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Yerel olmayan elastisite teorisine göre üç mesnetli nano kirişin doğrusal olmayan titreşim davranışı

Yıl 2024, Cilt: 39 Sayı: 4, 2447 - 2462, 20.05.2024
https://doi.org/10.17341/gazimmfd.1291811

Öz

Nano ölçekli cihazların önemi her geçen gün artmaktadır. Bu nedenle nano elektromekanik yapılarda nano kiriş, nano levha, nano çubuk vb. nano yapılar son zamanlarda mühendislerin odak noktası olmuştur. Bu noktadan hareketle, sunulan çalışmada üç mesnetli nano kirişin doğrusal olmayan titreşim davranışı sayısal olarak incelenmiştir. İlk olarak doğrusal doğal frekanslar hesaplanmış ve ardından doğrusal olmayan düzeltme terimleri sayesinde doğrusal olmayan doğal frekanslar bulunmuştur. Doğrusal olmayan davranışı açıklığa kavuşturmak için genliğe bağlı doğrusal olmayan doğal frekans değişim grafikleri ve doğrusal olmayan frekans tepki eğrileri çizilmiştir. Yerel olmayan parametre, ikinci mesnet konumu ve farklı mod etkileri kapsamlı bir şekilde incelenmiştir. Ayrıca farklı ilk ve son mesnet türleri irdelenmiştir. Yerel olmayan parametrenin ve ortadaki mesnet konumunun nano kiriş için büyük önem taşıdığı gösterilmiştir. Söz konusu durum yüksek modlarda daha net bir şekilde görülmüştür.

Kaynakça

  • 1. Kaynak B.E, Alkhaled M., Kartal E., Yanik C., Hanay M. S., Atmospheric Pressure Mass Spectrometry by Single-Mode Nanoelectromechanical Systems, Nano Letters, 23 (18), 8553–8559, 2023.
  • 2. Secme A., Pisheh H. S., Tefek U., Uslu H. D., Kucukoglu B., Alatas C., Kelleci M., Hanay M. S., On-Chip Flow Rate Sensing via Membrane Deformation and Bistability Probed by Microwave Resonators, Microfluidics and Nanofluidics, 27, 2023.
  • 3. Karakan M.Ç., Ari A.B., Kelleci M., Yanık C., Kaya I.I., Taştan Ö., Hanay M. S., Vapor Sensing of Colorectal Cancer Biomarkers in Isolation by Bare and Functionalized Nanoelectromechanical Sensors, IEEE Sensors, 23, 21113-21120, 2023.
  • 4. Aydoğdu M., A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration, Physica E: Low-dimensional Systems and Nanostructures, 41 (9), 1651-1655, 2009.
  • 5. Aya S.A., Tufekci E., Modeling and analysis of out-of-plane behavior of curved nanobeams based on nonlocal elasticity, Composites Part B: Engineering, 119, 184-195, 2016.
  • 6. Ruoccoa E., Reddy J.N., Buckling analysis of elastic–plastic nanoplates resting on a Winkler–Pasternak foundation based on nonlocal third-order plate theory, International Journal of Non-Linear Mechanics, 121, 103453, 2020.
  • 7. Malikan M., Nguyen V.B., Buckling analysis of piezo-magnetoelectric nanoplates in hygrothermal environment based on a novel one variable plate theory combining with higher-order nonlocal strain gradient theory, Physica E: Low-dimensional Systems and Nanostructures, 102, 8-28, 2018.
  • 8. Ma L.H., Ke L.L., Reddy J.N., Yang J., Kitipornchai S., Wang Y.S., Wave propagation characteristics in magneto-electro-elastic nanoshells using nonlocal strain gradient theory, Composite Structures, 199, 10-23, 2018.
  • 9. Karami B., Janghorban M., Tounsi A., Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory, Thin-Walled Structures, 129, 251-264, 2018.
  • 10. Villanueva L.G., Schmid S., Roukes M., Fundamentals of Nanomechanical Resonators, Springer International Publishing, Cham, Switzerland, 2016.
