Issue 49

A. Kumar et alii, Frattura ed Integrità Strutturale, 49 (2019) 515-525; DOI: 10.3221/IGF-ESIS.49.48

estimated with the concept of “Beam on Elastic Foundation” [4], such that the effect of attachment of waveguide on the ALIP body is negligible beyond this region. This region is represented approximately by a circle whose radius is equal to 1/β. 1/β is the distance beyond the application of load after which factors like deflection, slope, bending moment, etc. are negligible [4].

2 2 2 3(1 ) r h  





(2)

4

where, ν

= poisson ratio

r

= radius of curvature

h = thickness Substituting ν = 0.3,

1.285 rh

  For r= 0.189 m and h=0.003 m, β = 54m -1 = 0.054 mm -1 Hence, 1/β = 18.53 mm This is illustrated with the help of Fig. 6.

Figure 6 : Isometric view of modeled ALIP body and waveguide attached with weld

D YNAMIC ANALYSIS CARRIED ON MODEL

T

he vibration in the ALIP sets the waveguide also into vibration and the welded region experiences maximum alternating stress cycles. To estimate the stresses under vibration, first of all, natural frequency of the waveguide has been estimated. Natural frequency of waveguide The waveguide consists of different cross-sections and hence, its natural frequency needs to be estimated using FEM. In order to confirm the correctness of the modeling exercise using FEM, the natural frequency of a simple cantilever of 20 mm diameter and length of 300 mm was calculated using analytical formula as well as using FEM analysis. The natural frequency of a cantilever beam is given by the formula 3 [5]:

E I 

2   ( ) l 

n 

(3)

n

4





l

where, ω

= Angular velocity/ frequency

n

= Mode number

E

= Young’s modulus of the material = Length of the cantilever

l

519