عنوان مقاله [English]
نویسندگان [English]چکیده [English]
The main aim of this paper is to investigate the nonlinear free transverse vibration of representative volume element (RVE) of nanocomposites based on multiscale method, in order to predict the vibration behavior of nanocomposite beam at macro scale. To reach this object, first, mechanical properties of volume element containing carbon nanotube (CNT) is determined. In this regard, various RVEs with different length ratios are considered, where each of them represents a kind of distribution in the nanocomposite environment. Then with finite element modeling and analytical solutions, in linear domain, modal analysis of CNTs and RVEs are investigated. The results indicate that the higher ratio of nanotubes, which represents the uniform distribution of the nanotubes in the resin, has a higher natural frequency. Also, the results of analytical solution have shown good agreement with the FE modeling. In order to further validate the results of modal analysis is performed on CNT and compared with previous studies. Then, the vibration equations of volume element based on the Von-Kármán theory are obtained and nonlinear free vibration behavior of RVEs are investigated in different boundary conditions. The nonlinear frequency of volume element as a function of vibration amplitude showed that the boundary conditions and dispersion state of CNTs have a great effect on the rate of the system nonlinear behavior. Results indicate that in clamp-pinned condition the nonlinear frequency rate is approximately 20% more than clamp-clamp condition and also the values of frequency increase by improving the dispersion state of system.
 M. C. Weisenberger, R. Andrew, Carbon nanotube polymer composites, Solid State & Materials Science, Vol. 8, No. 1, pp. 31-37, 2004.
 R. F. Gibson, E. O. Ayorinde, Y. F. Wen, Vibrations of carbon nanotubes and their composites: A review, Composites Science and Technology, Vol. 67, No. 1, pp. 1-28, 2007.
 M. Simsek, Vibration analysis of a single-walled carbon nanotube under action of a moving harmonic load based on nonlocal elasticity theory, Physica E, Vol. 43, No. 1, pp. 182-191, 2010.
 M. Aydogdu, A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration, Physica E, Vol. 41, No. 9, pp. 1651-1655, 2009.
 P. Soltani, A. Kassaei, M. M. Taherian, A. Farshidianfar, Vibration of wavy single-walled carbon nanotubes based on nonlocal Euler Bernoulli and Timoshenko models, International Journal of Advanced Structural Engineering, Vol. 4, No. 3, pp. 1-10, 2012.
 J. N. Lü, H. B. Chen, P. Lü, P. Q. Zhang, Research of natural frequency of single-walled carbon nanotube, Chinese Journal of Chemical Physics, Vol. 20, No. 5, pp. 525-530, 2007.
 S. K. Georgantzinos, N. K. Anifantis, Vibration analysis of multi-walled carbon nanotubes using a spring-mass based finite element model, Computational Materials Science, Vol. 47, No. 1, pp. 168-177, 2009.
 S. Brischetto, A continuum elastic three-dimensional model for natural frequencies of single-walled carbon nanotubes, Composites Part B: Engineering, Vol. 61, pp. 222-228, 2014.
 M. Jamal-Omidi, M. ShayanMehr, R. Mosalmani, Investigating the effect of interphase and surrounding resin on carbon nanotube free vibration behavior, Physica E, Vol. 68, pp. 42-52, 2015.
 Z. Hong, D. Qing-tian, L. Shao-hua, Vibration of a single-walled carbon nanotube embedded elastic medium under a moving internal nanoparticle, Applied Mathematical Modelling, Vol. 37, No. 10-11, pp. 6940-6951, 2013.
 T. Murmu, S. Adhikari, Nonlocal elasticity based vibration of initially pre-stressed coupled nanobeam systems, European Journal of Mechanics-A/Solids,Vol. 34, pp. 52-62, 2012.
 K. I. Tserpes, A. Chanteli, Parametric numerical evaluation of the effective elastic properties of carbon, nanotube-reinforced polymers, Composite Structures, Vol. 99, pp. 366-374, 2013.
 R. Rafiee, Analysis of nonlinear vibrations of a carbon nanotube using perturbation technique, Modares Mechanical Engineering, Vol. 12, No. 3, pp. 60-67, 2012. (in Persianفارسی )
 M. R. Ayatollahi, S. Shadlou, M. M. Shokrieh, Multiscale modeling for mechanical properties of carbon nanotube reinforced nanocomposites subjected to different types of loading, Composite Structures, Vol. 93, No. 9, pp. 2250-2259, 2011.
 J. N. Reddy, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Mechanical Sciences, Vol. 45, No. 2-8, pp. 288-307, 2007.
 R. F. Gibson, Principles of Composite Material Mechanics, Second Edittion, pp. 97-134, CRC Press, 2007.
 A. Al Masud, A. K. M. Masud, Effect of interphase characteristic and property on axial modulus of carbon nanotube based composites, Journal of Mechanical Engineering ME, Vol. 41, No. 1, pp. 15-24, 2010.
 K. I. Tserpes, P. Papanikos, G., N. Labeas, Sp. G. Pantelakis, Multi-scale modeling of tensile behavior of carbon nanotube-reinforced composites, Theoretical and Applied Fracture Mechanics, Vol. 49, No. 1, pp. 51-60, 2008.
 M. J. S. Zuberi, V. Esat, Investigating the mechanical properties of single walled carbon nanotube reinforced epoxy composite through finite element modeling, Composites Part B: Engineering, Vol. 71, pp. 1-9, 2015.
 M. Zakeri, M. Shayanmehr, M. M. Shokrieh, Interface modeling of nanotube reinforced nanocomposites by using multi-scale modeling method, Modares Mechanical Engineering, Vol. 12, No. 5, pp. 1-11, 2013. (in Persianفارسی )
 A. H. Esbati, S. Irani, Mechanical properties and fracture analysis of functionalized carbon nanotube embedded by polymer matrix, Aerospace Science and Technology, Vol. 55, pp. 120-130, 2016.
 A. Fereidoon, , R. Rafiee, R. Maleki Moghadam, A modal analysis of carbon-nanotube-reinforced polymer by using a multicale finite-element method, Mechanics of Composite Materials, Vol. 49, No. 3, pp. 325-332, 2013.
 P. Joshi, S. H. Upadhyay, Evaluation of elastic properties of multi walled carbon nanotube reinforced composite, Computational Materials Science, Vol. 81, pp. 332-338, 2014.
 S. C. Her, C. Y. Lai, Dynamic behavior of nanocomposites reinforced with multi-walled carbon nanotubes (MWCNTs), Materials, Vol. 6, No. 6, pp. 2274-2284, 2013.
 C. DeValve, R. Pitchumani, Experimental investigation of the damping enhancement in fiber-reinforced composites with carbon nanotubes, Carbon, Vol. 63, pp. 71-83, 2013.
 R. Moradi-Dastjerd, M. Foroutan, A. Pourasghar, Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method, Materials & Design, Vol. 44, pp. 256-266, 2013.
 L. L. Ke, J. Yang, S. Kitipornchai, Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams, Composite Structures, Vol. 92, No. 3, pp. 676-683, 2010.
 P. Zhu, Z. X. Lei, K. M. Liew, Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory, Composite Structures, Vol. 94, No, 4, pp. 1450-1460, 2013.
 Z. X. Lei, K. M. Liew, J. L. Yu, Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment, Composite Structures, Vol. 106, pp. 128-138, 2013.
 S. S. Rao, Mechanical Vibration, Florida: Pearson Prentice Hall, 2005.