  • 11. Eringen A.C., Linear theory of nonlocal elasticity and dispersion of plane-waves, International Journal of Engineering Science, 10 (5), 233–248, 1972.
  • 12. Khaniki H.B., On vibrations of nanobeam systems. International Journal of Engineering Science, 124, 85–103, 2018.
  • 13. Ganapathi M., Polit O., Dynamic characteristics of curved nanobeams using nonlocal higher-order curved beam theory. Physica E, 91, 190-202, 2017.
  • 14. Şimşek M., Large amplitude free vibration of nanobeams with various boundary conditions based on the nonlocal elasticity theory, Composites Part B: Engineering, 56, 621-628, 2014.
  • 15. Wang Y.Z., Li F.M., Nonlinear free vibration of nanotube with small scale effects embedded in viscous matrix, Mechanics Research Communications, 60, 45–51, 2014.
  • 16. Kaghaziana A., Hajnayeb A., Foruzande H., Free vibration analysis of a piezoelectric nanobeam using nonlocal elasticity theory, Structural Engineering and Mechanics, 61 (5), 617-624, 2017.
  • 17. Reddy J.N., Pang S.D., Nonlocal continuum theories of beams for the analysis of carbon nanotubes, Journal of Applied Physics, 103 (2), 023511-023511, 2008.
  • 18. Hosseini S.A.H., Moghaddam M.H.N, Rahmani O., Exact solution for axial vibration of the power, exponential and sigmoid FG nonlocal nanobeam, Advances in Aircraft and Spacecraft Science, 7 (6), 517-536, 2020.
  • 19. Khorshidi M.A., Shariati M.A., Multi-spring model for buckling analysis of cracked timoshenko nanobeams based on modified couple stress theory, Journal of Theoretical and Applied Mechanics, 55 (4), 1127-1139, 2017.
  • 20. Malik M., Das D., Free vibration analysis of rotating nanobeams for flap-wise, chord-wise and axial modes based on Eringen’s nonlocal theory, International Journal of Mechanical Sciences, 179, 105655, 2020.
  • 21. Shaat M., Khorshidi M.A., Abdelkefi A., Shariati M., Modeling and vibration characteristics of cracked nanobeams made of nanocrystalline materials, International Journal of Mechanical Sciences, 115, 574–585, 2016.
  • 22. Chaht F.L., Kaci A., Houari M.S.A., Tounsi A., Bég O.A., Mahmoud S., Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect, Steel and Composite Structures, 18, 425–442, 2015.
  • 23. Karami B, Shahsavari D., Nazemosadat S.M.R., Li L., Ebrahimi A., Thermal buckling of smart porous functionally graded nanobeam rested on Kerr foundation, Steel and Composite Structures, 29 (3), 349-362, 2018.
  • 24. Barretta R., Diaco M., Feo L., Luciano R., Sciarra F.M.D., Penna R., Stress-driven integral elastic theory for torsion of nanobeams, Mechanics Research Communications, 87, 35–41, 2018.
  • 25. Mollamahmutoğlu, Ç., Mercan, A., A novel functional and mixed finite element analysis of functionally graded micro-beams based on modified couple stress theory, Composite Structures, 223, 110950, 2019.
  • 26. Akgöz, B., Civalek, Longitudinal vibration analysis for microbars based on strain gradient elasticity theory, Journal of Vibration and Control, 20, 606-616, 2014.
  • 27. Akgöz, B., Civalek, Ö., A novel microstructure-dependent shear deformable beam model, International Journal of Mechanical Sciences, 99, 10-20, 2015.
  • 28. Numanoğlu, H.M., Akgöz, B., Civalek, Ö., On dynamic analysis of nanorods, International Journal of Engineering Science, 130, 33-50, 2018.
  • 29. Trabelssi, M., El-Borgi, S., Fernandes, R., Ke, L.L. Nonlocal free and forced vibration of a graded Timoshenko nanobeam resting on a nonlinear elastic foundation, Composites Part B: Engineering, 157, 331-349, 2019.
