科研之友
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摘要
In this paper, nonlinear transverse vibration characteristics of representative volume element (RVE) of nanocomposites are examined in order to predict the vibration behavior of a nanocomposite beam at macro scale. In this regard, firstly by a bridging method the mechanical properties of nanocomposites in macro scale are determined for different state of dispersions based on the micro scale investigation. For this purpose, RVEs containing nanotubes are used with different length ratios which represent a certain state of dispersion on the macro scale. Then, the vibration equations of volume element are obtained and free vibration behavior of RVE is investigated in different boundary conditions (BCs). The non-dimensional natural frequency of nanocomposites as a function of vibration amplitude showed that the BCs have a great effect on the rate of the system nonlinear behavior. Results indicate that in clamped-pinned condition the nonlinear frequency rate is approximately 20% more than clamped-clamped condition, which shows a more nonlinear behavior. Next, the forced vibration behavior of RVE is determined using the three methods of perturbation theory, least squares and harmonic balance influenced by sinusoidal force and resonance phenomenon and the super harmonic behaviors of the systems are investigated. Results indicate that the methods for the solution of the equation of system are effective in predicting the element's behavior. The harmonic balance method shows results that are almost equal to the average of the two other methods. Moreover, most non-linear behavior is observed in the perturbation theory. The examination of the super harmonic behavior of RVEs indicated that jump phenomena in representative model with pinned-pinned BC for a constant force are more sensitive than other conditions.
- 出版日期2016-8
