PSI - Issue 52

Feifei Ren et al. / Procedia Structural Integrity 52 (2024) 730–739 Author name / Structural Integrity Procedia 00 (2023) 000–000

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7

ature variations on the group velocity can be evaluated, allowing for the identification of a temperature range where the group velocity remains stable. This knowledge becomes indispensable for the implementation of compensation techniques and ensuring accurate interpretation of guided wave signals in practical applications. In order to perform the sensitivity analysis of the group velocity, the definition of c g is first redefined as follows:

dc p c 2 p

dc p d ω

dc p d ( fd )

d ω d ξ

d ω c p −

ω c p

) − 1

) − 1

2 p [ c p − ω

] − 1

2 p [ c p − fd

] − 1

c g ( fd ) =

= d ω (

= c

= c

(14)

= d ω ( d

ω

The derivation of the group velocity with respect to temperature is presented in the following Equation:

d 

dc p d ( fd )  dT

p     dc p 2

   

dc p dT 

dc p d ( fd )  −  c p − fd

c 2

c p − fd

fd

2 c p

dT −

dc g dT

( fd , T ) =

(15)

dc p d ( fd ) 

The fractional (or relative) sensitivity of the phase and group velocity is defined by the analytical result divided by the corresponding value Yule et al. (2021):

dc p dT

( fd , T )

(16)

S cp ( fd , T ) =

c p ( fd , T )

dc g dT

( fd , T )

(17)

S cg ( fd , T ) =

c g ( fd , T )

The sensitivity of the dispersion curve to temperature is presented in Figure 3. It demonstrates that within a specific range of f · d , the deviation of the group velocity is not significantly a ff ected by temperature, indicating a constant influence of temperature on the group velocity within this range. This is consistent with the observation in Figure 2 To further investigate the correlation between the group velocity of the A 0 and S 0 modes and temperature variations, a linear regression analysis is conducted to fit the group velocity data in relation to temperature. The relationship is expressed by the following equations:

c p = a cp T + b cp

(18)

c g = a cg T + b cg

(19)