Free and forced vibration analysis of viscoelastic damped FG-CNT reinforced micro composite beams
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TECHNICAL PAPER
Free and forced vibration analysis of viscoelastic damped FG-CNT reinforced micro composite beams M. Mohammadimehr1
•
A. A. Monajemi1 • H. Afshari1
Received: 27 March 2017 / Accepted: 16 December 2017 Springer-Verlag GmbH Germany, part of Springer Nature 2017
Abstract In this paper, free and forced vibration analysis of viscoelastic microcomposite beam reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) is studied using the modified couple stress theory (MCST). The material properties of micro composite beam by generalized rule of mixtures carbon nanotubes are estimated. In addition, these properties are stated as uniform, and functionally graded (FG) distributions in the thickness direction. Energy method and Hamilton’s principle are employed to establish the governing equations of motion for the vibration of viscoelastic damped micro composite beam reinforced by SWCNTs based on the Kelvin–Voigt model. The influences of material length scale parameter, structural damping coefficient and different distributions of SWCNTs on non-dimensional complex natural frequency and amplitude vibration of the viscoelastic micro composite beam are investigated. The results reveal that the lowest vibration amplitude of FG microcomposite beam by the FG-X and the highest occurs by FG-e. Moreover, in the presence of external periodic load and the absence of structural damping coefficient, the vibration amplitude increases and FG microcomposite beam becomes unstable, even though the amplitude of vibration decreases with increasing structural damping coefficient. It is shown that the natural frequency of SWCNT reinforced composite is more than the frequency of multi-walled carbon nanotubes because SWCNT have more stiffness. In addition, the results illustrate that the experimental data by Lei et al. agree well with those predicted by the MCST in the present work.
1 Introduction The considerable mechanical properties by carbon nanotubes (CNTs) have attracted much attention because of the elastic modulus and tensile strength of CNTs reinforced microcomposite are much harder and stronger than steel, while the much lighter (Esawi and Farag 2007). The CNTs reinforced composite have many applications in various fields such as electromechanical devices, microsensors, biosensors, aerospace and shipping. Recently, many studies have been done in vibration analysis of micro/nano structures and functionally graded carbon nanotube (FG-CNT) reinforced composite materials. Yas and Samadi (2012) investigated free vibration and buckling analysis of nanocomposite Timoshenko beams reinforced by singlewalled carbon nanotubes (SWCNTs) resting on an elastic foundation. They concluded that the beams with FG-X & M. Mohammadimehr [email protected] 1
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
distribution have higher fundamental frequency as well as critical buckling load in comparison with other dis
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