Free-Vibration Analysis of Ring-Stiffened Branched Composite Shells of Revolution

Application of the multisegment numerical integration technique is extended to the free-vibration analysis of macroscopically anisotropic filament-wound branched shells of revolution with ring stiffeners, considering the variation of the thickness and winding angle. The solution procedure is based on a modified-frequency trial method, which processes on the numerically integrated transformed fundamental shell equations that are obtained in terms of finite exponential Fourier transform of the fundamental shell variables. The full macroscopically anisotropic form of the constitutive relations, including first-order transverse shear deformation and all components of translatory and rotary inertia, are included in the analysis. To handle branched shells of revolution, modifications that are necessary to incorporate junctions are added to the solution procedure. Inclusion of asymmetric circumferential stiffeners, with respect to the middle surface of the shell, into the semi-analytical solution method is demonstrated by presenting two alternative methods of analysis. The present solution methodology also incorporates the variation of the thickness and winding angle along the meridian of filament-wound shells of revolution, with general meridional curvature, by assuming placement of filaments along the geodesic fiber path on the surface of the shell of revolution.