DYNAMIC SHEAR STRESS ANALYSIS OF DISCS SUBJECTED TO VARIABLE ROTATIONS

Abstract

Dynamic circumferential displacements and shear stresses are analyzed for a hollow disc which rotates at variable speeds, and the inner face of which is fixed on a rigid shaft. The problem is solved by using the Laplace transform and Cauchy's integral theorem. For a disc accelerating exponentially with respect to time, ω (t) = ω₀ [1 - exp (-ct) ], the shear stress changes cyclically as a sine function of time. The relation between a parameter c in the above equation, which specifies an increasing rate of rotations, and the amplitude |Δτ^^-_rθ| of the cyclic variations of the shear stress becomes linear, that is, [numerical formula]. The ratio of the maximum dynamic and quasi-static stresses, and the period of the cycliclically changing stresses are obtained.