Elastik bir ortamdaki grafen tabakanın titreşim hesabı

Çiğdem Demir, Bekir Akgöz, Mehmet Cihad Erdinç, Kadir Mercan, Ömer Civalek
288 48

Öz


Grafen tabakalar uygulamada çoğu kez elastik bir malzeme ile temas halindedirler.  Bu çalışmada grafen tabakaların titreşim analizi yüksek mertebeden elastisite teorisi ile yapılmıştır. Grafen tabaka; elastik bir ortam üzerindeki ince plak şeklinde modellenmiştir. Zemin modeli olarak Winkler –Pasternak iki parametreli model kullanılmıştır. Boyut etkisine bağlı titreşim denklemi değiştirilmiş gerilme çifti yöntemi ile elde edilmiştir. Ayrık tekil konvolüsyon yöntemi ve analitik yöntem ile frekans değerleri elde edilmiştir.


Anahtar kelimeler


Nanoteknoloji; grafen tabakalar; titreşim; boyut etkisi

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Referanslar


Ventsel, E., Krauthammer, T., “Thin plates and shells: Theory, analysis, and applications”, CRC press, 2001.

Civalek, Ö., Demir, Ç. ve Akgöz, B., “Static analysis of single walled carbon nanotubes (SWCNT) based on Eringen’s nonlocal elasticity theory”, International Journal of Engineering and Applied Sciences, 47-56, 2009.

Akgöz, B., Civalek, Ö., “Free vibration analysis for single-layered graphene sheets in an elastic matrix via modified couple stress theory”, Materials & Design, Cilt 42, 164-171, 2012.

Akgöz, B., Civalek, Ö., “Buckling analysis of functionally graded microbeams based on the strain gradient theory”, Acta Mechanica, Cilt 224, No 9, 2185-2201, 2013.

Pradhan, S.C., Phadikar, J.K., “Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models” Physics Letters A, Cilt 373, No 11, 1062-1069, 2009.

Tsiatas, G.C., “A new Kirchhoff plate model based on a modified couple stress theory”, International Journal of Solids and Structures, Cilt 46, No 13, 2757-2764, 2009.

Akgöz, B., Civalek, Ö., “Modeling and analysis of micro-sized plates resting on elastic medium using the modified couple stress theory”, Meccanica, Cilt 48, No 4, 863-873, 2013.

Akgöz, B., Civalek, Ö., “Longitudinal vibration analysis for microbars based on strain gradient elasticity theory”, Journal of Vibration and Control, Cilt 20, No 4, 606-616, 2014.

Akgöz, B., Civalek, Ö., “Shear deformation beam models for functionally graded microbeams with new shear correction factors”, Composite Structures, Cilt 112, 214-225, 2014.

Akgöz, B., Civalek, Ö., “A new trigonometric beam model for buckling of strain gradient microbeams”, International Journal of Mechanical Sciences, Cilt 81, 88-94, 2014.

Akgöz, B., Civalek, Ö., “Thermo-mechanical buckling behavior of functionally graded microbeams embedded in elastic medium”, International Journal of Engineering Science, Cilt 85, 90-104, 2014.

Jomehzadeh, E., Noori, H.R. ve Saidi, A.R., “The size-dependent vibration analysis of micro-plates based on a modified couple stress theory”, Physica E, Cilt 43, No 4, 877-883, 2011.

Samaei, A.T., Abbasion, S. ve Mirsayar, M.M., “Buckling analysis of a single-layer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory”, Mechanics Research Communications, Cilt 38, No 7, 481-485, 2011.

Toupin, R.A., “Theory of elasticity with couple stresses”, Archive for Rational Mechanics and Analysis., Cilt 17, 85–112, 1964.

Mindlin, R.D., “Second gradient of strain and surface-tension in linear elasticity”, International Journal of Solids and Structures, Cilt 1, No 4, 417-438, 1965.

Mindlin, R.D., Tiersten, H.F., “Effects of couple-stresses in linear elasticity”, Archive for Rational Mechanics and Analysis, Cilt 11, No 1, 415–448, 1962.

Koiter, W.T., “Couple stresses in the theory of elasticity: I and II”, Proc. K. Ned. Akad. Wet. B-Phys. Sci., Cilt 67, 17–44, 1969.

Yang, F., Chong, A.C.M. ve Lam, D.C.C. ve Tong, P., “Couple stress based strain gradient theory for elasticity”, International Journal of Solids and Structures Cilt 39, No 10, 2731-2743, 2002.

