Free vibration analysis of functionally graded graphene nanocomposite beams partially in contact with fluid

This paper presents the free vibration analysis of functionally graded graphene platelets reinforced composite (FG-GPLRC) beams partially in contact with fluid based on the first-order shear deformation theory (FSDT). By considering the 3D-random orientation of graphene platelets (GPLs), the 3D Halpin-Tsai model is introduced to calculate the elastic modulus of graphene nanocomposites. The fluid velocity potential and hydrodynamic loading are determined by virtue of variable separation method. The equations of motion are derived by using Hamilton's principle and the natural frequencies are determined by the multidomain generalized differential quadrature (GDQ) approach together with an iterative scheme. Parametric studies are carried out to evaluate the influences of GPL distribution pattern, weight fraction and dimension, fluid depth and density, beam geometry and end supports on the free vibration behaviour of FG-GPLRC beam-fluid interaction systems. Results show that the beam-fluid interaction reduces the fundamental frequency most, but it hardly affects the first order vibration mode.