Research Article
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Year 2021, Volume: 13 Issue: 2, 43 - 55, 05.09.2021
https://doi.org/10.24107/ijeas.932580

Abstract

References

  • Ecsedi, I., Baksa, A., Free axial vibration of nanorods with elastic medium interaction based on nonlocal elasticity, Mechanics Research Communications, 86, 2017.
  • Simsek, M., Nonlocal effects in the free longitudinal vibration of axially functionally graded tapered nanorods, Computational Materials Science, 61, 257–265, 2012.
  • Yaylı, M.Ö., Buckling Analysis of a Rotationally Restrained Single Walled Carbon Nanotube Embedded in an Elastic Medium Using Nonlocal Elasticity, International Journal of Engineering & Applied Sciences, 8(2), 40-50, 2016.
  • Aydogdu, 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.
  • Danesh, M., Farajpour, A., Mohammadi, M., Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications, 39, 23–27, 2012.
  • Guo, S.Q, Yang, S.P., Axial vibration analysis of nanocones based on nonlocal elasticity theory, Acta Mech. Sin., 28(3), 801–807, 2012.
  • Murmu, T., Pradhan, S.C., Vibration analysis of nanoplates under uniaxial prestressed conditions via nonlocal elasticity, J. Appl. Phys., 106, 104301, 2009.
  • Berrabah, H.M., Tounsi, A., Semmah, A., Adda Bedia, E.A., Structural Engineering and Mechanics, 48(3), 351-365, 2013.
  • Faker, M., Bending and free vibration analysis of nanobeams by differential and integral forms of nonlocal strain gradient with Rayleigh–Ritz method, Mater. Res. Express, 2053-1591, 2017.
  • Akgöz, B., Civalek, Ö., Buckling analysis of functionally graded microbeams based on the strain gradient theory, Acta Mechanica, 224, 2185–201, 2013.
  • Attia, M.A., Mahmoud, F.F., Modeling and Analysis of Nanobeams Based on Nonlocal Couple-Stress Elasticity and Surface Energy Theories, International Journal of Mechanical Sciences, 105, 126-134, 2016.
  • Mahmoud, F.F., Eltaher, M.A., Alshorbagy, A.E, Meletis, E.I., Static analysis of nanobeams including surface effects by nonlocal finite element, Journal of Mechanical Science and Technology, 26(11), 3555-3563, 2012.
  • Norouzzadeh, A., Ansari, R., Rouhi, H., Nonlinear Bending Analysis of Nanobeams Based on the Nonlocal Strain Gradient Model Using an Isogeometric Finite Element Approach, Iran J Sci Technol Trans Civ Eng, 43(1), 533-547, 2018.
  • Amal, A.E., Eltaher, M.A., Mahmoud, F.F., Static analysis of nanobeams using nonlocal FEM, Journal of Mechanical Science and Technology, 27(7), 2035-2041, 2013.
  • Eltaher, M.A., Mahmoud, F.F., Assie, A.E., Meletis, E.I., Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams, Applied Mathematics and Computation 224, 760–774, 2013.
  • Arefi, M., Mohammad-Rezaei Bidgoli, E., Dimitri, R., Bacciocchi, M., Tornabene, F., Nonlocal bending analysis of curved nanobeams reinforced by graphene nanoplatelets, Composites Part B, 166, 1-12, 2018.
  • Lu, L., Guo, X., Zhao, J., Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory, International Journal of Engineering Science, 116, 12–24, 2017.
  • Nikam, R.D., Sayyad, A.S., A unified nonlocal formulation for bending buckling and free vibration analysis of nanobeams, Mechanics of Advanced Materials and Structures, 27, 807-815, 2018.
  • Shokrieh, M., Zibaei, I., Determination of the Appropriate Gradient Elasticity Theory for Bending Analysis of Nano-beams by Considering Boundary Conditions Effect, Latin American Journal of Solids and Structures, 12, 2208-2230, 2014.
  • Beni, Y., Size-dependent electromechanical bending, buckling, and free vibration analysis of functionally graded piezoelectric nanobeams, Journal of Intelligent Material Systems and Structures, 27(16), 2199-2215, 2016.
  • Ghadiri, M., Rajabpour, A., Akbarshahi, A., Non-linear forced vibration analysis of nanobeams subjected to moving concentrated load resting on a viscoelastic foundation considering thermal and surface effects, Applied Mathematical Modelling, 50, 676-694, 2017.
