Optimization and analysis of frequencies of multi-scale graphene/fibre reinforced nanocomposite laminates with non-uniform distributions of reinforcements

•Frequency optimization problems are defined for graphene/fibre reinforced plates.•Design efficiency indices are introduced to measure the effectiveness of optimization.•Effectiveness of non-uniform thickness, graphene/fibre reinforcements/angles is shown.•The increase of frequency may reach 50% comparing to plates with zero graphene.•Contribution of fibre types and boundary conditions is highlighted. Optimal design and analysis of three-phase graphene/fibre reinforced laminated nanocomposite plates with respect to maximizing the fundamental frequency is the subject of the present study. Optimal design solutions are given for four different sets of design parameters. First design problem determines the optimal graphene contents of individual layers, the second one both graphene and fibre contents, the third optimizes the graphene and fibre contents as well as the layer thicknesses of individual layers, and the fourth problem optimizes the graphene and fibre contents, layer thicknesses and fibre orientations. Purpose of this approach is to assess and compare different levels of optimization by means of a design efficiency index and as such to determine the effectiveness of different design parameters in maximizing the fundamental frequency. Optimization is implemented using a Sequential Quadratic Programming algorithm and the mechanical properties of graphene/fibre nanocomposite are determined via micromechanical relations. Vibration analysis is conducted by the finite element method using four-noded Mindlin plate elements. Results are obtained for simply supported (SSSS), clamped (CCCC) and simply supported-clamped boundary conditions for opposite edges (SCSC). It is observed that non-uniform distributions of graphene and fibre as well as fibre orientations are quite effective in improving the design efficiency.