  • 30. Zhao, X., Zhu, W.D., Li, Y.H. Analytical solutions of nonlocal coupled thermoelastic forced vibrations of micro-/nano-beams by means of Green's functions, Journal of Sound and Vibration, 481, 115407, 481.
  • 31. Karamanlı, A., Vo, T.P., Finite element model for free vibration analysis of curved zigzag nanobeams, Composite Structures, 282, 115097, 2022.
  • 32. Nalbant M.O., Bagdatli S.M., Tekin A. Investigation of nonlinear vibration behavior of the stepped nanobeam, Advances in Nano Research, 15 (3), 2023.
  • 33. Uzun B., Yayli M. Ö., Winkler-Pasternak foundation effect on the buckling loads of arbitrarily rigid or restrained supported nonlocal beams made of different FGM and porosity distributions, ZAMM, e202300569, 2023.
  • 34. Gholipour A., Ghayesh M.H., Nonlinear coupled mechanics of functionally graded nanobeams, International Journal of Engineering Science,150, 103221, 2020.
  • 35. Nalbant M.O., Bagdatli S.M., Tekin A. Free Vibrations Analysis of Stepped Nanobeams Using Nonlocal Elasticity Theory, Scientia Iranica, 2023.
  • 36. Zhang P., Qing H., Gao C.F., Exact solutions for bending of Timoshenko curved nanobeams made of functionally graded materials based on stress-driven nonlocal integral model, Composite Structures, 245, 112362, 2020.
  • 37. Jalaeia M.H., Arani A.G., Xuande H.N., Investigation of thermal and magnetic field effects on the dynamic instability of FG Timoshenko nanobeam employing nonlocal strain gradient theory, International Journal of Mechanical Sciences, 161–162, 105043, 2019.
  • 38. Arefi M., Pourjamshidian M., Arani A.G., Application of Nonlocal Strain Gradient Theory and Various Shear Deformation Theories to Nonlinear Vibration Analysis of Sandwich Nano-Beam with FG-CNTRCs Face-Sheets in Electro-Thermal Environment, Applied Physics A, 123, 323, 2017.
  • 39. Abdelrahman, A.A., Esen, I., Özarpa, C., Eltaher, M.A., Dynamics of perforated nanobeams subject to moving mass using the nonlocal strain gradient theory, Applied Mathematical Modelling, 96, 215-235, 2021.
  • 40. Aria, A.I., Friswell, M.I., A nonlocal finite element model for buckling and vibration of functionally graded nanobeams, Composites Part B: Engineering, 166, 233-246, 2019.
  • 41. Numanoğlu, H.M., Ersoy, H., Akgöz, B., Civalek, Ö. A new eigenvalue problem solver for thermo-mechanical vibration of Timoshenko nanobeams by an innovative nonlocal finite element method, Mathematical Methods in the Applied Sciences, 45, 2592-2614, 2022.
  • 42. Yan J., Tong L., Li C., Zhu Y., Wang Z., Exact solutions of bending deflections for nano-beams and nano-plates based on nonlocal elasticity theory, Composite Structures, 125, 304–313, 2015.
  • 43. Benguediab S., Tounsi A., Zidour M., Semmah A., Chirality and scale effects on mechanical buckling properties of zigzag double-walled carbon nanotubes, Composites Part B: Engineering, 57, 21–24, 2014.
  • 44. Chakraverty S., Behera L., Free vibration of non-uniform nanobeams using Rayleigh–Ritz method, Physica E: Low-dimensional Systems and Nanostructures, 67, 38–46, 2015.
  • 45. Sokół K., Uzny S., Instability and vibration of multi-member columns subjected to Euler’s load, Arch Appl Mech., 86, 883–905, 2016.
  • 46. Uzny S., Sokół K., Free Vibrations of Column Subjected to Euler's Load with Consideration of Timoshenko's Theory, Vibrations in Physical Systems, 26, 319-326, 2014.
  • 47. Akkoca Ş., Bağdatli S. M., Toğun N., Linear vibration movements of the mid-supported micro beam, Journal of the Faculty of Engineering and Architecture of Gazi University, 36 (2), 1089-1104, 2021.
