Parametric instability of rotating cylindrical shells subjected to periodic axial loads

In this paper, the parametric stability of rotating cylindrical shells under static and time dependent periodic axial loads is analyzed. The present work is on the basis of the dynamic version of linear Donnell type equations for thin cylindrical shells under simply-supported boundary conditions. The assumed mode method is employed to reduce the partial differential equations into a system of coupled Mathieu-Hill type equations describing the dynamic instability behaviors of the shell. Using Floquet exponent method, parametric instability regions of rotating cylindrical shells are determined. The correctness of present analysis is examined by comparing the results with those in the literature and very good agreement is observed. The results reveal that for rotating cylindrical shells under periodic axial loads there are only combination instability regions. It is also found that the instability of rotating cylindrical shells may be enhanced under some cases due to the existence of viscous damping. In addition, the influences of circumferential wave number, static loading and shell geometrical characteristics on the location and width of instability regions for rotating cylindrical shells are discussed in detail.