PSI - Issue 72

Victor Rizov / Procedia Structural Integrity 72 (2025) 128–134

131

i 1 1 1  i i z E E   z

  i



 

,

(14)

E E

z z 

 

i 1 1

i

i









where

 i i E E E   ,  i

(15)

1 1 1 1    i i z z z .

(16)

The quantities involved in Eqs. (5) and (6) are determined by an approach similar to that defined by Eqs. (7), (8), (9), (10) and (11). The total value of J under load, F a , is estimated by   q Fq J J F 2  (17) where J ( F q ) is determined by employing Eqs. (7), (8), (9), (10), (11), (12) and (13) after replacement of P with F q . The method for exploring structures under harmonic load reported by Malenov (1993) is applied in the current article. On this base, we obtain Eq. (18) for J dn under harmonic load.

(18)

dn J k J 

dn Fq

where

1

,

(19)

dn k



2   

  



1





P

30 n 

,

(20)

 

1

.

(21)





P

m 

P

Here, n is the number of revolutions of the motor per minute, δ is the displacement of point, H 3 , induced by the motor weight (Fig. 1). Equation (22) for δ is written by applying the integrals of Maxwell-Mohr (Malenov (1993)).

C 2 P

   

(22)

M dx i i

,

1 

where κ i is the curvature, M i is the bending moment from the virtual loading, C is the spring constant (the beam is supported by springs (Fig. 1)). The total J is obtained by Eq. (23).

st dn J J J   .

(23)

In fact, Equation (23) estimates J max . The minimum J is estimated by Eq. (24).