Forced periodic vibrations of cylindrical shells in laminated composites with curvilinear fibres

Geometrically non-linear forced vibrations of cylindrical shells with variable stiffness are analysed. The ordinary differential equations of motion are derived by the principle of virtual work in conjunction with a p-version finite element formulation. The shells are in composite laminates with curvilinear fibres, hence the stress–strain relation varies in space, leading to variable stiffness. External harmonic excitations are applied to the shell and periodic responses are sought, therefore, the solution can be expressed in a Fourier series. Distinctively, the harmonic balance method is applied via a procedure in the complex domain, with which one can employ as many harmonics as one wishes without manual changes in the algorithm or on its expressions. The resulting algebraic equation is solved by an arc-length continuation method. Studies of the convergence with the number of shape functions and with the number of harmonics are presented. The influence of the curvilinear fibre paths and of the curvature of the shells on the forced response are analysed.