Title: Free vibration analysis of carbon nanotubes reinforced beam with non-uniform distribution subjected to axial load

In this research, the free vibration analysis of carbon nanotubes reinforced beam with non-uniform distribution subjected to axial load is investigated by using the refined theory. The properties of carbon nanotubes reinforced with non-uniform distribution are considered to be along the beam and obeys the power law. Applying the Hamilton's principle and using the Navier type solution ,the motion equations are derived in terms of the frequency equations. Using the generalized differential quadrature method in axial direction and periodic differential matrix operators in circumferential direction, the equilibrium equations are discretized to obtain the natural frequencies of the beam reinforced carbon nanotubes with the mentioned non-uniform distribution. In addition, the results are compared with the forced nonlinear vibrations of a graduated Timoshenko composite beam reinforced carbon nanotubes. Numerical results indicate that the natural frequency decreases or increases due to changes in the states of different distributions of nanotubes and the amount of the presented volume and axial load. Naturally, the best manner contains the lowest frequency and the lowest vibration, finally.

کلیدواژه ها:

Carbon nanotubes ، Reinforced beam ، free vibration ، refined theory ، axial load