Free Vibration Analysis of Shallow Shells using the Superposition-Galerkin Method

Abstract

A procedure to apply the Superposition-Galerkin method for the vibration analysis of a completely free doubly curved shallow shell is presented. To handle mixed derivatives in the equation of boundary conditions of the free edge, the sine series and the cosine series are used independently in the displacement functions of building blocks. The solution to each building block is obtained using the Galerkin method and expressed in term of its driving coefficients. The method is expected to work as the superimposed set of the building blocks can satisfy the free edge conditions. However, presence of extra natural frequencies proves to be a challenge. Currently work is in progress to eliminate the spurious modes.