The Free Vibration Equations, Natural Frequencies and Modal Characteristics of Closed Circular Cylindrical Shells

摘要

The relative accuracies of the representative classical theories of thin shells are examined. The order of magnitude comparison of terms involved in the governing equations for the free vibrations of a circular cylindrical shell is the method utilized. The boundary conditions for the shells are taken into account and it is shown that the classical theories yield valid solutions accurate enough when taking into consideration the errors inherent in the Kirchhoff-Love hypothesis. A first approximation, consistent with the order of magnitude estimate, leads to a system of free vibration and boundary constraining equations. The approximation enabled a qualitative estimate of the forms of the characteristic solutions. The accuracy of the Donnell type approximation is investigated and a detailed account of the historical developments of the subject is provided.