An h-p finite element vibration analysis of open conical sandwich panels and conical sandwich frusta

The vibration study of a general three-layer conical sandwich panel based on theh –p version of the finite element method is presented in this paper. No restriction is placed on the degree of curvature of the shell, thereby relaxing the strictures associated with shallow shell theory. The methodology incorporates a new set of trigonometric functions to provide the element p -enrichment, and elements may be joined together to model either open conical panels, or complete conical frusta (circumferentially connected, but open at each end). The full range of classical boundary conditions, which includes free, clamped, simply supported and shear diaphragm edges, may be applied in any combination to open and closed panels, thereby facilitating the study of a wide range of conical sandwich shells. The convergence properties of this element have been established for different combinations of the h - and p -parameters, thereby assuring its integrity for more general use. Since very little work has been reported on the vibration characteristic of either circumferentially closed or open conical sandwich panels, the main thrust of this work has been to present and validate an efficient modelling technique, rather than to perform numerous parameter and/or sensitivity studies. To this end, some new results are presented and subsequently validated using a commercially available finite element package. It is shown that for results of comparable accuracy, models constructed using the h–p formulation require significantly fewer degrees of freedom than those assembled using the commercial package. Some preliminary experimental results are also included for completeness.

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