Free vibration of agglomerated carbon nanotube reinforced composite sandwich beam using an enriched finite beam element

Free vibration of carbon nanotube reinforced composite (CNTRC) sandwich beams,taking into account the effect of CNT agglomeration, is studied using an efficient beam element.The sandwich beams consist of three layers, a homogeneous core and two agglomerated CNTRCface sheets with material properties being estimated by the Eshelby-Mori-Tanaka approach. Basedon the trigonometric shear deformation theory, a finite beam element is formulated and used toconstruct the discretized equation of motion for the beams. To improve the efficiency of theelement, hierarchical functions are employed to enrich the conventional Lagrange and Hermiteinterpolation functions. The numerical investigation shows that the formulated beam element isefficient, and it is capable to give accurate natural frequencies by using a small number ofelements. It is also foundation the frequencies of the beams are significantly influenced by theCNT agglomeration, and the increase of CNT reinforcement may not be useful for the beam withsevere CNT agglomeration. A parametric study is carried out to investigate the effects of theagglomeration, the volume fraction of CNTs as well as the layer thickness ratio on the vibrationof the sandwich beams.