Influence of asymmetrical initial form imperfections on fre oscillations of thin shells

In the framework of the theory of shallow shells we studied the effect of the initial deviations from the ideal circular cylindrical shape on flexural vibrations of thin isotropic shells. For the first time the possibility of an additional zone of splitting the flexural frequency spectrum due to the presence of initial shell form imperfections is shown in the paper. It is found that the splitting of the frequency spectrum occurs not only in cases when the number of waves of circumferential dynamic strain is equal to the number of waves of shell form imperfections  as generally agreed at present, but also in cases when the number of shape-generating waves is half that of wave imperfections. In the first case, both the split frequencies are lower than the corresponding frequency of the ideal shell. It was established that for some geometrical parameters of the shell the frequencies of radial vibrations may be commensurate with the flexural ones.  Solutions that take into account the interaction of bending and radial mode shapes are complemented with new results and conclusions. It was concluded that under the influence of periodic loads that inevitably arise in the operating conditions of shell structures, non-resonant zones defned according to the traditional approach can, in fact, be resonant. Resonance hazardous vibration conditions of shell structures with irregularities of this kind can occur at frequencies much lower or higher than the traditional theory predicted. This behavior of imperfect shells may lead to high stress-strain state of the structure and complex types of dynamic instability under operating conditions. The results and conclusions obtained in this work call for the revision of problems of the dynamics of shells with form imperfections that were solved earlier.