Solution :

Let us assume the disc is on element 2. The shaft element is taken such that the disc is always at the node point. The phase is measured with respect to some physical reference on the shaft. Let us assume that reference mark is aligned with y axis at time t =0. The sense of rotation of the rotar is in thecounter-clockwise direction as seen in Figure 12.11. The FE equation for element 1 in the vertical plane x-z is given as