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An Innovative Method for Vibration Analysis of Nanostructures using Equivalent Lattice Stiffness

Ebadollahi, Mohammad Amin | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 50282 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Dehghani Firouzabadi, Rouhollah
  7. Abstract:
  8. In the following research a novel method for vibration analysis of nano-structures has been presented. This method is based on equalizing the lattice stiffness to a continuous model. In this method, an equivalent continuous system is considered for each atomic lattice and for the equivalent system a modified differential equation is presented. The governing equation of the continuous system is modified in such a way that the displacement field of the atomic lattice obtained by solving this differential equation gives similar responses to the displacement field of atomic lattice. This differential equation is derived from the Taylor expansion of the displacement field about the lattice atoms. The basis of the method is to use higher order Taylor series and to achieve the equivalent differential equation.One of the advantages of the proposed method which is used for modeling of atomic lattices that are widely used in nanostructures is deriving the differential equation of the continuous model that can simulate the behavior of the structure. This method makes the Complexity of the molecular dynamics analysis of the complex system easy. The other advantage of this method is the ability of parametric study of lattice with the least time and cost. Finally, another advantage of this method is the simplicity of deriving the differential equation in comparison to other theorems, such as nonlocal and strain gradient theories.To verify the proposed method, nanotube, nano-beam, nano-scaled plates vibrations are investigated as case studies and frequencies, mode shapes of each model have been presented. The dispersion curves of each model have been also compared to the different order of ELS method. One of the major goals of the present research is to compare the proposed method with the nonlocal and the strain gradient theories and to discuss the results
  9. Keywords:
  10. Dispersion Relation ; Nanostructure ; Nanobeam ; Molecular Dynamics ; Equivalent Stiffness Matrix ; Non-Classical Continum Mechanics Theories ; Lattice Stiffness

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