PSI - Issue 6

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

211

Relative acceleration is defined by accelerations of relative coordinates of a point C :

r   

( , , ) u v w   

Acceleration in translation is defined by

) r                   (3) Where   – vector describing angular acceleration of the rotational movement of ground. (Yin et al., 2016)   – vector describing the angular speed of the rotational movement of ground. ( oc oc e o r

( o a a a    , , x y z

- vector describing linear accelerations of mobile system of coordinates (ground).

)

Components of this vector are set by accelerograms.

Coriolis's acceleration is defined by a formula:



V       2

(4)

c

r

( , , ) V u v w     

– the relative speed of a point of C .

Where

Vector of absolute angular acceleration of PS:

      a

  

(5)

Where    – a vector of accelerations of relative angles of rotation of PS concerning axes of X,Y,Z . In a formula (5) angles are considered as small. At this assumption of the equation of the movement PS have an appearance: ( ) 1 m R P V a          (6)

      p a R I M M 

(7)

( ) 2   

Where

R  - vector describing summarized force from all rods; R M  - vector of the summarized moment from forces in rods concerning the center of masses C ;

 ,

p M  - summarized force and moment from plastic dampers (hysteresis devices);

P

( ), 1 V 

 ( ) 2    - summarized forces and moment arising from viscous damping. The first group of equations describes the dynamics of the PS under the above-mentioned forces and external kinematic effects. For the pendulum type SIS in the absence of rotational excitations and absolutely rigid devices these equations permanently transform into the famous equations of oscillations of the physical pendulum. In a formula (3) as a result of small two last composed it is possible to neglect. Then, substituting formulas (2)-(5) in (7), (8) after some transformations we receive: