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Developing an Equivalent Shell Model Based on Classical and Nonlocal Theory for Vibration Analysis of Carbon Nanoscrolls

Taraghi Osguei, Amin | 2018

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 50994 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Ahmadian, Mohammad Taghi; Asghari, Mohsen
  7. Abstract:
  8. Carbon nanoscroll (CNS) is a graphene sheet rolled into a spiral structure. The Equilibrium structure of a CNS depends on the elastic bending energy and van der Waals interactions between layers. In recent decade, research on CNSs received high attention after discovering new techniques to produce high purity CNSs. Modal analysis of the CNS is essential in various applications like sensors and actuators. Therefore, in this research, a shell model for free vibration analysis of the CNS is proposed. After considering CNS as an equivalent shell, the assumed mode technique is used to extract natural frequencies and mode shapes of CNSs in different boundary conditions. The effect of geometric parameters on the vibration characteristics of a CNS is studied and the results show that ratio of circumferential length to longitudinal length plays the most important role on natural frequencies and mode shapes of the CNS. Natural frequencies and mode shapes of equivalent shell in different boundary conditions are determined and the results are compared with those of ABAQUS. Then, based on equivalent shell and modeling van der Waals interactions between layers, natural frequencies and mode shapes of the CNS are determined through the classical shell model. Unlike Multi wall carbon nanotube (MWCNT), the CNS contains two extra boundaries parallel to the central axes. For clamped boundary condition at the mentioned boundaries, the first natural frequency of the CNS and that of corresponding MWCNT is close to each other. However, considering free boundary condition at the extra edges leads to similar mode shapes for CNS and the corresponding MWCNT while the natural frequencies of the CNS and MWCNT are completely different. Additionally, the effect of external electric field parallel to axis of the CNS is modeled by reduction of van der Waals interactions between the layers of the CNS. The results indicate that as the electric field increases, the natural frequencies decrease. Finally, the size effect is studied using nonlocal elastic shell model. To this end, a trial variational function is proposed based on nonlocal elasticity. Using proposed variational function, natural frequencies and mode shapes of the CNS in different boundary conditions are determined. It is observed that although nonlocal module has considerable effect on natural frequencies, it doesn’t change mode shapes consideribaly. By assuming nonlocal module and the ratio of inner radius to longitudinal length to be 1nm2 and 0.01 respectively, the results show that if the inner radius of CNS is higher than 1nm, the difference between results of classical model and nonlocal model is lower than 5 percent
  9. Keywords:
  10. Natural Frequency ; Nonlocal Elasticity Theory ; Vibrational Analysis ; Carbon Nanoscroll ; Equivalent Shell Model ; Classical Theory

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