Sensitivity of Forced Vibrations of the Frame with an Unbalanced Rotor to the Variations of Bracing Stiffness

Most of the literature in the rotor dynamics field is focused on the analysis of rotor behavior and rotor support properties. The influence of the rotor on the vibrations of the elastic supporting structure requires further study. As the rotation speed increases, even a small imbalance may cause an impermissible amplitude of forced vibrations of the given structural unit. This article presents the analysis of sensitivity of the forced vibration amplitude of the given unbalanced rotor frame to the bracing stiffness variations. The bracing stiffness is equivalent to the linear (torsional) integral stiffness of the frame segments. Conventional finite element software of the MSC.Nastran type normally does not have the facilities to directly formulate and solve the sensitivity analysis problem, therefore the lumped parameter method is proposed. The frame with the rotor is replaced by an equivalent multimass model. An important characteristic of the model is the flexibility matrix where the elements are generally not represented analytically but numerically. The authors present calculation formulae of the flexibility matrix derivatives with respect to the bracing stiffness variations. These formulae do not required matrix differentiation.

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