Frequency Change and Mode Shape Transformation in Free Vibration Analysis of Three-Phase Composite Thin Plate Under Different Boundary Conditions

Background The plate structure is one of the typical components of the mechanical system and its vibration research has attracted full attention. Graphene platelet is a new high-performance nano-reinforced filler and its emergence provides an opportunity to improve the vibration properties of conventional composite plate structures. Purpose The free vibration characteristics of the three-phase composite thin plate reinforced synergistically by graphene platelets (GPLs) and carbon fibers are studied in this paper, and we also analyze the influences of the content changes of different reinforcements on the natural frequencies and mode shapes of the three-phase composite thin plate. Methods The effective material properties of the three-phase composite material are calculated according to a combination of the Halpin–Tsai model and the micromechanics approach. The separation method of variables is used to obtain the natural frequencies and mode shapes of the three-phase composite thin plate under different boundary conditions. The accuracy of results from the separation method of variables is verified by comparison with the references. Conclusions The synergistic effect of GPLs and carbon fibers can increase the natural frequencies of a composite thin plate under different boundary conditions. The mode shape transformation phenomena mostly appear in the higher order vibrations of the three-phase composite thin plate when the GPLs content increases. The appearance of mode shape transformation is accompanied by a change in the rate of frequency growth. These results have important theoretical significance for a widespread engineering application of the three-phase composite structure.