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2 Rizov Victor

2 2024

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Common Solution of the Energy Dissipation Problem in Shafts Under Time-Dependent Angles of Twist

Rizov Victor

Inżynieria Mineralna

2024

Vol. 1, no. 2

art. no. 23

The present paper deals with the energy dissipation problem in viscoelastic continuously inhomogeneous stepped shafts under time-dependent angles of twist. The shafts analyzed in the paper have circular cross-section. Common solution of the energy dissipation problem is derived. Statically determinate as well as statically indeterminate shafts are considered. The viscoelastic behavior of the shafts is treated by models representing systems of springs and dashpots under time-dependent shear strain. The shafts are continuously inhomogeneous along the radius of the cross-section. Because of this, the shaft properties are continuously distributed along the radius. The common solution for the energy dissipation is obtained by analyzing the stresses and strains in the dashpots of the viscoelastic models (actually, this approach uses the fact that in models with springs and dashpots the energy is dissipated by the dashpots). An example illustrating the application of the common solution is presented. The dissipated energy (DE) is derived also by direct integration in the time domain for verification. The DE in the statically determinate shafts is compared with this in an indeterminate shaft. It is demonstrated that the common solution is applicable also when the shafts are under angles of twist whose number is less that the number of the shaft portions.

Analyzing of Delamination in Semirings Attached to Non-Linear Elastic Torsional Springs

Rizov Victor

Inżynieria Mineralna

2024

Vol. 1, no. 2

art. no. 24

The current paper is focused on analysis of delamination of a semiring engineering structure attached to non-linear elastic torsional springs that are situated in the semiring plane. The semiring has arbitrary number of circumferential layers made of nonlinear viscoelastic materials that are inhomogeneous along the thickness. The semiring undergoes time-dependent bending rotation at a given cross-section. The delamination is treated from view point of the strain energy release rate (SERR). A methodology for determination of the SERR in semirings attached to torsional springs is worked out on the basis of analysis of the energy balance. The results yielded by this methodology are verified by extracting the SERR from the complementary strain energy. The study presented in the paper provides useful insights into delamination performance of semiring engineering structures which is a premise for enhancing the structural reliability. The effects of various parameters of the semiring geometry, inhomogeneity of layers, non-linear constitutive laws of torsional springs, external loading, number of springs and their locations are examined and clarified.