Coupled dynamics of double beams reinforced with bidirectional functionally graded carbon nanotubes

The coupled dynamics of a double beam system connected via an elastic layer is investigated. The double beam is reinforced with bidirectional functionally graded carbon nanotubes. Independent transverse and axial motions for each beam, as well as their couplings, are considered in the model. The two interconnected beams are functionally graded with patterns of UD, FGV, FGO, and FGX in the thickness direction, and a power-law function in the longitudinal direction, and a power-law function in both the thickness and longitudinal directions. The results suggested that increasing the carbon nanotube volume fraction in the thickness or length or both the directions of the two beams leads to an increase in both series of the axial and transverse natural frequencies. The study also identifies that when the double beams are reinforced with UD, FGO, or FGX patterns, with the same volume fraction, which are symmetrical about the transverse axis, they possess the same axial natural frequencies. It is also revealed that increasing the stiffness of the elastic layer place in-between the two beams, causes an increase in the second series of the transverse natural frequency, for all cases, whether it is reinforced by carbon nanotube in the thickness or in the length or in both thickness and length directions of the beams. These results will form crucial considerations when designing double beam systems to improve reliability and safety.