PSI - Issue 33

K. Mysov et al. / Procedia Structural Integrity 33 (2021) 365–370 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

366

2

1. Main text

Nomenclature a

radius at which cone’s bottom face is loca ted

b radius at which cone’s upper face is located 1 1 , a b radiuses between which crack is located  cone’s opening angle  crack’s opening angle M torque applied to overlay J overlay’s known inertia moment  steady state frequency G cone’s shear modulus  cone’s density  is the unknown rotation angle

Fig. 1. Geometry of the problem.

, , a r b         −   −  

The twice truncated elastic cone is considered in the spherical coordinate system , a r b        = −   (Fig. 1). The problem is stated for the case of steady state oscillations, thus ( ) , , , f r t   with a cone-shaped crack 1 1 ,

( f r  t

)

i

e

, ,

takes place for all

=

 

functions.

, , r a       = −   −   is in adhesion with an absolutely rigid overlay through which

Bottom spherical face

the torsion dynamic moment impacts the cone:

( ) r a w lF   = = ,

(1.1)

here ( ) , w r u r    = is tangential displacement, l b a = − , ( ) F  is an arbitrary continuous function. The latter should be found from the movement equation of the overlay ( ) ,