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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.

Vibration characteristics of variable stiffness filament wound composite shells of revolution are investigated utilizing a numerical integration based solution method that is developed. Filaments are assumed to be placed along the geodesic and semi-geodesic fiber paths on the surface of the shell of revolution resulting in the variation of the stiffness coefficients and the thickness of the shell wall along the axis of the composite shell of revolution with general meridional curvature. For geodesic and semi-geodesic winding, relations giving the meridional variation of the winding angle and thickness are derived for truncated conical and spherical shells of revolution which are studied as the sample shell geometries. The effect of constant preset friction, applied during the winding process, on the stiffness and vibration characteristics of filament wound composite shells of revolution is studied in depth. In the most general case, multi-segment numerical integration technique is extended to the solution of the free vibration problem of composite shells of revolution which are wound along the semi-geodesic fiber paths counting on the preset friction used during the winding process. The effect of initial winding angle and the starting edge of the winding operation on the variation of the thickness, stiffness coefficients and free vibration characteristics of filament wound shells of revolution are investigated. Case studies are also performed on the comparison of the frequencies calculated by incorporating the actual variation of the winding angle and thickness, and the frequencies calculated based on constant winding angle and thickness which are taken as average and mid meridian values.

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