  • 48. Yapanmış B.E., Elastik Zemin ve Manyetik Alan Etkisi Altındaki Kademeli Kirişin Doğrusal Titreşim Analizi, Mühendislik Bilimleri ve Tasarım Dergisi, 11 (3), 1109-1119, 2023.
  • 49. Pakdemirli M., Öz H.R., Infinite mode analysis and truncation to resonant modes of axially accelerated beam vibrations, J. Sound Vib., 311 (3-5), 1052-1074, 2008.
  • 50. Nayfeh A.H., Introduction to Perturbation Techniques, New York, ABD, John Wiley, 1981.
  • 51. Nayfeh A.H., Mook D.T., Lobitz D.W., Numerical-Perturbation method for the nonlinear analysis of structural vibrations, AIAA Journal, 12 (9), 1222-1228, 1974.
  • 52. Ghadiri M., Soltanpour M., Yazdi A., Safi M., Studying the influence of surface effects on vibration behavior of size-dependent cracked FG Timoshenko nanobeam considering nonlocal elasticity and elastic foundation, Appl. Phys. A. 122 (5), 1-21, 2016.
  • 53. Öz H.R., Boyacı H., Transverse vibrations of tensioned pipes conveying fluid with time-dependent velocity, J. Sound Vib., 236 (2), 259-276, 2000.
  • 54. Bagdatli S.M., Oz H.R., Ozkaya E., Dynamics of axially accelerating beams with an intermediate support. J. Vib. Acoust., 133 (3), 031013, 2011.
  • 55. Yapanmış B.E., Nonlinear vibration and internal resonance analysis of microbeam with mass using the modified coupled stress theory, J. Vib. Eng. Technol, 11 (5), 2167-2180, 2023.
  • 56. Akkaya M. K., Yılmaz A. E., Kuzuoğlu M., Analytic and numeric perturbation techniques approach for the solution of electromagnetic wave problems, Journal of the Faculty of Engineering and Architecture of Gazi University, 39, (1), 299-314, 2024.
  • 57. Reddy J.N., Nonlocal theories of bending, buckling and vibration of beams, International Journal of Engineering Science, 45 (2-8), 288–307, 2007.
  • 58. Eltaher M.A., Alshorbagy A. E., Mahmoud F.F., Vibration analysis of Euler–Bernoulli nanobeams by using finite element method, Applied Mathematical Modelling, 37, 4787–4797, 2013.
  • 59. Thai H., T., A nonlocal beam theory for bending, buckling, and vibration of nanobeams. International Journal of Engineering Science, 52, 56-64, 2012.
  • 60. Bagdatlı S.M., Nonlinear vibration of nanobeams with various boundary condition based on nonlocal elasticity theory, Composites Part B, 80, 43-52, 2015.
  • 61. Ansari R., Gholami R., Rouhi H., Size-dependent nonlinear forced vibration analysis of magneto-electro-thermo-elastic Timoshenko nanobeams based upon the nonlocal elasticity theory, Composite Structures, 126, 216–226, 2015.
Yıl 2024, Cilt: 39 Sayı: 4, 2447 - 2462, 20.05.2024
https://doi.org/10.17341/gazimmfd.1291811

Öz

Kaynakça

  • 1. Kaynak B.E, Alkhaled M., Kartal E., Yanik C., Hanay M. S., Atmospheric Pressure Mass Spectrometry by Single-Mode Nanoelectromechanical Systems, Nano Letters, 23 (18), 8553–8559, 2023.
  • 2. Secme A., Pisheh H. S., Tefek U., Uslu H. D., Kucukoglu B., Alatas C., Kelleci M., Hanay M. S., On-Chip Flow Rate Sensing via Membrane Deformation and Bistability Probed by Microwave Resonators, Microfluidics and Nanofluidics, 27, 2023.
