Issue 60

C. O. Bulut et al., Frattura ed Integrità Strutturale, 60 (2022) 114-133; DOI: 10.3221/IGF-ESIS.60.09

L

L

L

1

2

v

v

v

1

1

1

 

  





  





  





 0







     t d



     t d



     t d

N t

R

R

R

sin

sin

sin

 

 

 

(19)







i

i

i

i

i

i

i

1

2

3

 i





i L

i L

1

2

v

v

The formulation can be written according to the desired number of cracks in the structure similarly. In this study, triple cracked beam has been analyzed and   i N t has been determined accordingly. After some simplifications, the following formulation is obtained. For the first beam segment,  1 t L v

L v

1

1

 

         sin[ ] t d

 0



N t

R

(20)

i

i

i

1

 i

  1 2 L t L v v

For the second beam segment,

L

L

1

2

v

v

1

1

 

 





 





 0





      sin[ ] t d

     sin[ ] t d

N t

R

R

(21)

i

i

i

i

i

1

2

 i



i L v

1

  3 2 L t L v v

For the third beam segment,

L

L

L

3

1

2

v

v

v

1

1

1

 

 





  





  





 0







      sin[ ] t d

     t d



     t d

N t

R

R

R

sin

sin

 

 

(22)





i

i

i

i

i

i

i

1

2

3

 i





i L

i L

1

2

v

v

  3 L t L v v

For the fourth beam segment,

L

L

1

2

v

v

1

1

 

  





  





 0





     t d



     t d



N t

R

R

sin

sin

 

 





i

i

i

i

i

1

2

 i



i L v

1

(23)

L

L

3

v

v

1

1

  





  











     t d



     t d

R

R

sin

sin

 

 





i

i

i

i

3

4





i L

i L

2

3

v

v

Duhamel integral method has been applied to get the solution of Eqn. (19) and Eqn. (23). In MATLAB program, a code has been prepared for this purpose. Different numerical damage scenarios have been exemplified using MATLAB code.

E XPERIMENTAL STUDY he dynamic investigation of damaged structures under transit loading has been carried out by many researchers theoretically and using various finite elements software. These studies do not reflect a real modeling; instead they provide an approximation to the real models. In order to overcome this limitation, an experimental set-up has been established and the laboratory tests have been executed to validate the results of the numerical and finite elements T

120