Abstract
Free vibration of a bimaterial circular nano-tube is investigated. The tube is formed by bonding together a Si3N4/SUS304 functionally graded upper semi tube and a ZrO2/Ti-6Al-4V functionally graded lower semi tube. The material properties of the tube are assumed to vary along the radius according to power law with the power index of upper semi tube differing from that of lower semi tube. Based on non-local elasticity theory and Hamilton’s principle, a refined beam model considering the effect of transverse shear deformation is used to derive the governing equations, then analytical solution is obtained by using a two-steps perturbation method. Our results were compared with the existing ones. The effects on tube’s linear and non-linear frequency are analyzed of the factors, including small scale parameter, temperature, the double volume fraction indexes, slenderness ratio and different types of beam model. A new approach is suggested in this article to change the natural frequency of the tubes by adjusting constituent materials. In contrast to conventional approach, the new one can result in more accurate frequency control in the same dimensionless size of tubes.
Highlights
Non-homogeneous composite materials composed of functionally graded material (FGM) in which the effective material properties can be changed in a certain direction have captured extensive attention in a multitude of industries (Jha et al, 2013; Koizumi, 1997)
We fully utilize above analytical solution to discuss the vibration behavior of the nanotubes consisted of functionally graded bi-semi-tubes
Table. 6 gives comparisons on non-dimension natural frequency among various types of functionally graded tubes. It can be seen from this table that the non-dimension natural frequency of the tube consisted of functionally graded bi-semitubes is between that of conventional functionally graded tube(Si3N4/SUS304) and that of conventional functionally graded tube (ZrO2/Ti-6Al-4V) when material indexes(N) of different types of functionally graded tube are equal
Summary
Non-homogeneous composite materials composed of functionally graded material (FGM) in which the effective material properties can be changed in a certain direction have captured extensive attention in a multitude of industries (Jha et al, 2013; Koizumi, 1997). With emerging new demands in manufacturing and engineering, most of the previous studies related to FGMs whose effective material properties only vary in the direction of thickness or length can’t meet those needs and challenges very well (Nemat-Alla, 2003; Fan et al, 2013; Lü et al, 2009; Wang et al, 2016; Lei et al, 2016; Gupta et al, 2015; Thang and Nguyen-Thoi, 2016). In recent years, more and more researchers have been studying structural components made of two or three-directional functionally graded materials and subjected to different types of functionally graded distribution (Şimşek, 2015; Hao and Wei, 2016; Lü et al, 2008; Nguyen et al, 2017; Pydah and Sabale, 2017; Nejad and Hadi, 2016a; Nejad and Hadi, 2016b; Nejad et al, 2016).
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