Vibrations of a composite shell of hemiellisoidal-cylindrical shell having variable thickness with and without a top opening

• Published in: Thin-walled structures Vol. 119; pp. 677 - 686
• Main Authors: Yang, Yeong-Bin, Kang, Jae-Hoon
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2017
• Subjects: Circular cylindrical hole; Circular cylindrical shell; Composite shell; Deep shell; Free vibration; Legendre polynomial; Ritz method; Shallow shell; Shell of revolution, hemi-ellipsoidal shell; Three-dimensional analysis; Variable thickness; Shell of revolution, hemi-ellipsoidal shell; Variable thickness; Circular cylindrical hole; Three-dimensional analysis; Free vibration; Shallow shell; Composite shell; Ritz method; Legendre polynomial; Deep shell; Circular cylindrical shell
• ISSN: 0263-8231; 1879-3223
• DOI: 10.1016/j.tws.2017.07.019

Natural frequencies and mode shapes of a composite shell of revolution consisting of a circular cylindrical shell and a deep or shallow hemi-ellipsoidal shell with variable thickness having a circular cylindrical hole or not are determined by the Ritz method using a mathematically three-dimensional analysis instead of two-dimensional 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 three-dimensional shell coordinates have been commonly used. Using the Ritz method, the 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 composite shells. The frequencies from the present three-dimensional method are compared with those from three types of two-dimensional thin shell theories (finite element method, finite difference method, and numerical integration) by previous researchers. The present analysis is applicable to very thick shells as well as thin shells; and to shallow shells as well as deep shells. •Frequencies are calculated for combined hemiellipsoidal-cylindrical shells.•The shells have variable thickness.•The hemiellipsoidal shells have a top opening or not.•The hemiellipsoidal shell are deep or shallow.•The analysis is based on mathematically three-dimensional theory.•The Legendre polynomials are used as admissible functions using the Ritz method.•The analysis is applicable to very thick shells as well as very thin shells.