Vibrations of a cylindrical shell closed with a hemi-spheroidal dome from a three-dimensional analysis

The natural frequencies of a circular cylindrical shell closed with a hemi-spheroidal dome are determined by the Ritz method using a three-dimensional (3-D) analysis instead of two-dimensional (2-D) thin shell theories or higher-order thick shell theories. The present analysis is based upon the circular cylindrical coordinates,while in the traditional shell analyses 3-D shell coordinates have been usually used. Using the Ritz method, the Legendre polynomials, which are mathematically minimal or orthonormal, are used as admissible functions instead of ordinary simple algebraic polynomials. Natural frequencies are presented for different boundary conditions. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the combined shell. The frequencies from the present 3-D method are compared with those from 2-D thin shell theories. The present method is applicable to very thick shells as well as thin shells.