of mass as motion of point C relatively mobile system of coordinates of XYZ according to formulas of relative motion:

r e c         a

  

(2)

Where a  

– absolute acceleration of point C , r  

– relative acceleration, e  

– acceleration in translation, c   –

Coriolis acceleration.