Free Vibrations of Ring Stiffened Toroidal Shells. Part I. Analytical Formulation.
POLYTECHNIC INST OF BROOKLYN N Y DEPT OF AEROSPACE ENGINEERING AND APPLIED MECHANICS
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The free vibrations of ring stiffened toroidal shells are studied. Stiffening rings are assumed placed at meridional sections, and treated as discrete members. An arbitrary number of rings differing in properties and unequally spaced is considered. The shell segments, are coupled to the stiffeners by imposing compatibility at the junctions. The Love-Reissner shell theory is employed for analyzing the torus segments. The shell equations are first converted into a set of eight partial differential equations with variable coefficients, expressing first derivatives, in the circumferential direction, of the eight shell functions which appear in the natural boundary conditions at a meridional section. The shell functions are subsequently expanded into a Fourier series in the meridional coordinate and substituted in the aforementioned eight equations which are then transformed with the aid of some trigonometric identities, into two uncoupled infinite sets of ordinary differential equations. Author
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