Calculation of Natural Frequencies of Specially Orthotropic Multilayered Thin Circular Cylinders,
UNIVERSITY OF MANCHESTER INST OF SCIENCE AND TECHNOLOGY (ENGLAND)
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It is the main aim of this paper to present a simple theoretical analysis for determining the natural analytical frequencies of thin walled circular cylindrical shells with layers of homogeneous isotropic or specially orthotropic material symmetrically situated about the shell mid-surface with a variety of end conditions viz clamped-free, clamped-supported, clamped-clamped etc. The theory governing the response is based on the Love-Timoshenko hypothesis regarding deformation and is capable of handling a shell structure comprised of an arbitrary number of thin bonded layers which can have different thicknesses and elastic material properties. The procedure adopted for the solution of governing equations is a simple one. It is an application of the Rayleigh-Ritz approximate variational procedure. Various boundary conditions are incorporated via the approximation of the longitudinal modal forms by the characteristic functions of a vibrating beam. These functions were successfully used by one of the authors in dealing with the vibration characteristics of isotropic thin circular cylinders 7. Procedure yields a cubic frequency equation. Out of the three roots of this cubic which is solved exactly two are several orders higher that the third one and are not of any immediate practical interest.