Dynamic Stability of Rotating FG-CNTRC Cylindrical Shells under Combined Static and Periodic Axial Loads

The dynamic stability behavior of rotating functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells under combined static and periodic axial forces is investigated. The governing equations are derived based on the first-order shear deformation theory (FSDT) of shells. The initial mechanical stresses due to the steady state rotation of the shell are evaluated by solving the dynamic equilibrium equations. The equations of motion under different boundary conditions are discretized in the spatial domain and transformed into a system of Mathieu-Hill type equations using the differential quadrature method (DQM) together with the trigonometric series. The influences of both the initial mechanical stresses and Coriolis acceleration are considered. Then, the parametric resonance is analyzed and the dynamic instability regions are determined by employing the Bolotin's first approximation. After validating the approach, the effects of rotational speed, Coriolis acceleration, carbon nanotubes (CNTs) distribution in the thickness direction, CNTs volume fraction, length and thickness-to-mean radius ratios on the principal dynamic instability regions are examined in detail.