Beam (structure)

Composite number

Materials science

Vibration

Acoustics

Matrix (chemical analysis)

Volume fraction

Physics

Timoshenko beam theory

Carbon nanotube

Optics

Microstructure

Length scale

Composite material

Nanotube

Mechanics

Reinforcement

Mathematical Methods in the Applied Sciences

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.

Vibration analysis of carbon nanotube‐reinforced composite microbeams