Keywords: cylindrical shell, transversely isotropy, shell equation, eigenfrequency, power series..

The dynamic equations for a thin cylindrical shell made of a homogeneous, but transversely isotropic material are derived. First the displacement components are expanded in a power series in the thickness coordinate direction (around the mid-surface of the shell). The recursion relations are obtained among the expansion functions by inserting the aforementioned expansions into the three-dimensional elastodynamic equations. These recursion relations can be used to express all higher-order expansion functions in terms of the six lowest-order ones. The power series expansions of the displacement components are inserted into the stress-free boundary conditions on the two cylindrical surfaces of the shell leading to six power series in the shell thickness. Eliminating all but the six lowest-order expansion functions with the help of the recursion relations finally gives six dynamic equations for the shell. To investigate the properties of the resulting shell equations the eigenfrequencies for the transversely isotropic cylindrical shell are computed for a simply supported shell. Comparisons are made with exact three-dimensional calculations and membrane theory for some simple cases. The calculated eigenfrequencies for the shell equations agree very well with exact three-dimensional theory when the order of the shell equations is increased.

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