PSI - Issue 83

Victor Rizov et al. / Procedia Structural Integrity 83 (2026) 85–94

88



 h H H dl 

2 h

  

  

gr

H H

z

 



.

(6)

1

gr

gr H - value of H on the upper surface of the beam,

dl H - value of H on the lower

The notations in Eq. (6) are:

surface of the beam,  - parameter. Let's consider any point on the beam, for example, point R located at a distance, 1 x , from the left end of the beam (Fig. 1). The rotation of the beam around s induces only normal acceleration, Rn a , of point, R , since the angular acceleration of the beam is zero (this follows from the law of rotation in Eq. (1)). ) ( 1 2 l x a Rn    , (7)

where

x l   1 0 .

(8)

The notations used in Eqs. (8) and (7) are:  - angular velocity, l - length of the beam. The angular velocity is

dt d 

 

.

(9)

Thus, from Eq. (1) we have    .

(10)

Therefore, normal acceleration of point, R , is ) ( 1 2 l x a Rn    .

(11)

The acceleration, Rs a , of point, R , due to the motion of the beam up the axis, s , is found as given below.

2 dt d OL 2

a Rs 

3

.

(12)

The combination of Eqs. (2) and (12) leads to  2  Rs a .

(13)

The two accelerations of point, R , are shown in Fig. 1. The inertia terms, Rn q and Rs q , in point, R , are

Rn Rn q ma  , Rs Rs q ma  ,

(14) (15)