PSI - Issue 83

Victor Rizov et al. / Procedia Structural Integrity 83 (2026) 95–104

98

d   

r



.

(7)

dt

Determining the inertial load in the frame-like component requires first deriving the acceleration. The accelerations in bar,

1 2 DD , of the frame-like component are treated first. Consider any point, 1 L , on bar,

1 L a 

1 2 DD . The acceleration,

, of 1 L is written in Eq. (8).

5 L D a a a      1

,

(8)

 1

L

where  1 L a is the normal acceleration (the tangential acceleration is zero since the angular acceleration of the frame-like component is zero). The normal acceleration is derived in conventional way:

2 

1 a L

D L

 

,

(9)

5 1

5 1 D L is the distance between points, 5 D and 1 L . Using Eq. (7), formula (9) yields the form

where

5 1 2 1 a r D L L   .

(10)

The three components of the acceleration of point, 1 L , are sketched in Fig. 1. We move on to determining the acceleration of any point on the bar,

2 L a 

2 4 D D . The acceleration,

, of point,

2 L , can be written in the following form:

5 L D a a a      2

,

(11)

 2

L

 2 L a is the normal acceleration. The latter is

where

2 

2 a L

D L

 

.

(12)

5 2

With Eq. (7), Eq. (12) reduces to

5 2 2 2 a r D L L   .

(13)

The accelerations involved in Eq. (11) are sketched in point, 2 L , in Fig. 1. Finally, the acceleration, 3 L a 

, at any point, 3 L , on the bar, 4 5 D D , is extracted by making use of Eq. (14), i.e.

5 L D a a a      3

.

(14)

 3

L

 3 L a , is related to the angular velocity by

The normal acceleration,

5 3 2 3 a r D L L   .

(15)