Natural Vibrations of Nanostructures Using a Developed 3D Model Based on Nonlocal Theory of Elasticity<br/><br/>

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Natural Vibrations of Nanostructures Using a Developed 3D Model Based on Nonlocal Theory of Elasticity

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 43627 (45)
University: Sharif University of Technology
Department: Aerospace Engineering
Advisor(s): Dehghani Firoozabadi, Rouhollah
Abstract:
The goal of this thesis is to survey natural frequencis of nanostructures such as nanobeams and nanoplates using nonlocal theory of elasticity by finite element method. In nonlocal theory of elasticity,the constitutive relation appears as an integral form so that the stress of a point is a function of the strain of all points in the field such that by getting away from the assumed point, the effect of strains on the stress of that point decreases. In fact, the stress on a point is an average of stress in the field and the effect of stress of other points in determined by a function called the kernel function. In order to achieve natural frequencies and shape modes of a structure, we need to calculate stiffness and mass matrices. To do so, weak form of equations is derived using Hamilton’s principle based on nonlocal theory of elasticity and stiffness and mass matrices of each element and interaction between elements are extracted. The extracted formulation is implemented by a computer code and natural vibrations of three dimensional structures such as beams and plates are surveyed
Keywords:
Finite Element Method ; Nanostructure ; Nonlocal Elasticity Theory ; Natural Vibrations ; Three Dimentional Solid

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