Vibration analysis of carbon nanotube-reinforced composite microbeams

In the present article, free vibration behavior of carbon nanotube-reinforced composite (CNTRC) microbeams is investigated. Carbon nanotubes (CNTs) are distributed in a polymeric matrix with four different patterns of the reinforcement. The material properties of the CNTRC microbeams are predicted by using the rule of mixture. The microstructure-dependent governing differential equations are derived by applying Hamilton's principle on the basis of couple stress theory and several beam theories. The obtained vibration equation is solved by using Navier's solution method. The effects of length scale parameter, length/thickness ratio, volume fraction and the reinforcement pattern of CNTs on frequencies are examined. It is observed that the biggest frequencies occur in X-Beam while O-Beam has the lowest ones. It is also found that the size effect is more prominent when the thickness of the beam is close to the length scale parameter and this effect nearly disappears as the thickness of the beam increases.

Automated summary

This article investigates the free vibration behavior of CNTRC microbeams with CNTs distributed in a polymeric matrix using four different reinforcement patterns. Material properties and microstructure-dependent governing differential equations are derived based on the rule of mixture and various beam theories. The obtained vibration equation is solved using Navier's solution method, and the effects of length scale parameter, length/thickness ratio, volume fraction, and reinforcement pattern on frequencies are examined. It is observed that X-Beam has the highest frequencies, while O-Beam has the lowest ones, and the size effect is more pronounced when the thickness of the beam is close to the length scale parameter.