Frequency and Mode Shapes of Au Nanowires Using the Continuous Beam Models

Abstract

Free vibration analysis of Au nanowires has been investigated. Au nanowire is modeled via thin beam using the linear theory. Three-different cross-sections such as circular, rectangular and triangular are taken into consideration for ultra thin nanowires. Frequency values have been obtained for different geometric parameters and simply supported of boundary condition. This study is helpful for design of the nanowires based instruments in modern NEMS technology.

Keywords

• Nanowires,Au,Frequency,Mode shapes,Mechanical properties

References

1. [1] Li, Y., Song, J., Fang, B., Zhang, J., Surface effects on the postbuckling of nanowires, Journal of Physics D: Applied Physics, 44, 425304, 2011.
2. [2] Wang D, Zhao, J, Hu, S, Yin X, Liang S, Liu Y, Deng S., Where, and how, does a nanowire break?, Nano Letter, 7, 1208, 2007.
3. [3] Wang Z, Zu, X, Gao F, Weber W.J., Atomistic simulations of the mechanical properties of silicon carbide nanowires, Phys. Rev. B., 77, 224113, 2008.
4. [4] Miller R.E., Shenoy V.B., Size-dependent elastic properties of nanosized structural elements, Nanotechnology,11, 139, 2000.
5. [5] Kutucu B., Nanoteknoloji ve Çift Duvarlı Karbon Nanotüplerin İncelenmesi, Yüksek Lisans Tezi, İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2010.
6. [6] Uzun, B., Karbon Nanotüplerin Kiriş Modeli ve Titreşim Hesabı, Lisans Tezi, Akdeniz Üniversitesi, 2016.
7. [7] Yetim, A., Karbon Nanotüpler, Yüksek Lisans Tezi, Çukurova Üniversitesi, 2011.
8. [8] Wei, G.W., Discrete singular convolution for the solution of the Fokker–Planck equations. J Chem Phys, 110, 8930-8942, 1999.

9. [9] Wei, G.W., Solving quantum eigenvalue problems by discrete singular convolution, J.Phys. B: At. Mol.Opt.Phys. 33, 343-352, 2000.
10. [10]Wei, G.W., Discrete singular convolution for the Sine-Gordon equation, Physica D, 137, 247-259, 2000.
11. [11]Wei, G.W., A unifed approach for the solution of the Fokker-Planck equation, J.Phys. A:Math. Gen., 33, 4935-4953, 2000.
12. [12]Wei, G.W., Wavelets generated by using discrete singular convolution kernels, J.Phys.A: Math.Gen., 33, 8577-8596, 2000.
13. [13] Wei, G.W., Zhang, D.S., Althorpe, S.C., Kouri, D.J., Hoffman, D.K., Wavelet-distributed approximating functional method for solving the Navier-Stokes equation, Comp. Physics Commun., 115, 18-24, 1998.
14. [14]Wei, G.W., Kouri, D.J., Hoffman, D.K., Wavelets and distributed approximating functionals, Comp. Physics Commun. 112, 1-6, 1998.
15. [15]Zhao, S., Wei, G.W., Xiang, Y., DSC analysis of free-edged beams by an iteratively matched boundary method, J. Sound Vibr. 284, 487-493, 2005.
16. [16]Hou, Z.J., Wei, G.W., A new approach to edge detection, Pattern Recognition, 35, 1559-1570, 2002.
17. [17] Lim, C.W., Li, Z.R., Xiang, Y., Wei, G.W., Wang, C.M., On the missing modes when using the exact frequency relationship between Kirchhoff and Mindlin plates, Advances in Vibration Eng. 4, 221-248, 2005.
18. [18] Lim, C.W., Li, Z.R., Wei, G.W., DSC-Ritz method for high-mode frequency analysis of thick shallow shells, Int. J. Num. Methods Eng., 62, 205-232, 2005.
19. [19] Civalek, Ö., An efficient method for free vibration analysis of rotating truncated conical shells, Int. J. Pressure Vessels and Piping 83, 1-12, 2006.
20. [20]Civalek, Ö., Three-dimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method, Int. J. Mech. Sciences 49, 752-765, 2007.
21. [21]Civalek, Ö., Nonlinear analysis of thin rectangular plates on Winkler-Pasternak elastic foundations by DSC-HDQ methods, Applied Mathematical Modeling 31, 606-624, 2007.
22. [22]Civalek, Ö., Free vibration analysis of composite conical shells using the discrete singular convolution algorithm, Steel and Composite Structures, 6(4), 353-366, 2006.
23. [23]Civalek, Ö., Numerical analysis of free vibrations of laminated composite conical and cylindrical shells: discrete singular convolution (DSC) approach, Journal of Computational and Applied Mathematics, 205, 251– 271, 2007.
24. [24]Civalek, Ö., Korkmaz, A.,Ç Demir, Ç., Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two-opposite edges
25. Advances in Engineering Software, 41, 557-560, 2010.
26. [25]Gürses, M., Akgöz, B., Civalek, Ö., Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation, Applied Mathematics and Computation, 219, 3226-3240, 2012.
27. [26]Gürses, M., Civalek, Ö., Korkmaz, A.K., Ersoy, H., Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first-order shear deformation theory. International journal for numerical methods in engineering, 79, 290-313, 2009.
28. [27]Civalek, Ö., Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches,
29. Composites Part B: Engineering, 50, 171-179, 2013.
30. [31]Mercan, K., Civalek, Ö., Buckling Analysis of Silicon Carbide Nanotubes (SiCNTs), International Journal of Engineering & Applied Sciences, 8 (2), 101-108, 2016.
31. [32]Demir, Ç., Civalek, Ö., Nonlocal Finite Element Formulation for Vibration, International Journal of Engineering & Applied Sciences, 8(2), 109-117, 2016.
32. [33]Demir, Ç., Civalek, Ö., Nonlocal deflection of microtubules under point load, International Journal of Engineering and Applied Sciences, 7(3), 33-39, 2015.
33. [34]Akgöz, B., Civalek, Ö., Analysis of microtubules based on strain gradient elasticity and modified couple stress theories, Advances in Vibration Engineering, 11(4), 385-400, 2012.
34. [35] Rao S.S., Vibration of Continuous Systems, John Wiley & Sons, 2007.
35. 27
36. [28]Civalek, Ö., Diferansiyel Quadrature Metodu ile Elastik Çubukların Statik, Dinamik Ve Burkulma Analizi, XVI Mühendislik Teknik Kongresi, Kasım, ODTÜ, Ankara, 2001.
37. [29]Civalek, Ö., Ülker, M., HDQ-FD integrated methodology for nonlinear static and dynamic response of doubly curved shallow shells, Struct Eng Mech, 19(5), 535-550, 2005.
38. [30]Civalek, Ö., Nöro-Fuzzy Tekniği ile Dikdörtgen Plakların Analizi, III. Ulusal Hesaplamalı Mekanik Konferansı, 1998.