We developed a computational method for effectively conducting the free vibration analysis of axisymmetric shells with various shapes. This paper describes a computational algorithm for the free vibration analysis of axisymmetric shells using the Sylvester-transfer stiffness coefficient method (S-TSCM). From the free vibration analyses of three axisymmetric shells (joined conical-cylindrical shell, hermetic capsule and built-up shell), we verified the applicability of the S-TSCM. We then confirmed that the computational power of the S-TSCM is much better than both the finite element-transfer matrix method and finite element-transfer stiffness coefficient method, in terms of computational accuracy and time. In particular, when axisymmetric shells are modeled into a large number of conical shell elements, the S-TSCM is superior to both the bisection method using Sturm sequence property and Jacobi method, in terms of computational time and storage.
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