  • 3. Karakan M.Ç., Ari A.B., Kelleci M., Yanık C., Kaya I.I., Taştan Ö., Hanay M. S., Vapor Sensing of Colorectal Cancer Biomarkers in Isolation by Bare and Functionalized Nanoelectromechanical Sensors, IEEE Sensors, 23, 21113-21120, 2023.
  • 4. Aydoğdu M., A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration, Physica E: Low-dimensional Systems and Nanostructures, 41 (9), 1651-1655, 2009.
  • 5. Aya S.A., Tufekci E., Modeling and analysis of out-of-plane behavior of curved nanobeams based on nonlocal elasticity, Composites Part B: Engineering, 119, 184-195, 2016.
  • 6. Ruoccoa E., Reddy J.N., Buckling analysis of elastic–plastic nanoplates resting on a Winkler–Pasternak foundation based on nonlocal third-order plate theory, International Journal of Non-Linear Mechanics, 121, 103453, 2020.
  • 7. Malikan M., Nguyen V.B., Buckling analysis of piezo-magnetoelectric nanoplates in hygrothermal environment based on a novel one variable plate theory combining with higher-order nonlocal strain gradient theory, Physica E: Low-dimensional Systems and Nanostructures, 102, 8-28, 2018.
  • 8. Ma L.H., Ke L.L., Reddy J.N., Yang J., Kitipornchai S., Wang Y.S., Wave propagation characteristics in magneto-electro-elastic nanoshells using nonlocal strain gradient theory, Composite Structures, 199, 10-23, 2018.
  • 9. Karami B., Janghorban M., Tounsi A., Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory, Thin-Walled Structures, 129, 251-264, 2018.
  • 10. Villanueva L.G., Schmid S., Roukes M., Fundamentals of Nanomechanical Resonators, Springer International Publishing, Cham, Switzerland, 2016.
  • 11. Eringen A.C., Linear theory of nonlocal elasticity and dispersion of plane-waves, International Journal of Engineering Science, 10 (5), 233–248, 1972.
  • 12. Khaniki H.B., On vibrations of nanobeam systems. International Journal of Engineering Science, 124, 85–103, 2018.
  • 13. Ganapathi M., Polit O., Dynamic characteristics of curved nanobeams using nonlocal higher-order curved beam theory. Physica E, 91, 190-202, 2017.
  • 14. Şimşek M., Large amplitude free vibration of nanobeams with various boundary conditions based on the nonlocal elasticity theory, Composites Part B: Engineering, 56, 621-628, 2014.
  • 15. Wang Y.Z., Li F.M., Nonlinear free vibration of nanotube with small scale effects embedded in viscous matrix, Mechanics Research Communications, 60, 45–51, 2014.
  • 16. Kaghaziana A., Hajnayeb A., Foruzande H., Free vibration analysis of a piezoelectric nanobeam using nonlocal elasticity theory, Structural Engineering and Mechanics, 61 (5), 617-624, 2017.
  • 17. Reddy J.N., Pang S.D., Nonlocal continuum theories of beams for the analysis of carbon nanotubes, Journal of Applied Physics, 103 (2), 023511-023511, 2008.
  • 18. Hosseini S.A.H., Moghaddam M.H.N, Rahmani O., Exact solution for axial vibration of the power, exponential and sigmoid FG nonlocal nanobeam, Advances in Aircraft and Spacecraft Science, 7 (6), 517-536, 2020.
  • 19. Khorshidi M.A., Shariati M.A., Multi-spring model for buckling analysis of cracked timoshenko nanobeams based on modified couple stress theory, Journal of Theoretical and Applied Mechanics, 55 (4), 1127-1139, 2017.
  • 20. Malik M., Das D., Free vibration analysis of rotating nanobeams for flap-wise, chord-wise and axial modes based on Eringen’s nonlocal theory, International Journal of Mechanical Sciences, 179, 105655, 2020.
  • 21. Shaat M., Khorshidi M.A., Abdelkefi A., Shariati M., Modeling and vibration characteristics of cracked nanobeams made of nanocrystalline materials, International Journal of Mechanical Sciences, 115, 574–585, 2016.
