Free vibration analysis of doubly curved shallow shells on rectangular planform using three-dimensional elasticity theory

Abstract The free vibration analysis of homogeneous and laminated doubly curved shells on rectangular planform and made of an orthotropic material has been presented using the three-dimensional elasticity equations. A solution is obtained utilizing the asumption that the ratio of the shell thickness to its middle surface radius is negligible, as compared to unity. However, it is shown that by dividing the shell thickness into layers of smaller thickness and matching the interface displacement and stress continuity conditions, very accurate results can be obtained even for very thick shells. The two-dimensional shell theories have been compared for their accuracy in the light of the present three-dimensional elasticity analysis.

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