Small Scale Effect on Free Vibration of Imperfect Carbon Nanotube Based on Nonlocal Elasticity

Carbon nanotubes (CNTs) may have some defects which cause different changes in their behaviors. Geometrical imperfection is one type of these defects which may occur during CNTs manufacturing. In present work, free vibration analysis of carbon nanotubes with small initial curvature is studied based on Euler Bernoulli beam theory. Eringen's nonlocal elasticity theory is implemented accounting for small size effect. Winkler type and Pasternak type foundation models are used to simulate the effect of matrix. Governing equations are derived using Hamilton's principle. These equations are solved analytically for the vibration frequencies of imperfect CNTs. The effects of nonlocal parameters, length, initial curvature and elastic foundation on frequencies are studied and discussed. Results are presented and compared with that of the available in the literature. It is shown that results are reasonable. Frequencies of CNTs are strongly dependent on the nonlocal parameters, initial imperfection and stiffness of the surrounding medium.

کلیدواژه ها:

Carbon nanotubes ، Free vibration ، Elastic foundation ، Scale effect