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Advances in Nano Research
  Volume 6, Number 1, March 2018 , pages 57-80

Vibration analysis of carbon nanotubes with multiple cracks in thermal environment
Farzad Ebrahimi and Fatemeh Mahmoodi

    In this study, the thermal loading effect on free vibration characteristics of carbon nanotubes (CNTs) with multiple cracks is studied. Various boundary conditions for nanotube are taken in to account. In order to take the small scale effect, the nonlocal elasticity of Eringen is employed in the framework of Euler-Bernoulli beam theory. This theory states that the stress at a reference point is a function of strains at all points in the continuum. A cracked nanotube is assumed to be consisted of two segments that are connected by a rotational spring which is located in the position of the cracked section. Hamilton's principle is used to achieve the governing equations. Influences of the nonlocal parameter, crack severity, temperature change and the number of cracks on the system frequencies are investigated. Also, it is found that at room or lower temperature the natural frequency for CNT decreases as the value of temperature change increases, while at temperature higher than room temperature the natural frequency of CNT increases as the value of temperature change increases. Various boundary conditions have been applied to the nanotube.
Key Words
    nonlocal elasticity theory; vibration; thermal effect; crack; carbon nanotube
Mechanical Engineering Department, Faculty of Engineering, Imam Khomeini International University, Qazvin, P.O.B. 16818-34149, Iran.

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