Influence of Small Added Mass on Splitting Flexural Frequency Spectrum of Circular Ring with Initial Imperfection of Shape

摘要

The paper presents the results of the research into the problem of vibration of the infinitely long circular cylindrical shell, which has a symmetrical initial shape imperfection. The infinitely long shell is viewed as the ring of a single width in situations of planar deformation. It was discovered that the effect of splitting the bending spectrum frequency of the isolated ring not only occurs when the number of waves of asymmetric imperfection coincides with the number of waves of dynamic deformations, but also where the number of imperfections is twice as big as the number of the forming waves. This conclusion is correct provided that the number of waves of shape imperfection is even. An opportunity to remove the splitting frequency of the bending spectrum of a thin imperfect circular ring by acceding to it little linear mass is studied. The research has shown that neither the selection of attaching point of added mass nor its size allow discarding the unwanted in terms of a dynamic strength and reliability of the constructions, effect of staggering frequency. During the research a range of qualitative effects caused by the ring having inevitable deviations from the perfect geometrical form were identified.