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

Abstrakt

"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."