Photonic crystals in biology
Photonic crystals in biology
Photonic crystals in biology
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Poster Session, Tuesday, June 15<br />
Theme A1 - B702<br />
Cont<strong>in</strong>uum Buckl<strong>in</strong>g Analysis of Double-Walled Carbon Nanotubes with Different Inner and Outer<br />
Boundary Conditions<br />
Seck<strong>in</strong> Filiz 1 , Met<strong>in</strong> Aydogdu 2 *<br />
1 Graduate School of Natural and Applied Sciences, Trakya University, Edirne, Turkey<br />
2 Department of Mechanical Eng<strong>in</strong>eer<strong>in</strong>g, Trakya University, Edirne, 22180, Turkey<br />
Abstract- Buckl<strong>in</strong>g of <strong>in</strong>-plane loaded doublewalled carbon nanotubes is studied by us<strong>in</strong>g cont<strong>in</strong>uum Euler-Bernoulli beam theory. Different<br />
boundary conditions are assumed for <strong>in</strong>ner and outer carbon nanotubes. A f<strong>in</strong>ite difference method is proposed for the solution of govern<strong>in</strong>g<br />
equations.<br />
In recent years, small scale eng<strong>in</strong>eer<strong>in</strong>g members have been<br />
used <strong>in</strong> many scientific and <strong>in</strong>dustrial applications. Carbon<br />
nanotubes are one of these small elements which are used due<br />
to their extraord<strong>in</strong>ary mechanical, electrical, low weight and<br />
optical properties [1-4].<br />
Mechanical properties of CNTs were studied by some<br />
researchers <strong>in</strong> the last two decades. Buckl<strong>in</strong>g is one of the<br />
problems which occur due to external loads. Studies related<br />
with static and dynamic analysis of CNTs can be divided <strong>in</strong> to<br />
two parts: molecular dynamic simulations [5-7] and<br />
cont<strong>in</strong>uum mechanics models [8-10]. In the previous studies it<br />
was shown that molecular dynamic simulations are limited<br />
with small number of atoms and short time <strong>in</strong>tervals. Due to<br />
this fact cont<strong>in</strong>uum beam and shell models were used <strong>in</strong> the<br />
previous analysis [8-10]. It is important to mention that<br />
previous studies are limited to simply supported boundary<br />
conditions or same boundary conditions for all nested carbon<br />
nanotubes. In the real eng<strong>in</strong>eer<strong>in</strong>g applications it is possible to<br />
have different boundary conditions for nested CNTs. Actually<br />
it is not possible to have a classical boundary conditions for<br />
<strong>in</strong>ner tubes other then free one. This important issue is not<br />
considered <strong>in</strong> the previous studies.<br />
In the present study, a f<strong>in</strong>ite difference cont<strong>in</strong>uum beam<br />
model based on classical Euler-Bernoulli beam theory is<br />
proposed to analyze buckl<strong>in</strong>g of multiwalled CNTs. After<br />
general formulation, buckl<strong>in</strong>g of double walled carbon<br />
nanotubes is studied us<strong>in</strong>g classical Euler-Bernoulli beam<br />
model. Different boundary conditions are assumed for <strong>in</strong>ner<br />
and outer CNTs. It is believed that us<strong>in</strong>g different boundary<br />
conditions for nested tubes is more realistic when compared<br />
with previous studies.<br />
In the present study, the deflections of the nested tubes are<br />
coupled through the van der Waals <strong>in</strong>tertube <strong>in</strong>teraction<br />
pressure. Nondimensional critical buckl<strong>in</strong>g loads will be given<br />
for different boundary conditions and mode numbers. The<br />
proposed f<strong>in</strong>ite difference formulation of multiwalled CNT<br />
can also be used for other dynamic and static analysis of CNT<br />
related problems.<br />
[8] J. Yoon, C.Q. Ru, A. Mioduchowski, Compos. Part B-Eng. 35,<br />
87(2004).<br />
[9] M. Aydogdu, M.C. Ece, Turkish J. Eng. Env. Sci. 31, 305 (2007).<br />
[10] M. Aydogdu, Physica E. 41, 1651 (2009).<br />
*Correspond<strong>in</strong>g author: met<strong>in</strong>a@trakya.edu.tr<br />
[1] S. Iijima, Nature (London) 354, 56 (1991).<br />
[2] P. Kim and C.M. Lieber, Science 286, 2148 (1999).<br />
[3] J. Kong, Science 287, 622 (2000).<br />
[4] E.T. Thostenson, Z. Ren and T.W. Chou, Comp.Sci. Techno l. 61,<br />
1899 ( 2001).<br />
[5] B.I. Yakobson, C.J. Brabec and J.Bernholc, Phys. Rev.Lett. 76,<br />
19<br />
71 (1996).<br />
[6] B.I. Yakobson and R.E. Smalley, Am.Sci., 85, 324 (1997).<br />
[7] Y.G. Hu, K.M. Liew, Q. Wang, X.Q. He, B.I. Yakobson, J. Mech.<br />
Phys. Solids 56, 3475 (2008).<br />
6th Nanoscience and Nanotechnology Conference, zmir, 2010 382