Stability analysis of restrained nanotubes placed in electromagnetic field
- PDF / 1,244,653 Bytes
- 12 Pages / 595.276 x 790.866 pts Page_size
- 57 Downloads / 170 Views
(0123456789().,-volV)(0123456789(). ,- volV)
TECHNICAL PAPER
Stability analysis of restrained nanotubes placed in electromagnetic field Bu¨s¸ra Uzun1
•
Ug˘ur Kafkas1
•
Mustafa O¨zgu¨r Yaylı1
Received: 13 March 2020 / Accepted: 8 April 2020 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this present work, buckling analysis of restrained nanotubes placed in electromagnetic field is studied on the basis of Euler–Bernoulli beam theory in conjunction with Eringen’s nonlocal elasticity theory. The modal displacement function is assumed for the stability analysis in order to discretize the derived governing equation. A Fourier sine series with Stoke’s transformation is utilized to investigate the buckling response. The essential advantage of this transformation is its ability of dealing with various boundary conditions to determine the buckling loads. For demonstrate the effects of various parameters such as Hartmann parameter, spring parameter and mode number on the stability response and critical buckling load of electromagnetic nanobeam a detailed study is presented. Variations of buckling loads, critical buckling loads and buckling load ratios of the nanobeam are exhibited with a number of tables and plotted figures. The results obtained from the analysis are discussed on the tables and figures.
1 Introduction Nanobeams (carbon nanotubes) have been come the focal points of researches in recent years with technological progress. Various applications of nanobeams are observed in many areas, especially electronics, engineering and medicine. Nanobeams with superior mechanical and electrical properties are emerging with potential applications in electronics, optics and other areas of nanotechnology. Typical sizes of nanobeams are in sub-microns and microns. However classical continuum theories such as Euler–Bernoulli (Khalili et al. 2010; Li and Batra 2013; Avcar 2014), Timoshenko (Li and Batra 2013) and some higher-order shear deformation (Giunta et al. 2011) beam theories are theories that without size parameter. These theories are not efficient at the computability of small-size effects resulting from lack of the size parameters. To & Bu¨s¸ ra Uzun [email protected] Ug˘ur Kafkas [email protected] ¨ zgu¨r Yaylı Mustafa O [email protected] 1
Department of Civil Engineering, Faculty of Engineering, Bursa Uludag University, Go¨ru¨kle Campus, 16059 Bursa, Turkey
overcome small-size effects, nonclassical continuum theories are used. Differential equation type, integral type or gradient nonlocal elasticity type models abandons the classical elasticity assumption of the local model and has stated that stress is not just dependent to strain on that point. There are various size-dependent theories such as strain gradient theory (Mindlin 1965; Aifantis 1999), couple stress theory (Mindlin and Tiersten 1962; Toupin 1962; Mindlin 1963; Koiter 1964), micropolar theory (Eringen 1967), nonlocal elasticity theory (Eringen 1972, 1983), modified strain gradient theory (Lam et al. 2003), mo
Data Loading...