  • 22. Chaht F.L., Kaci A., Houari M.S.A., Tounsi A., Bég O.A., Mahmoud S., Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect, Steel and Composite Structures, 18, 425–442, 2015.
  • 23. Karami B, Shahsavari D., Nazemosadat S.M.R., Li L., Ebrahimi A., Thermal buckling of smart porous functionally graded nanobeam rested on Kerr foundation, Steel and Composite Structures, 29 (3), 349-362, 2018.
  • 24. Barretta R., Diaco M., Feo L., Luciano R., Sciarra F.M.D., Penna R., Stress-driven integral elastic theory for torsion of nanobeams, Mechanics Research Communications, 87, 35–41, 2018.
  • 25. Mollamahmutoğlu, Ç., Mercan, A., A novel functional and mixed finite element analysis of functionally graded micro-beams based on modified couple stress theory, Composite Structures, 223, 110950, 2019.
  • 26. Akgöz, B., Civalek, Longitudinal vibration analysis for microbars based on strain gradient elasticity theory, Journal of Vibration and Control, 20, 606-616, 2014.
  • 27. Akgöz, B., Civalek, Ö., A novel microstructure-dependent shear deformable beam model, International Journal of Mechanical Sciences, 99, 10-20, 2015.
  • 28. Numanoğlu, H.M., Akgöz, B., Civalek, Ö., On dynamic analysis of nanorods, International Journal of Engineering Science, 130, 33-50, 2018.
  • 29. Trabelssi, M., El-Borgi, S., Fernandes, R., Ke, L.L. Nonlocal free and forced vibration of a graded Timoshenko nanobeam resting on a nonlinear elastic foundation, Composites Part B: Engineering, 157, 331-349, 2019.
  • 30. Zhao, X., Zhu, W.D., Li, Y.H. Analytical solutions of nonlocal coupled thermoelastic forced vibrations of micro-/nano-beams by means of Green's functions, Journal of Sound and Vibration, 481, 115407, 481.
  • 31. Karamanlı, A., Vo, T.P., Finite element model for free vibration analysis of curved zigzag nanobeams, Composite Structures, 282, 115097, 2022.
  • 32. Nalbant M.O., Bagdatli S.M., Tekin A. Investigation of nonlinear vibration behavior of the stepped nanobeam, Advances in Nano Research, 15 (3), 2023.
  • 33. Uzun B., Yayli M. Ö., Winkler-Pasternak foundation effect on the buckling loads of arbitrarily rigid or restrained supported nonlocal beams made of different FGM and porosity distributions, ZAMM, e202300569, 2023.
  • 34. Gholipour A., Ghayesh M.H., Nonlinear coupled mechanics of functionally graded nanobeams, International Journal of Engineering Science,150, 103221, 2020.
  • 35. Nalbant M.O., Bagdatli S.M., Tekin A. Free Vibrations Analysis of Stepped Nanobeams Using Nonlocal Elasticity Theory, Scientia Iranica, 2023.
  • 36. Zhang P., Qing H., Gao C.F., Exact solutions for bending of Timoshenko curved nanobeams made of functionally graded materials based on stress-driven nonlocal integral model, Composite Structures, 245, 112362, 2020.
  • 37. Jalaeia M.H., Arani A.G., Xuande H.N., Investigation of thermal and magnetic field effects on the dynamic instability of FG Timoshenko nanobeam employing nonlocal strain gradient theory, International Journal of Mechanical Sciences, 161–162, 105043, 2019.
  • 38. Arefi M., Pourjamshidian M., Arani A.G., Application of Nonlocal Strain Gradient Theory and Various Shear Deformation Theories to Nonlinear Vibration Analysis of Sandwich Nano-Beam with FG-CNTRCs Face-Sheets in Electro-Thermal Environment, Applied Physics A, 123, 323, 2017.
  • 39. Abdelrahman, A.A., Esen, I., Özarpa, C., Eltaher, M.A., Dynamics of perforated nanobeams subject to moving mass using the nonlocal strain gradient theory, Applied Mathematical Modelling, 96, 215-235, 2021.
