PSI - Issue 33

O. Pozhylenkov et al. / Procedia Structural Integrity 33 (2021) 385–390 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

389

5

1 2 + 12 0 − 2 + 1 22 2 − 1 0 1 2 + 12 0 − 2 + 1 22 2 1 0 2 2 + 22 0 − 2 + 1 22 2 − 2 0 2 2 + 22 0 − 2 + 1 22 2 2 0

0 ( ) = 1 2 1 ( ) = − − 1 2 2 ( ) = 2 2 3 ( ) = − − 2 2

1 ∗ ( 12 − 22 ) ( 1 ∗ ( 12 − 22 ) ( 2 ∗ ( 22 − 12 ) ( 2 ∗ ( 22 − 12 ) (

1 0 1 2 − 2 − 0 2 + 1 12 2 ) − 1 0 1 2 − 2 − 0 2 + 1 12 2 ) 2 0 2 2 − 2 − 0 2 + 1 12 2 ) − 2 0 2 2 − 2 − 0 2 + 1 12 2 )

(11)

The solution of the homogeneous vector problem was constructed: ( ) = 1 + 1 0 ( 0 ( ) + 1 ( )) 1 + 1 + 1 0 ( 2 ( ) + 3 ( )) 2 , = 1,2 (12) The matrices , = 1,2, = 1,2 were found from the linear algebraic system after the boundary conditions satisfying. Solution of the stated problem in the transforms domain:

12 + 12 0 − 2 + 2 2 2 ) ( 1 − − 1 ) 11 − 1 0 ( 1 + − 1 ) 21 2 1 ( 1 2 − 2 2 ) ] + 22 + 22 0 − 2 + 2 2 2 ) ( 2 − − 2 ) 12 − 2 0 ( 2 + − 2 ) 22 2 2 ( 2 2 − 1 2 ) ] 1 0 ( 1 − − 1 ) 11 + ( 12 − 2 − 2 0 + 2 1 2 ) ( 1 + − 1 ) 21 2 1 ( 1 2 − 2 2 ) ] + 2 0 ( 2 − − 2 ) 12 + ( 22 − 2 − 2 0 + 2 1 2 ) ( 2 + − 2 ) 22 2 2 ( 22 − 12 ) ]

( ) = 1 + 1 0 [ ( + 1 + 1 0 [ ( ( ) = 1 + 1 0 [

+ 1 + 1 0 [

{

(13)