PSI - Issue 44

Guglielmo Amendola et al. / Procedia Structural Integrity 44 (2023) 1427–1434 Guglielmo Amendola et al./ Structural Integrity Procedia 00 (2022) 000 – 000

1430

4

equations becomes:      +

  7

   

2 g        

 

1 1

1 1

2 g

  

  

5



 

 

 

 

 

 

 

  7 

    + +             

1

p

+

+

+

+

2

sgn

                 

 







7

6

5

4

3

2

1

7

7

6

7

8

p

p

p

p

p

d

pi

2

2

R

a

R





1

i



1

0

1

p d

a d



  

( ) sgn 

  

1 9 a  

  

 

5



 

 

 

( )           +

  =

(

)







6

7

8

pi

a

  





1

i



0

  7

   

   

 

1 1

2 g

 

 

 

 

 

 

 

  7 

1

p

+

+

+

+

+

 

  

sgn

            

 





6

5

4

3

2

1

7

sp

p

p

p

p

p

2

R

a



1

0

p d

  6

  



 

1 2

1 1

  

 

    6

  6 ( )       sp

2

p

sgn

g



 



sp

2

R

a



 

 

2

0

p d

   

   

 

  

  

( ) sgn 

 

  

1 1

2 g

2 g

1 9 a  

  

  

5

5

  

  





    + +             

 

 

 

     8 sa

( )           +









6

7

8

6

7

8

pi

pi

2

a

R



 





1

1

i

i





0

1

a d

  8

 

 

  

1 2

1 1

  

 

 

  8 ( )      sa

2

a

sgn

g



 

 



8

sa

2

R

a



 

2

0

a d

p p   2

p 

 

 

 

 

 

  5 5          5 2 d d p p p   5

    5 p

5 5

 

 

2

              







5

5

4

3

2

1

p

p

p

p

p

p

2  d

d

  6

  



 

1 2

1 1

  

 

    6

  6      = 5 ( ) p

2

p

sgn

g

 





sp

2

R

a



 

 

2

0

p d

2 p 

2 p 

p 

p 

 

 

 

 

 

 

 

 

5

4

5

4

5 5                         5 4 4 4 5 5 4 4 4 2 2 ( ) p p p p p p p p p p p d = 2

 

 

2

           



4

4

3

2

1

p

p

p

p

p

d

d

d

2 p 

2 p

                               =       4 3 4 3 4 4 4 3 3 3 4 4 3 3 3 2 2 2 2 ( ) p  p  p p p p p p p p p p p d d d d

 

 

 

         

  



3

3

2

1

p

p

p

p

2 p

2 p

 

 

 

 

          

3

2

3

2

p

p

=



2

2

( )

  3 3                            2 2                      = 3 2 2 2 3 3 2 2 2 2 2 2 2 p p p p p p p p p p p d d d d p p d        1 2 1 1 1 1 2 2 1 1 1 2 2 2 ( ) p p p p p p p p p p p



2

2

1

p

p

p

  1 1          2 2 2 p p p p

d

d

d

(5 a,b,c,d,e,f,g,h)

with the following non-dimensional parameters:

m



pi

pi

,

,

,

 

   

 



i 

i 

pi

sa

sa



m

d 

d

  7

  9

g

 

g

 

(6 a,b,c,d,e,f,g,h,i)

  9 

  7    1 p 

1

p

1

a

,

,

,

    

1

sp

sp

a





a

a

0

0

  6

  8

g

 

g

 

  8    2 a 

  6    2 p 

2

p

2

a

,

,

 



pi



a

a

pi

0

0

In the end, the maximum response in terms of non-dimensional parameters is evaluated as:

2

2

2

u

x





(

)

x x 



,max

,max

d

d

d

d

6 7 max

d

,

=

,









u

x

a

a

a

d

d

(7 a,b,c)

0

0

0

5

   

   

2



x



i

d

2

u



1

i



,max

p

d

max







u

a

a

p

0

0

3. Parametric analysis by varying the main structural properties In the following, the outcomes of the performed parametric analysis for the bridge isolated with DCFP bearings are provided in terms of non-dimensional parameters.