  • 40. Aria, A.I., Friswell, M.I., A nonlocal finite element model for buckling and vibration of functionally graded nanobeams, Composites Part B: Engineering, 166, 233-246, 2019.
  • 41. Numanoğlu, H.M., Ersoy, H., Akgöz, B., Civalek, Ö. A new eigenvalue problem solver for thermo-mechanical vibration of Timoshenko nanobeams by an innovative nonlocal finite element method, Mathematical Methods in the Applied Sciences, 45, 2592-2614, 2022.
  • 42. Yan J., Tong L., Li C., Zhu Y., Wang Z., Exact solutions of bending deflections for nano-beams and nano-plates based on nonlocal elasticity theory, Composite Structures, 125, 304–313, 2015.
  • 43. Benguediab S., Tounsi A., Zidour M., Semmah A., Chirality and scale effects on mechanical buckling properties of zigzag double-walled carbon nanotubes, Composites Part B: Engineering, 57, 21–24, 2014.
  • 44. Chakraverty S., Behera L., Free vibration of non-uniform nanobeams using Rayleigh–Ritz method, Physica E: Low-dimensional Systems and Nanostructures, 67, 38–46, 2015.
  • 45. Sokół K., Uzny S., Instability and vibration of multi-member columns subjected to Euler’s load, Arch Appl Mech., 86, 883–905, 2016.
  • 46. Uzny S., Sokół K., Free Vibrations of Column Subjected to Euler's Load with Consideration of Timoshenko's Theory, Vibrations in Physical Systems, 26, 319-326, 2014.
  • 47. Akkoca Ş., Bağdatli S. M., Toğun N., Linear vibration movements of the mid-supported micro beam, Journal of the Faculty of Engineering and Architecture of Gazi University, 36 (2), 1089-1104, 2021.
  • 48. Yapanmış B.E., Elastik Zemin ve Manyetik Alan Etkisi Altındaki Kademeli Kirişin Doğrusal Titreşim Analizi, Mühendislik Bilimleri ve Tasarım Dergisi, 11 (3), 1109-1119, 2023.
  • 49. Pakdemirli M., Öz H.R., Infinite mode analysis and truncation to resonant modes of axially accelerated beam vibrations, J. Sound Vib., 311 (3-5), 1052-1074, 2008.
  • 50. Nayfeh A.H., Introduction to Perturbation Techniques, New York, ABD, John Wiley, 1981.
  • 51. Nayfeh A.H., Mook D.T., Lobitz D.W., Numerical-Perturbation method for the nonlinear analysis of structural vibrations, AIAA Journal, 12 (9), 1222-1228, 1974.
  • 52. Ghadiri M., Soltanpour M., Yazdi A., Safi M., Studying the influence of surface effects on vibration behavior of size-dependent cracked FG Timoshenko nanobeam considering nonlocal elasticity and elastic foundation, Appl. Phys. A. 122 (5), 1-21, 2016.
  • 53. Öz H.R., Boyacı H., Transverse vibrations of tensioned pipes conveying fluid with time-dependent velocity, J. Sound Vib., 236 (2), 259-276, 2000.
  • 54. Bagdatli S.M., Oz H.R., Ozkaya E., Dynamics of axially accelerating beams with an intermediate support. J. Vib. Acoust., 133 (3), 031013, 2011.
  • 55. Yapanmış B.E., Nonlinear vibration and internal resonance analysis of microbeam with mass using the modified coupled stress theory, J. Vib. Eng. Technol, 11 (5), 2167-2180, 2023.
  • 56. Akkaya M. K., Yılmaz A. E., Kuzuoğlu M., Analytic and numeric perturbation techniques approach for the solution of electromagnetic wave problems, Journal of the Faculty of Engineering and Architecture of Gazi University, 39, (1), 299-314, 2024.
  • 57. Reddy J.N., Nonlocal theories of bending, buckling and vibration of beams, International Journal of Engineering Science, 45 (2-8), 288–307, 2007.
