Dönel yaylar ile mesnetlenmiş bir karbon nanotüpün yerel olmayan Timoshenko kiriş teorisine göre serbest titreşim analizi

Mustafa Özgür Yaylı

Öz


Bu çalışmada dönel yaylar ile mesnetlenmiş bir karbon nanotüpün değişik sınır şartları için çözümü incelenmiştir. Küçük boyut etkisini problemin çözümüne dahil etmek için yerel olmayan elastisite teorisi kullanılmış ve Timoshenko kiriş teorisinde uygulanan kabuller göz önünde tutulmuştur. Yatay yer değiştirme fonksiyonu olarak Fourier sinüs serisi seçilmiştir. Sınır koşullarında esneklik sağlanması bakımından bir matematiksel dönüşüm olarak adlandırılan Stoke dönüşümü yüksek mertebeden sınır koşullarına uygulanmıştır. Matematiksel hesaplardan sonra içinde yay sabitleri ve boyut parametresi de bulunan bir katsayılar matrisi elde edilmiştir. Bu katsayılar matrisinin öz değerleri serbest tireşim frekanslarını vermektedir. Söz konusu katsayılar matrisinin doğal titreşim frekanslarını bulabilme yeteneği bir çok matematiksel örnekte test edilmiş ve literatürde bulunan sonuçlar ile karşılaştırılmıştır.  Çözülen örneklerden titreşim frekanslarının dönel yay sabitlerine ve yerel olmayan parametreye bağlı olarak değiştiği sonucuna ulaşılmıştır. 


Tam Metin:

PDF

Referanslar


Chong, A.C.M., Lam, D C C., Strain gradient plasticity effect in indentation hardness of polymers, Journal of Materials Research, 14, 4103-4110, (1999).

McFarland, A.W., Colton, J.S., Role of material microstructure in plate stiffness with relevance to micro cantilever sensors, Journal of Micromechanics Microengineering, 15, 1060-1067, (2005).

Bodily, B.H., Sun, C.T., Structural and equivalent continuum properties of single-walled carbon nanotubes, International Journal of Materials and Product Technology, 18(4–6), 381-397, ( 2003).

Li, C., Chou, T.W., A structural mechanics approach for the analysis of carbon nanotubes, International Journal of Solids and Structures, 40(10), 2487–2499, (2003) .

Li, C., Chou, T.W., Single-walled carbon nanotubes as ultrahigh frequency nanomechanical resonators, Physical Review B, 68(7), 073405, (2003).

Aydogdu, M., Axial vibration of the nanorods with the nonlocal continuum rod model, Physica E, 41, 5, 861–864, (2009).

Pradhan, S.C., Phadikar, J. K., Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models, Physics Letters A, 373, 11, 1062– 1069, (2009).

Reddy, J.N., Pang, S.D., Nonlocal continuum theories of beams for the analysis of carbon nanotubes, Journal of Applied Physics, 103, 2, 023511, (2008).

Ball, P., Roll up for the revolution, Nature, 414, 6860, 142–144, (2001).

Baughman, R.H., Zakhidov, A.A., de Heer, W.A., Carbon nanotubes-the route toward applications, Science, 297, 5582, 787–792, (2002).

Wang, C.M., Tan, V.B C., Zhang, Y.Y., Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes, Journal of Sound and Vibration, 294, 4, 1060–1072, (2006).

Wang, Q., Vardan, V. K., Characteristics of carbon nanotubes, International Journal of Solids and Structures, 43, 254–265, (2005).

Toupin, R.A., Elastic materials with couple-stresses, Archieve of Rational Mechanics and Analysis, 11, 385–414, (1962).

Mindlin, R.D., Tiersten, H.F., Effects of couple-stresses in linear elasticity, Archieve of Rational Mechanics and Analysis, 11, 415–448, (1962).

Eringen, A.C., Nonlocal polar elastic continua, International Journal of Engineering Science,. 10, 1–16, (1972).

Gurtin, M. E., Weissmuller, J. Larche, F., The general theory of curved deformable interfaces in solids at equilibrium, Philosophical Magazine, 78, 1093–1109, (1998).

Aifantis, E.C., Strain gradient interpretation of size effects. International Journal of Fracture, 95, 1–4, (1999).

Yang, F., Chong, A.C.M., Lam, D.C., Tong, P., Couple stress based strain gradient theory for elasticity. International Journal of Solids and Structures. 39 2731–2743, (2002).

Park, S.K., Gao, X.L., Bernoulli-Euler beam model based on a modified couple stress theory, Journal Micromechanics Microengineering 16, 2355–2359, (2006).

Ma, H.M., Gao, X.L., Reddy, J.N., A microstructure-dependent Timoshenko beam model based on a modified couple stress theory, Journal of the Mechanics and Physics of Solids 56, 3379–3391, (2008).

Simsek, M., Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory. International Journal of Engineering and Science. 48, 1721–1732, (2010).

Akgoz, B., Civalek, O., Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams. International Journal of Engineering Science. 49, 11, 1268-1280, (2011).

Kahrobaiyan, M.H., Asghari, M., Rahaeifard, M., Ahmadian M. T., A nonlinear strain gradient beam formulation. International Journal of Engineering Science, 49, 1256–1267, (2011).

Artan, R., Tepe, A., Nonlocal effects in curved single-walled carbon nanotubes, Mechanics of Advanced Materials and Structures, 18, 347–351, (2011).

Xu, L.Z., Jia, X.L., Electromechanical dynamics for micro beams. International Journal of Structural Stability and Dynamics, 6(2), 233–251, (2006).

Wang, C.M., Zhang, Y.Y., He, X.Q., Vibration of nonlocal Timoshenko beams. Nanotechnology.18, 10, 105401. (2007).

Yayli, M.Ö., An analytical solution for free vibrations of a cantilever nanobeam with a spring mass system, Int J Eng Appl Sci, 7(4), 10-18, (2016).

Yayli, M.Ö., Buckling analysis of a rotationally restrained single walled carbon nanotube.Acta Physica Polonica A. 127(3), 678-683, (2015).

Yayli, M.Ö., A compact analytical method for vibration analysis of single-walled carbon nanotubes with restrained boundary conditions, Journal of Vibration and Control. 22, 10, 2542-2555, (2016).

Yayli, M.Ö., Buckling analysis of a cantilever single-walled carbon nanotube embedded in an elastic medium with an attached spring, Micro & Nano Letters. 12, 4, 255-259, (2017) .

Benzair, A., Tounsi, A., Besseghier, A., Heireche, H., Moulay, N., Boumia, L. The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory, Journal of Physics D: Applied Physics, 41(22), 225404 (2008).

Ke, L.L., Yang, J., Kitipornchai, Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams, Composite Structures, 92(3), 676-683, (2010).


Refback'ler

  • Şu halde refbacks yoktur.


Telif Hakkı (c) 2018 Mustafa Özgür Yaylı

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.