Dynamic stability analysis of periodic axial loaded cylindrical shell with time-dependent rotating speeds

Abstract

Dynamic stability of periodic axial loaded cylindrical shell with time-dependent rotating speeds is investigated. Utilizing the Donnell’s thin shell theory and assumed mode method, the equations of motion for a rotating cylindrical thin shell subjected to time-periodic axial load are derived. Both the time-dependent rotating speed and axial load are assumed to be small and sinusoidal perturbations superimposed upon constant terms. Considering the time-varying rotating speed and axial load, the second-order differential equations of the system have time-periodic gyroscopic and stiffness coefficients. The multiple scales method is utilized to obtain the instability boundaries analytically. Numerical simulations based upon the discrete state transition matrix method are conducted to verify the analytical results. With the constant axial load varying from compressive to tensile loads, all of the instability regions move toward the high frequency range. Their widths almost have no change, except for the combination instability region of certain mode. When both the rotating speed and axial load are time periodic, the cylindrical shell system would always be unstable if the parametric phase does not equal to the integer multiple of \(\pi \). Applying the periodic rotation and axial load simultaneously brings significant impact on the combination instability region, while it almost has no influence on the primary instability regions. In certain conditions, the combination instability region induced by periodic rotating speed would be reduced (even vanished) by the operation of periodic axial load. However, in other conditions, such instability region would be enlarged continuously. The conditions for increasing or decreasing such instability region are obtained analytically and verified by numerical simulations.