Traveling wave analysis of rotating cross-ply laminated cylindrical shells with arbitrary boundaries conditions via Rayleigh–Ritz method

Abstract

This paper presents the analysis on free vibration of rotating cross-ply laminated circular cylindrical shells under arbitrary elastic boundary conditions via Rayleigh–Ritz method. Based on the Donnel’s shell theory, the energy equations of the composite shell which take into account of initial hoop tension, centrifugal and Coriolis forces are derived. By employing a set of orthogonal polynomials as the admissible function, the Rayleigh–Ritz method is used to formulate the equations of motion of the rotating composite cylindrical shell with traditional boundary conditions. Then, the assumed elastic springs applying on boundaries of the shell are employed to simulate the arbitrary elastic supports of the rotating composite shells, which contribute the total system energy as elastic spring potential energy. Further, some numerical examples are presented to confirm the influence of variations elastic boundary conditions and lamination schemes on the frequency of rotating composite cylinders. The current strategy is excellent to investigate the traveling waves of rotating composite shell with various boundaries including the classical constrains, elastic cases and the combinations of them availably and accurately.