Issue 70

S.K. Shandiz et alii, Frattura ed Integrità Strutturale, 70 (2024) 24-54; DOI: 10.3221/IGF-ESIS.70.02

I

0 0 0 0 0

       

        

0

m

0

0 0 0 0

0

m

0 0

0 0 0

1

 

(A1)

M

T

m

0 0 0

0 0

2

m

0 0 0 0

0

t

0

m

0 0 0 0 0

t

1

        

        

2 c b c b c b c b  2 1 1 2 2 1 1 2 2

 

1 1 c b c b   2 2 c c

0 0 0 0

0 0 0 0

1 1 2 2 c b c b 

c c 

1 2

1

2



 

0 0 0 

c b

c

c c

0  0 0

1 1

1

1 3

 

(A2)

C

T

c b

c

c c

2 2

2

2 4

c  

c

0 0

0 0

t

t

1

2 c





c

c

t

t

t

2

1

2

        

        

2 kb k b kb k b   2



kb

k b

0 0 0 0

0 0 0 0

1 1

2 2

1 1

2 2

1 1

2 2

1 1 kb k b  2 2

k k 





k

k

1

2

1

2



 

0 0 0 

kb

k k k

0  0 0

1 1

1

1

3

 

(A3)

K

T

k b

k

k k

2 2

2

2

4

 

1 k k k k  2 t t k

0 0

0 0



t

t

t

2

1

2

0 0

        

       

3 1 3 1 k z c z k z c z  4 2 4 2 ˆ

 

(A4)

F T

ˆ  

0

2 3 k z c z ˆ t t

2 3  

The parameter z in matrix Eqn. (A4) is as follows:

1 ( , ) ( ) z u x t r x z u x t r x z u x t r x z u x t r x v z u x t r x v z u x t r x v                   1 1 2 2 2 3 3 3 ( , ) ( ), ( , ) ( ) , ( , ) ( ), ( , ) ( ), ˆ ˆ ˆ ( , ) ( ) ,

(A5)

1

1

1

2

2

2

3

3

3

A PPENDIX B: F REQUENCY S PECTRUM he frequency spectrum for other damage cases (A1-A3, B1-B3, C1-C3) are shown as below figures. T

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