Dynamic stability of rotating blades (beams) eccentrically clamped to a shaft with fluctuating speed

In-plane bending vibrations of a beam rotating with a periodically fluctuating speed are considered. The partial differential equation of motion is discretisized via Galerkinʹs method and a set of Mathieu–Hill equations is obtained. The constant speed rotation problem is reviewed and its reflections onto the fluctuating speed problem are underlined. Dynamic stability analysis is performed via a monodromy matrix method and a generalized Bolotin method. Examples of stability charts are worked out reflecting stabilityʹs dependence on various pairs of system parameters.