Elastik bir ortamdaki grafen tabakanın titreşim hesabı
Grafen tabakalar uygulamada çoğu kez elastik bir malzeme ile temas halindedirler. Bu çalışmada grafentabakaların titreşim analizi yüksek mertebeden elastisite teorisi ile yapılmıştır. Grafen tabaka; elastik birortam üzerindeki ince plak şeklinde modellenmiştir. Zemin modeli olarak Winkler-Pasternak iki parametreli model kullanılmıştır. Boyut etkisine bağlı titreşim eşitliği değiştirilmiş gerilme çifti teorisi ile elde edilmiştir.Ayrık tekil konvolüsyon yöntemi ve analitik yöntem ile frekans değerleri elde edilmiştir.
Free vibration analysis of graphene sheets on elastic matrix
Graphene sheets are generally surrounded by an elastic matrix in applications. In the present study, freevibration analysis of graphene sheets is investigated via higher-order elasticity theory. Graphene sheet ismodeled via thin plate on elastic medium. Winkler-Pasternak two-parameter elastic foundation model is usedas foundation. The method of modified couple stress theory is used for size-dependent vibration. Frequencies have been calculated by discrete singular convolution and analytical method.
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- 1. Demir Ç., Civalek Ö., Torsional and longitudinal frequency and wave response of microtubules based on the nonlocal continuum and nonlocal discrete models, Appl. Math. Modell., 37 (22), 9355-9367, 2013.
- 2. Civalek Ö., Demir Ç., Akgöz B., Static analysis of single walled carbon nanotubes (SWCNT) based on Eringen’s nonlocal elasticity theory, Int. J. Eng. Appl. Sci., 1 (2), 47-56, 2009.
- 3. Akgöz B., Civalek Ö., Modeling and analysis of microsized plates resting on elastic medium using the modified couple stress theory, Meccanica, 48 (4), 863- 873, 2013.
- 4. Shen H.S., Nonlocal shear deformable shell model for postbuckling of axially compressed microtubules embedded in an elastic medium, Biomech. Model. Mechanobiol., 9 (3), 345-357, 2010.
- 5. Akgöz B., Civalek Ö., Longitudinal vibration analysis for microbars based on strain gradient elasticity theory, J. Vib. Control, 20 (4), 606-616, 2014
- 6. Akgöz B., Civalek Ö., Thermo-mechanical buckling behavior of functionally graded microbeams embedded in elastic medium, Int. J. Eng. Sci., 85, 90-104, 2014.
- 7. Akgöz B., Civalek Ö., A new trigonometric beam model for buckling of strain gradient microbeams, Int. J. Mech. Sci., 81, 88-94, 2014.
- 8. Akgöz B., Civalek Ö., Shear deformation beam models for functionally graded microbeams with new shear correction factors, Compos. Struct., 112, 214-225, 2014.
- 9. Tsiatas G.C., A new Kirchhoff plate model based on a modified couple stress theory, Int. J. Solids Struct., 46 (13), 2757-2764, 2009.
- 10. Jomehzadeh E., Noori H.R., Saidi A.R., The sizedependent vibration analysis of micro-plates based on a modified couple stress theory, Physica E, 43 (4), 877- 883, 2011.
- 11. Pradhan S.C., Phadikar J.K., Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models, Phys. Lett. A, 373 (11), 1062-1069, 2009.
- 12. Samaei A.T., Abbasion S., Mirsayar M.M., Buckling analysis of a single-layer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory, Mech. Res. Commun., 38 (7), 481-485, 2011.
- 13. Akgöz B., Civalek Ö., Free vibration analysis for singlelayered graphene sheets in an elastic matrix via modified couple stress theory, Mater. Des., 42, 164-171, 2012.
- 14. Eichler A., Moser J., Chaste J., Zdrojek M., Wilson-Rae I., Bachtold, A., Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene, Nat. Nanotechnol., 6 (6), 339-342, 2011.
- 15. Ji Y., Choe M., Cho B., Song S., Yoon J., Ko H.C., Lee T., Organic nonvolatile memory devices with charge trapping multilayer graphene film, Nanotechnol., 23 (10), 105202-105207, 2012.
- 16. Murmu T., Adhikari S., Nonlocal mass nanosensors based on vibrating monolayer graphene sheets, Sens. Actuators, B, 188, 1319-1327, 2013.
- 17. Toupin R.A., Theories of elasticity with couple-stress, Arch. Ration. Mech. Anal.,17 (2), 85-112, 1964.
- 18. Mindlin R.D., Second gradient of strain and surfacetension in linear elasticity, Int. J. Solids Struct., 1 (4), 417-438, 1965.
- 19. Mindlin R.D., Tiersten H.F., Effects of couple-stresses in linear elasticity, Arch. Ration. Mech. Anal., 11 (1), 415-448, 1962.
- 20. Koiter W.T., Couple stresses in the theory of elasticity: I and II, Proc. K. Ned. Akad. Wet. B-Phys. Sci., 67, 17- 44, 1969.
- 21. Yang F., Chong A.C.M., Lam D.C.C., Tong P., Couple stress based strain gradient theory for elasticity, Int. J. Solids Struct., 39 (10), 2731-2743, 2002.
