Free vibration of laminated composite shell structures filled with fluid

Abstract

Free vibration of layered truncated conical and circular cylindrical shells filled with fluid based on Love’s first approximation theory are analysed in this research. In addition, investigation regarding the free vibration of laminated composite circular cylindrical shells filled with fluid using the first order shear deformation theory also presented. In this study, the shell is filled with quiescent fluid and analysed using the spline method. The shell equations are assumed to be in a separable form, which hence a set of coupled ordinary differential equations in the term of displacement functions is obtained for the case of the Love’s first approximation theory. For the case under first order of shear deformation theory, the rotational functions are included. These functions are approximated using the spline function, bringing into a set of field equations together with boundary conditions, that reduce to a system of homogeneous simultaneous algebraic equations on the assumed spline coefficients. The resulting generalised eigenvalue problem is solved to get as many eigen frequencies as required by starting from the least. From the eigenvectors on the spline coefficients, the mode shapes can be constructed. In the first case, the effects of the relative layer thickness, cone angle, length ratio, and boundary conditions on the frequencies of truncated conical shell filled with fluid are presented. Through the application of the same theory, the effect of the relative layer thickness, length-to-radius ratio, thickness-to-radius ratio, circumferential node number, and boundary conditions on the frequencies of circular cylindrical shell filled with fluid are investigated. In the case of first order shear deformation theory; a cross-ply, anti-symmetric angle-ply, and symmetric angle-ply laminated composite circular cylindrical shell filled with fluid are analysed. Parametric studies have been conducted with respect to the length-to-radius ratio, thickness-to-radius ratio, material properties, ply orientations, number of layers, and boundary conditions on the frequencies. The contribution of this research is to provide solutions for free vibration of laminated composite conical and cylindrical shells filled with fluid using spline method. The frequency of the shell filled with fluid is found to be lower than the frequency of the shell without fluid due to the effect of fluid in the shell that acts as the added mass to it. Material properties, ply orientations, number of layers, boundary conditions, relative layer thickness, length-to-radius ratio, thickness-to-radius ratio, circumferential node number, cone angle, and length ratio significantly affect the frequencies of the shell. Furthermore, simply supported boundary conditions are found to have the lowest frequency followed by clamped-free and clamped-clamped boundary conditions.