سعیدرضا محب پور

Studying mechanical behavior of nono structural elements is today’s topic of many scientific investigations and technology. This is because of special properties of these materials which introduced them as ideal reinforcement, mass and strain sensor with high sensitivity. Hence modeling these structures in order to percept behavioral properties of these structures is so important. Since the mechanical properties of nanotubes depends on atomic distributions, modeling different kinds of them using extended continuum theory is impossible and in this theory atomic data is not completely effected. That’s why using molecular dynamic for modeling and analyzing different nanotube structures is inevitable. In this work after defining geometry of nanotubes and preparation of appropriate molecular dynamic model, transverse free vibration of nanotubes was investigated. Since molecular dynamic analysis is a fundamental method in simulating process in nano domain, results of this modeling were considered as physical response of system. By introducing corresponding problem, its formulation was acquired according to theoretical studies and solved by numerical method. Governing equations and boundary conditions were derived using Timoshenko’s and Euler-Bernoulli’s beam theory considering Eringen’s nonlocal stress theory and Hamilton’s principle. The differential quadrature method (DQM) as an accurate and computationally efficient numerical tool is employed to discretize the governing differential equations together with the related boundary conditions then the natural frequency and nonloal scale parameter of model for the first five frequency subjected to various boundary conditions was studied. Formulation, solution method and molecular dynamic simulations validation was compared with available scientific sources. By comparing acquired response from this investigation with physical response of model accuracy and capacity of these methods were evaluated. In second part, the free vib