Vibration analyses of symmetrically laminated composite cylindrical shells with arbitrary boundaries conditions via Rayleigh–Ritz method

In this paper, the free vibrations of the symmetrically laminated composite cylindrical shells with arbitrary boundaries are analyzed by employing a set of artificial springs. Firstly, by employing a set of orthogonal polynomials as the admissible function, the Rayleigh–Ritz method is used to derive the equations of motion of the composite cylindrical shells with classical boundary conditions. Then, the equivalent elastic constraint is imposed on cylinder edges and to be used to simulate the arbitrary boundary conditions of the symmetrically composite cylindrical shell, and so as to formulate the frequency equations of it, in which the potential energy of the artificial springs is considered. Several comparisons are carried out to validate the approach method in current study, and the convergence investigations are checked at the same time. At last, the influence of boundary stiffness and lamination schemes on natural frequencies of the symmetrically laminated composite cylindrical shells is investigated. The results indicate that the present method is powerful to analyze the vibrations of the shells subjected to various boundaries including the classical constraints, elastic constraints and the combination of them efficiently.