PSI - Issue 58

Victor Rizov et al. / Procedia Structural Integrity 58 (2024) 137–143 V. Rizov / Structural Integrity Procedia 00 (2019) 000–000

141

5

A    ( )

N

dA

,

(17)

where N is the axial force (here,

0  N ), A is the cross-section area.

The unit dissipation energy, 0 u , is given by

t



 dt

  0

u

 

     ,

(18)

0

nld

 

  and   are the stress and strain in the linear dashpot, respectively. For the dissipated energy, U , in the beam we get

where

U u dV V 0 ( )   ,

(19)

where V is the volume of the beam (the integral in (19) is solved by the MatLab software). 3. Numerical results The numerical results are derived with purpose to investigate the change of the dissipated energy due to variation of the properties of the model, the loading conditions and the beam geometry.

0.2

0.5

0.8

3  

3  

3  

1  (curve 1 – at

Fig. 3. Dissipated energy versus parameter,

, curve 2 – at

and curve 3 – at

).

/200  

0.400  l m,

0.006  b m,

0.010  h m,



When deriving the numerical results, we assume that

0

and 0.004   . The results are graphically presented below (refer to Fig. 3, Fig. 4 and Fig. 5). First, we investigate how the dissipated energy in the beam is influenced by parameters, 1  and 3  . The variation of the dissipated energy is shown in Fig. 3. The rise of parameter, 1  , induces a gradual growth of the dissipated energy (Fig. 3). The influence of parameter, 3  , over the dissipated energy is similar to this of 1  as indicated by Fig. 3. The curves shown in Fig. 4 illustrate the influence which parameter, 4  , has over the dissipated energy for three