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

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.