Vibrations of Complex Shells with Variable Thickness

Abstract

Natural frequencies and mode shapes of a complex shell composed of a circular cylindrical shell and hemispherical shell with variable thickness are determined by the Ritz method using a mathematically three-dimensional (3D) analysis instead of two-dimensional (2D) thin-shell theories or higher-order thick-shell theories. The present analysis is based upon the circular cylindrical coordinates, whereas in traditional shell analyses, 3D shell coordinates have usually been used. Using the Ritz method, Legendre polynomials, which are mathematically 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 3D method are compared with those from three types of 2D thin-shell theories found by previous researchers. The present method is applicable to very thick shells as well as thin shells and complex shells with variable thickness.