Influence of CNTs distributions on three-dimensional vibration of sandwich plates with functionally-graded face sheets

For a thick sandwich plate, transverse stretching vibration and in-plane vibration might occur before bending vibration in practical applications, which may threaten the dynamic safety of composite structures. Therefore, this work attempts to improve the in-plane and transverse stretching stiffness of sandwich structures by using carbon nanotubes (CNTs) to reinforce face sheets. To this end, it is necessary to understand well the influence of CNTs distributions on the three-dimensional (3D) vibration of functionally graded sandwich plates. Therefore, an extended global–local higher-order model will be proposed to accurately predict 3D vibration behaviors of sandwich structures reinforced by the CNTs, as the existing equivalent single-layer models will encounter difficulties in accurately analyzing such issues. Based on the proposed model, analytical solutions and finite element formulation have been presented to study the dynamic behaviors of sandwich plates with reinforcement of the CNTs, which have been verified by 3D elasticity solutions and three-dimensional finite element results. Moreover, the influence of the CNTs distributions and volume fractions on the vibration behaviors of sandwich plates has been investigated. Finally, by selecting appropriate profiles of the CNTs through the thickness, the in-plane and transverse stretching stiffness of sandwich structures can be significantly improved.