Free vibration of cross-ply layered circular cylindrical shells filled with quiescent fluid under first order shear deformation theory

Free vibration of layered circular cylindrical shell filled with fluid with cross-ply walls including first order shear deformation theory is presented. The fluid is assumed to be quiescent and inviscid. The governing equations are obtained in terms of displacement and rotational functions and the normal displacement is coupled with fluid equation. These functions are assumed in a separable form, resulting in a system of differential equations. By applying Bickley-type splines of order three to approximate the functions, along with the boundary conditions, an eigenvalue problem is obtained. The eigenvalue is solved numerically for frequency parameters with an associated eigenvectors of the spline coefficients from which the mode shapes are constructed. Parametric studies with respect to thickness to radius ratio and length to radius ratio under different boundary conditions are carried out to analyse the frequency of the shell. The effects of material properties, number of layers and angle orientations are also studied.