(Solved): How to find the boundary conditions here in r=0 and r=R (Question 6) A flywheel is a disk mount ...

How to find the boundary conditions here in r=0 and r=R (Question 6)

A flywheel is a disk mounted on a rotating shaft (see figure 1(a)), which is intended to increase the moment of inertia about the axis of rotation. It acts as a buffer between the engine and the load by smoothing the engine speed when discontinuities occur in the evolution of the engine torque in time. Indeed, a flywheel stores kinetic rotational energy, thus its principle is based on the storage and retrieval of kinetic energy. In other words, it acts as a regulator that enables to provide continuous energy when the energy source of the engine is discontinuous. We consider the thin flywheel shown in figure 1(b), rotating about a fixed axis at constant speed \( \omega \). Describing the motion within the rotating frame comes down to describe the flywheel submitted to inertia body forces \( \mathbf{f} \). The flywheel is made of a homogeneous, elastic, linear and isotropic material. Figure 1: Thin flywheel in rotation about a fixed axis. We will assume in the sequel the flywheel as thin \( (e<