Park, S.K., Gao, X.-L., “Bernoulli-Euler beam model based on a modified couple stress theory”. Journal of Micromechanics and Microengineering., Cilt 16, No 11, 2355-2359, 2006.

Kong, S., Zhou, S., Nie, Z. ve Wang, K., “The size-dependent natural frequency of Bernoulli-Euler micro-beams”, International Journal of Engineering Science, Cilt 46, No 5, 427-437, 2008.

Ma, H.M., Gao, X.-L. ve Reddy, J.N., “A microstructure-dependent Timoshenko beam model based on a modified couple stress theory”, Journal of the Mechanics and Physics of Solids, Cilt 56, No 12, 3379-3391, 2008.

Erdinç, M.C., Elastik zemine oturan grafen tabakaların mekanik özelliklerinin belirlenmesi, Yüksek Lisans Tezi, Akdeniz Üniversitesi, Fen bilimleri Enstitüsü, 2016.

Wei, G.W., “Discrete singular convolution for the solution of the Fokker–Planck equations”, Journal of Chemical Physics, Cilt 110, 8930-8942, 1999.

Wei, G.W., “Solving quantum eigenvalue problems by discrete singular convolution”, The Journal of Physics B: Atomic, Molecular and Optical Physics, Cilt 33, 343-352, 2000-a.

Wei, G.W., “Discrete singular convolution for the Sine-Gordon equation”, Physica D, Cilt 137, 247-259, 2000-b.

Wei, G.W., “A unified approach for the solution of the fokker-planck equation”, Journal of Physics A : Mathematical and General., Cilt 33, 4935-4953, 2000-c.

Wei, G.W., “Wavelets generated by using discrete singular convolution kernels”, Journal of Physics A : Mathematical and General., Cilt 33, 8577-8596, 2000-d.

Wei, G.W., Yun, G., “Conjugate filter approach for solving burgers’ equation”, Journal of Computational and Applied Mathematics, Cilt 149, 439-456, 2002.

Wei, G.W., Zhao, Y.B., ve Xiang, Y., “Discrete singular convolution and its application to the analysis of plates with internal supports; part 1: theory and algorithm”, International Journal for Numerical Methods in Engineering, Cilt 55, 913-946, 2002.

Wei, G.W., Zhao, Y.B. ve Xiang, Y., “A novel approach for the analysis of high-frequency vibrations”, Journal of Sound and Vibration, Cilt 257, No 2, 207-246, 2002-a.

Wei, G.W., “Vibration analysis by discrete singular convolution”, Journal of Sound and Vibration, Cilt 244, 535-553, 2001-a.

Wei, G.W., “Discrete singular convolution for beam analysis”, Engineering Structures, Cilt 23, 1045-1053, 2001-b.

Wei, G.W., Zhao, Y.B. ve Xiang, Y., “The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution”, International Journal of Mechanical Sciences, Cilt 43, 1731-1746, 2001.

Zhao, S., Wei, G.W. ve Xiang, Y., “DSC analysis of free-edged beams by an iteratively matched boundary method”, Journal of Sound Vibration, Cilt 284, 487-493, 2005.

Civalek, Ö., “The determination of frequencies of laminated conical shells via the discrete singular convolution method”, Journal of Mechanics of Materials and Structures, Cilt 1, No 1, 163-182, 2006.

Civalek, Ö., “Fundamental frequency of isotropic and orthotropic rectangular plates with linearly varying thickness by discrete singular convolution method”, Applied Mathematical Modelling, Cilt 33, No 10, 3825-3835, 2009.

Civalek, Ö., “Free vibration and buckling analysis of composite plates with straightsided quadrilateral domain based on DSC approach”, Finite Elements in Analysis and Design, Cilt 43, No 13, 1013-1022, 2007.

Civalek, Ö., Gürses, M., “Free vibration analysis of rotating cylindrical shells using discrete singular convolution technique”, International Journal of Pressure Vessels and Piping, Cilt 86, No 10, 677-683, 2009.

Lin, R.M., “Nanoscale vibration characterization of multi-layered graphene sheets embedded in an elastic medium”, Computational Materials Science, Cilt 53, 44–52, 2012.

Foroushani, S.S., Azhari, M., “On the use of bubble complex finite strip method in the nonlocal buckling and vibration analysis of single-layered graphene sheets”, International Journal of Mechanical Sciences, Cilt 85, 168–178, 2014.




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