An admissible function for vibration and flutter studies of FG cylindrical shells with arbitrary edge conditions using characteristic orthogonal polynomials

Abstract

A general approach for the vibration and aeroelastic stability of the functionally graded cylindrical shell with arbitrary boundary conditions is firstly presented. The Sanders' shell theory, a steady-state heat transfer equation and the piston theory are employed to establish the motion equation, where the thermo-mechanical properties of material are set to be location- and temperature- dependent. The orthogonal polynomials series generated by employing the Gram–Schmidt process are taken as the admissible functions to express the general formulations of displacement. Moreover, the artificial spring technique is introduced to simulate the elastic constraints imposed on the cylinders' edges. The frequency equations are derived considering the strain energy of artificial springs during the Rayleigh–Ritz procedure, and the motion equation of cylindrical shells subjected to combined thermal and aerodynamic loads is established based on the Hamilton principle. A few comparisons for the frequency and critical flutter pressure are performed to validate the proposed approach. The influences of the volume fraction, thermal gradient, boundary conditions and spring stiffness on the flutter characteristics are highlighted. This paper overcomes the limitations of previous vibration and flutter studies which are confined to the structure under simply supported or clamped boundaries.