- 22. Park S.K., Gao X.-L., Bernoulli-Euler beam model based on a modified couple stress theory, J. Micromech. Microeng., 16 (11), 2355-2359, 2006.
- 23. Kong S., Zhou S., Nie Z., Wang K., The size-dependent natural frequency of Bernoulli-Euler micro-beams, Int. J. Eng. Sci., 46 (5), 427-437, 2008.
- 24. Ma H.M., Gao X.-L., Reddy J.N., A microstructuredependent Timoshenko beam model based on a modified couple stress theory, J. Mech. Phys. Solids, 56 (12), 3379-3391, 2008.
- 25. Ventsel E. ve Krauthammer T., Thin Plates and Shells: Theory, Analysis, and Applications, CRC Press, 2001.
- 26. Pradhan S.C., Murmu T., Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory, Physica E, 42 (5), 1293-1301, 2010.
- 27. Reddy J.N., Theory and Analysis of Elastic Plates and Shells, second ed. Taylor & Francis, Philadelphia, 2007.
- 28. Erdinç M.C., Elastik zemine oturan grafen tabakaların mekanik özelliklerinin belirlenmesi, Yüksek Lisans Tezi, Akdeniz Üniversitesi, Fen bilimleri Enstitüsü, Antalya, 2016.
- 29. Wei G.W., Discrete singular convolution for the solution of the Fokker–Planck equation, J. Chem. Phys., 110 (18), 8930-8942, 1999.
- 30. Wei G.W., Solving quantum eigenvalue problems by discrete singular convolution, J. Phys. B: At. Mol. Opt. Phys., 33 (3), 343-352, 2000.
- 31. Wei G.W., Discrete singular convolution for the sineGordon equation, Physica D, 137 (3), 247-259, 2000.
- 32. Wei G.W., A unified approach for the solution of the Fokker-Planck equation J. Phys. A: Math. Gen., 33 (27), 4935-4953, 2000.
- 33. Wei G.W., Wavelets generated by using discrete singular convolution kernels, J. Phys. A: Math. Gen., 33 (47), 8577-8596, 2000.
- 34. Wei G.W., Yun G., Conjugate filter approach for solving Burgers’ equation, J. Comput. Appl. Math., 149 (2), 439-456, 2002.
- 35. Wei G.W., Zhao Y.B., Xiang Y., Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm, Int. J. Numer. Methods Eng., 55 (8), 913-946, 2002.
- 36. Wei G.W., Zhao Y.B., Xiang Y., A novel approach for the analysis of high-frequency vibrations, J. Sound Vib., 257 (2), 207-246, 2002.
- 37. Wei G.W., Vibration analysis by discrete singular convolution, J. Sound Vib., 244 (3), 535-553, 2001.
- 38. 38. Wei G.W., Discrete singular convolution for beam analysis, Eng. Struct. , 23 (9), 1045-1053, 2001.
- 39. Wei G.W., Zhao Y.B., Xiang Y., The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution, Int. J. Mech. Sci., 43 (8), 1731-1746, 2001.
- 40. Zhao S., Wei G.W., Xiang Y., DSC analysis of freeedged beams by an iteratively matched boundary method, J. Sound Vib., 284 (1), 487-493, 2005.
- 41. Civalek Ö., The determination of frequencies of laminated conical shells via the discrete singular convolution method, J. Mech. Mater. Struct., 1 (1), 163- 182, 2006.
- 42. Civalek Ö., Fundamental frequency of isotropic and orthotropic rectangular plates with linearly varying thickness by discrete singular convolution method, Appl. Math. Modell., 33 (10), 3825-3835, 2009.
- 43. Civalek Ö., Free vibration and buckling analysis of composite plates with straight-sided quadrilateral domain based on DSC approach, Finite Elem. Anal. Des., 43 (13), 1013-1022, 2007.
- 44. Civalek Ö., Gürses M., Free vibration analysis of rotating cylindrical shells using discrete singular convolution technique, Int. J. Press. Vessels Pip., 86 (10), 677-683, 2009.
- 45. Çakır M.T., Improving the efficiency performance of heat pipes using Alumina containing nano-fluids, Journal of the Faculty of Engineering and Architecture of Gazi University, 30 (4), 547-556, 2015.
- 46. Gökmeşe H., Bostan B., Microstructural characterization and synthesis by mechanochemical method of nano particle Al2O3/B4C ceramic phase, Journal of the Faculty of Engineering and Architecture of Gazi University, 29 (2), 289-297, 2014.
- 47. Çiloğlu D., Bölükbaşı A., Çifci H., Experimental investigation of pool boiling heat transfer in nanofluids around spherical surfaces, Journal of the Faculty of Engineering and Architecture of Gazi University, 30 (3), 405-415, 2015.
- 48. Turgut A., Sağlanmak Ş., Doğanay S., Experimental investigation on thermal conductivity and viscosity of nanofluids: particle size effect, Journal of the Faculty of Engineering and Architecture of Gazi University, 31 (1), 95-103, 2016.
- 49. Lin R.M., Nanoscale vibration characterization of multilayered graphene sheets embedded in an elastic medium, Comput. Mater. Sci., 53 (1), 44-52, 2012.
- 50. 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, Int. J. Mech. Sci., 85, 168–178, 2014.