Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Non-Central Shell Segment

Abstract

In this study, the “Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by A Bonded Non-Central Shell Segment” are analyzed and investigated in some detail. The “full” circular cylindrical “base” shell and the non-centrally bonded circular cylindrical shell “stiffener” are assumed to be made of dissimilar orthotropic materials. The “base” shell and the “stiffening” shell segment are adhesively bonded by an in-between, relatively very thin, yet linearly elastic adhesive layer. In the theoretical analysis, for both shell elements, a “First Order Shear Deformation Shell Theory (FSDST)” such as “Timoshenko-Mindlin -(and Reissner)” type is employed. The damping effects in the entire system are neglected. The sets of dynamic equations of both “base” shell and “stiffening” shell segment and the adhesive layer are combined together, manipulated and are, finally, reduced to a “Governing System of First Order Ordinary Differential Equations” in Forms of the “state vectors” of the problem. This result constitutes a so-called “Two-Point Boundary Value Problem” for the entire composite shell system, which facilitates the present solution procedure. The final system of equations is numerically integrated by means of the “Modified Transfer Matrix Method (MTMM) (with Chebyshev Polynomials)”. The typical mode shapes with their natural frequencies are presented for several sets of support conditions. The very significant effect of the “hard” and the “soft” adhesive layer on the mode shapes and the natural frequencies are demonstrated. Some important parametric studies (such as the “Joint Length Ratio”, etc.) are also presented.