Abstract
This paper presents a three-dimensional (3D) analysis for the natural frequencies of completely free, toroidal shells of revolution with hollow circular cross-sections by the Ritz method. The displacement components [Formula: see text], [Formula: see text], and [Formula: see text] in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in [Formula: see text], and of the ordinary algebraic simple polynomials in the [Formula: see text] and [Formula: see text] directions. The potential (strain) and kinetic energies of the torus are formulated, and the upper bound values of the frequencies are obtained by a minimization procedure. As the degree of the polynomials increases, the frequencies computed converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the torus. Comparisons are made between the frequencies from the present 3D method, a 3D finite element method, experimental methods, and thin and thick ring theories.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Structural Stability and Dynamics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
