Non-linear vibrations of variable stiffness composite laminated plates

It is the objective of this work to analyze vibrations of variable stiffness composite laminated plates (VSCL), and investigate the differences between the oscillations of these plates and traditional laminates. The analysis is based on numerical experiments and a new p-version finite element with hierarchic basis functions, which follows first order shear deformation theory and considers geometrical non-linearity, is derived. Considering first linear oscillations, the natural frequencies and mode shapes of different VSCL are computed and compared with the ones of constant stiffness laminates. The linear natural frequencies of the present model are also compared with the ones computed using a recently developed higher-order model for VSCL. After, numerical tests are carried out in the time domain and, for the first time in VSCL, taking geometric non-linearity into account, to investigate the response to external forces. The non-linear ordinary differential equations of motion are solved by Newmark's method. It is verified that the variation of the fibre orientation can lead to significant differences in the amplitudes of the non-linear response.