“…If we put e x = e y = 0 into [ K ] in equation (4) and solve the characteristic equation (i.e. |[ K ] − ω 2 [ M ]| = 0), we find that ω N = ( K N / M ) 0.5 , {φ N } = {1 + tanβ 0} T ; ω T = ( K T / M ) 0.5 , {φ T } = {−tanβ 1 0} T ; ω Θ = ( K Θ / I ) 0.5 , {φ Θ } = {0 0 1} T , where {φ N } and {φ T } represent the translational mode-shapes along the n - and t -axes, respectively, and {φ Θ } represents the rotational mode-shape (Amjadian, 2010; Kalantari and Amjadian, 2010b). These mode-shapes are graphically illustrated in Figure 3.…”