Experimental and analytical studies on eliminating natural frequency splitting of an axisymmetric structure with cyclically symmetric feature groups

Abstract

This work analytically and experimentally investigates natural frequency splitting behaviors for an axisymmetric stepped plate with circumferentially periodic groups of mass blocks. The simplified mathematical model of a stepped plate is derived using Hamilton's principle. Solving for the natural frequencies with a perturbation approach and Galerkin discretization yields the same closed-form conditions for natural frequency splitting or non-splitting. These closed-form conditions lead to analytical rules that govern splitting or non-splitting of natural frequencies for two different configurations of identical mass blocks in a group. These rules readily extend to other cyclically symmetric periodic structures of similar configurations. Simulations and experiments with a test rig show splitting or non-splitting of natural frequencies for the two configurations agrees with the analytical rules. Both the analytical and experimental results show the weight of mass blocks has no influence on the splitting or non-splitting of natural frequencies, but larger weight leads to larger differences between split natural frequencies. These tests also demonstrate the validity of these natural frequency splitting elimination rules for significant mode contamination. An experimental evaluation of the natural frequency splitting behaviors with respect to mass block weight and angular position deviations gives that the splitting of natural frequencies is insensitive to these deviations, but the non-splitting can be sensitive (i.e., natural frequencies that do not split without these deviations can split). This study provides guidelines for eliminating or reducing natural frequency splitting for cyclically symmetric systems like gyroscopes.