PSI - Issue 82

Victor Rizov et al. / Procedia Structural Integrity 82 (2026) 246–252 V. Rizov/ Structural Integrity Procedia 00 (2026) 000–000

251

6

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The dependency of the energy dissipation on

at various

ratios can be observed in Fig. 3. The

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curves in Fig. 3 indicate that increase of that the dissipated energy increases when

induces increase of the dissipated energy in the beam. It is evident also

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ratio increases (Fig. 3).

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The influence of the velocity,

, of the angle of twist of the beam free end on the dissipated energy is studied

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too. The dependency of the dissipated energy on

at three

ratios is illustrated in Fig. 4. One can

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observe in Fig. 4 that when the velocity,

, increases, the dissipated energy also increases.

$ % = " ! # # %

#"!

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Fig. 4. The non-dimensional dissipated energy presented as a function of

(curve 1 – at

, curve 2 - at

$ # = " ! # # #

#"!

$ % = " ! # # %

#"!

and curve 3 – at

).

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The increase of

also generates increase of the dissipated energy (Fig. 4).

4. Conclusions The influence of time-dependent coefficient of viscosity on the dissipated energy in multilayered functionally graded viscoelastic beam structure under torsion is analyzed theoretically. The rheological model of Maxwell is used for dealing with viscoelastic behaviour of the beam under consideration. The coefficient of viscosity of the viscous component of the model depends exponentially on time. The stress-strain-time relation of the rheological model is derived and applied when analyzing the dissipated energy in the beam structure. The analysis clarifies the influence of time-dependent coefficient of viscosity and the material gradient on the dissipated energy in the beam. The time-