  • 58. Eltaher M.A., Alshorbagy A. E., Mahmoud F.F., Vibration analysis of Euler–Bernoulli nanobeams by using finite element method, Applied Mathematical Modelling, 37, 4787–4797, 2013.
  • 59. Thai H., T., A nonlocal beam theory for bending, buckling, and vibration of nanobeams. International Journal of Engineering Science, 52, 56-64, 2012.
  • 60. Bagdatlı S.M., Nonlinear vibration of nanobeams with various boundary condition based on nonlocal elasticity theory, Composites Part B, 80, 43-52, 2015.
  • 61. Ansari R., Gholami R., Rouhi H., Size-dependent nonlinear forced vibration analysis of magneto-electro-thermo-elastic Timoshenko nanobeams based upon the nonlocal elasticity theory, Composite Structures, 126, 216–226, 2015.
Toplam 61 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Burak Emre Yapanmış 0000-0003-0499-6581

Süleyman Murat Bağdatlı 0000-0002-5152-9604

Necla Toğun 0000-0001-7921-6290

Erken Görünüm Tarihi 17 Mayıs 2024
Yayımlanma Tarihi 20 Mayıs 2024
Gönderilme Tarihi 3 Mayıs 2023
Kabul Tarihi 30 Aralık 2023
Yayımlandığı Sayı Yıl 2024 Cilt: 39 Sayı: 4

Kaynak Göster

APA Yapanmış, B. E., Bağdatlı, S. M., & Toğun, N. (2024). Yerel olmayan elastisite teorisine göre üç mesnetli nano kirişin doğrusal olmayan titreşim davranışı. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 39(4), 2447-2462. https://doi.org/10.17341/gazimmfd.1291811
AMA Yapanmış BE, Bağdatlı SM, Toğun N. Yerel olmayan elastisite teorisine göre üç mesnetli nano kirişin doğrusal olmayan titreşim davranışı. GUMMFD. Mayıs 2024;39(4):2447-2462. doi:10.17341/gazimmfd.1291811
Chicago Yapanmış, Burak Emre, Süleyman Murat Bağdatlı, ve Necla Toğun. “Yerel Olmayan Elastisite Teorisine göre üç Mesnetli Nano kirişin doğrusal Olmayan titreşim davranışı”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 39, sy. 4 (Mayıs 2024): 2447-62. https://doi.org/10.17341/gazimmfd.1291811.
EndNote Yapanmış BE, Bağdatlı SM, Toğun N (01 Mayıs 2024) Yerel olmayan elastisite teorisine göre üç mesnetli nano kirişin doğrusal olmayan titreşim davranışı. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 39 4 2447–2462.
IEEE B. E. Yapanmış, S. M. Bağdatlı, ve N. Toğun, “Yerel olmayan elastisite teorisine göre üç mesnetli nano kirişin doğrusal olmayan titreşim davranışı”, GUMMFD, c. 39, sy. 4, ss. 2447–2462, 2024, doi: 10.17341/gazimmfd.1291811.
ISNAD Yapanmış, Burak Emre vd. “Yerel Olmayan Elastisite Teorisine göre üç Mesnetli Nano kirişin doğrusal Olmayan titreşim davranışı”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 39/4 (Mayıs 2024), 2447-2462. https://doi.org/10.17341/gazimmfd.1291811.
JAMA Yapanmış BE, Bağdatlı SM, Toğun N. Yerel olmayan elastisite teorisine göre üç mesnetli nano kirişin doğrusal olmayan titreşim davranışı. GUMMFD. 2024;39:2447–2462.
MLA Yapanmış, Burak Emre vd. “Yerel Olmayan Elastisite Teorisine göre üç Mesnetli Nano kirişin doğrusal Olmayan titreşim davranışı”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, c. 39, sy. 4, 2024, ss. 2447-62, doi:10.17341/gazimmfd.1291811.
Vancouver Yapanmış BE, Bağdatlı SM, Toğun N. Yerel olmayan elastisite teorisine göre üç mesnetli nano kirişin doğrusal olmayan titreşim davranışı. GUMMFD. 2024;39(4):2447-62.