Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Mechanical and Materials Engineering


Professor Anand V. Singh


In this thesis, first the fundamental characterizations of carbon nano-structures and basic atomistic models of the carbon nanotubes and graphitic sheets are reviewed extensively. Different simulation methods used in this field of study are discussed critically. Advantages and shortfalls of each method are reported in detail. A new structural approach based on the lattice atomic structure is selected as an accurate and efficient model for simulating carbon nano-structures. This method is used comprehensively in the present work along with continuous shell and plate theories to study the mechanical and vibrational characteristics of single-walled carbon nanotubes and single and multi-layered graphene sheets. Covalent bonds are modeled using three-dimensional frame elements in finite element simulation. Nucleus of each carbon atom is considered as a node with concentrated mass and six degrees of freedom. Highly nonlinear van der Waals interactions between adjacent layers of graphitic sheets are modeled successfully and their true nonlinear nature is preserved. Free and forced vibrations are studied accordingly to investigate the natural frequencies and frequency spectrums. Mode shapes are obtained from eigen-analyses and results are compared with other methods available in the literature. Effects of size, atomic structure and boundary conditions on vibrational behaviors of these structures are studied in detail. Static analysis of single-layered graphene sheets is also carried out to obtain the Young’s modulus of elasticity of graphitic sheets under various loading conditions. Two different continuous models are proposed for simulating the in-plane and transverse vibrations of graphene sheets. Results of the continuous models are compared with the lattice structure approach for rectangular, skewed and circular graphenes to show the accuracy of the models. Forced nonlinear vibration of multi-layered graphenes is investigated subsequently to study the effects of van der Waals interactions on the vibrational characteristics. Time-histories and fast Fourier transforms are obtained for in-plane and transverse vibrations and effects of inter-layer interactions are studied in detail.