PSI - Issue 33

4

Victor Rizov et al. / Procedia Structural Integrity 33 (2021) 416–427 Author name / Structural Integrity Procedia 00 (2019) 000–000

419

          

     

      3

2 h z h



1 sin

   UP

 

,

(8)

2

where

3 h z h   

.

(9)

2

2

Fig. 2. Viscoelastic model.

UP E 1

UP E 2

1 E

2 E

UP 



In formulae (6), (7) and (8),

,

and

are, respectively, the values of

,

and

at the upper

3 z

 



surface of the beam,

is the vertical centroidal axis of the beam. The material properties, ,

and , control

1 E

2 E



the distributions, respectively, of

,

and

along the thickness of the beam.

UP E 1

UP E 2

UP 

The distributions of

,

and

along the length of the beam are expressed as

  

     

  

 l l x 3



1

sin

 E E UP 1





,

(10)

1

UPF

F

2

1

  

     

  

 l l x 3



1

sin

 E E UP 2





,

(11)

2

UPF

F

2

1

  

     

  

 l l x 3



1

sin











,

(12)

UP

UPF

F

2

1

where