Non-linear free periodic vibrations of variable stiffness composite laminated plates

Steady-state free vibrations, with large amplitude displacements, of variable stiffness composite laminated plates (VSCL) are analysed. The intentions of this research are: (1) to find out how the natural frequencies and (mode) shapes evolve with the displacement amplitude in this new type of laminated composite material; (2) to describe modal interactions in VSCL due to energy interchanges under the coupling induced by non-linearity; (3) to compare the VSCL with traditional, constant stiffness, laminated plates. The VSCL of interest here have curvilinear fibres and the numerical analysis carried out is based on a recently developed p-version finite element with hierarchic basis functions. The element follows first-order shear deformation theory and considers Von Karman's non-linear terms. The time domain equations of motion are first reduced using the linear modes of vibration and then transformed to the frequency domain via the harmonic balance method. These frequency domain equations are solved by an arc-length continuation method.