PSI - Issue 82

Victor Rizov et al. / Procedia Structural Integrity 82 (2026) 246–252 V. Rizov/ Structural Integrity Procedia 00 (2026) 000–000

248

3

, ! " " " ! ! " ! = ! ! ! # !" ! =

,

(4) (5) (6)

!

!

! ! " ! " " =

,

!

"

!

"

where

and

are the shear strains in the spring and in the viscous component,

and

are shear stresses

! "

! "

! !

! !

" !

in the spring and the viscous component, yield the following differential equation: , "! A # A "! # # # 'B A '& B ! ! ! + = #

is the first derivative with respect to time. Dependencies (2) – (6)

! !

(7)

#

#

#

!

which is solved with respect to

. The result is

! "

(

) ! ! ! #" !

# &B

" #!

" B &' A " "

" B &'

" " "

A

" "

A

"

=

!

.

(8)

B

"

"

"

By using Eq. (4) and Eq. (8), one obtains . ( ) = $ $ ! #" ! " " " " A # &B #! " B &' A A ( )

% $ & '

! " #

(9)

"

"

"

From Eq. (6) it follows that Eq. (9) can be applied also for obtaining of .

! !

Fig. 2. Multilayered vscoelastic beam of circular cross-section.