Application of linear shallow shell theory of Reissner to frequency response of thin cylindrical panels with arbitrary lamination

Abstract

A free vibration response of arbitrarily laminated – crafted with advanced fiber reinforced composite materials – thin and shallow cylindrical panels on rectangular planform with simply supported boundary conditions is analytically investigated. The thin shallow shell formulation of Reissner that follows the classical Kirchhoff–Love hypothesis of small displacements is considered to include arbitrarily laminated behaviors. The simply supported boundary condition having normal, tangential, and transverse displacements restrained at the edges is implemented. The solution functions in a form of mixed boundary continuous and discontinuous double Fourier series are assumed into the analytical solution formulation. The efficiency and accuracy of the solution methodology are determined by studying numerically the convergence behavior of frequencies for various parametric effects. The analytically obtained numerical results and mode shapes are compared with available finite element solutions, and the analytical results can be capitalized as base-line solutions for future comparisons.