The effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic shells Part I: Coupled transverse-circumferential mode shapes of isotropic circular cylindrical shells of infinite length

The effects of large vibration amplitudes on the first and second coupled r adial-circumferential mode shapes of isotropic circular cylindrical shells of infinite length are examined. A theoretical model based on Hamilton's pr inciple and spectral analysis developed previously for clamped-clamped beam s and fully clamped rectangular plates is extended to shell type structures , reducing the large-amplitude free vibration problem to the solution of a set of non-linear algebraic equations. The transverse and circumferential d isplacements are assumed to be harmonic and expanded in the form of a finit e series of functions. The Donnel-Mushtarie shell theory, taking into accou nt the coupling between extensional and flexural deformations is used. Then . the non-linear deformation energy is expressed by taking into account the non-linear term due to the considerable stretching of the middle surface o f the shell induced by large deflections. Tables of numerical results are g iven for the first and second non-linear modes, for a wide range of the vib ration amplitude, which may be used for engineering purposes. For each valu e of the vibration amplitude considered, the corresponding contributions of the basic functions defining the non-linear transverse and circumferential displacement shapes are given, with the corresponding non-linear frequenci es. Selected pints of mode shapes and bending stress distributions are pres ented, with an extensive discussion of the effects of non-linearity on the dynamic behaviour of shells. (C) 2000 Academic Press.