  • Behera, L., Chakraverty, S., Application of Differential Quadrature method in free vibration analysis of nanobeams based on various nonlocal theories, Computers and Mathematics with Applications, 69(12), 1444-1462, 2015.
  • Hadi, A., Nejad M., Hosseini, M., Vibrations of three-dimensionally graded nanobeams, International Journal of Engineering Science, 128, 12–23, 2018.
  • Ebrahimi, F., Salari, E., Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments, Composite Structures, 128, 363-380, 2015.
  • Lin, S.C., Hsiao, K.M., Vibration analysis of a rotating Timoshenko beam, Journal of Sound and Vibration, 240(2), 303-322, 2001.
  • Ebrahimi, F., Barati, M., Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment, Journal of Vibration and Control, 24(3), 549-564, 2016.
  • Ansari, R., Mohammadi, V., Faghih Shojaei, M., Gholami, R., Rouhi, H., Nonlinear vibration analysis of Timoshenko nanobeams based onsurface stress elasticity theory, European Journal of Mechanics, 45, 143-152, 2014.
  • Jena, S., Chakraverty, S., Free vibration analysis of Euler-Bernoulli Nano beam using differential transform method, International Journal of Computational Materials Science and Engineering, 7(3), 2018.
  • Akbas, S., Forced vibration analysis of functionallygraded nanobeams, International Journal of Applied Mechanics, 7(4), 736-743, 2017.
  • Shafiei, N., Kazemi, M., Safi, M., Ghadiri, M., Nonlinear vibration of axially functionally graded non-uniform nanobeams, International Journal of Engineering Science, 106, 77–94, 2016.
  • Wang, J., Shen, H., Zhang, B., Liu, J., Zhang, Y., Complex modal analysis of transverse free vibrations for axially moving nanobeams based on the nonlocal strain gradient theory, Physica E: Low-dimensional Systems and Nanostructures, 14(1),119-137, 2018.
  • 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.
  • Faraji Oskouie, M., Ansari, R., Linear and nonlinear vibrations of fractional viscoelastic Timoshenko nanobeams considering surface energy effects, Applied Mathematical Modelling, 43(3), 337-350, 2016.
  • Zhang, R., Pang, M., Fan, M., Analyses of transverse vibrations of axially pretensioned viscoelastic nanobeams with small size and surface effects, Physics Letters A, 380(29-30), 2294-2299, 2016.
  • Yang, T., Tang, Y., Li, Q., Yang, X-D., Nonlinear bending, buckling and vibration of bidirectional functionally graded nanobeams, Composite Structures, 156, 319-331, 2018.
  • Zheng, L., Liu, H., Nonlinear bending response of functionally graded nanobeams with material uncertainties, International Journal of Mechanical Sciences, 12, 134, 2017.
  • Yan, J.W., Tong, L.H., Li, C., Zhu, Y., Wang, Z.W., Exact Solutions of Bending Deflections for Nano-beams and Nano- plates Based on Nonlocal Elasticity Theory, Composite Structures, 125, 304-313, 2015.
  • Barretta, R., Sciarra, R., A new nonlocal bending model for Euler-Bernoulli nanobeams, Mechanics Research Communications, 62, 25-30, 2014.
  • Civalek, O., Finite Element analysis of plates and shells, Master thesis, Elazığ, Fırat University, 1998. (in Turkish) Civalek, O., Kiracioglu, O., Free vibration analysis of Timoshenko beams by DSC method, International Journal for Numerical Methods in Biomedical Engineering, 26(12), 1890-1898, 2010.
  • Mercan, K., Demir, Ç., Civalek, O., Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique, Curved and Layered Structures, 3(1), 82-90, 2016.
  • Demir, C., Civalek, O., On the analysis of microbeams, International Journal of Engineering Science, 121, 14-33, 2017.
  • Jalaei, M., Civalek, O., On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam, International Journal of Engineering Science, 143, 14-32, 2019.
  • Civalek, O., Dastjerdi, S., Akbaş, S.D., Akgöz, B., Vibration Analysis of Carbon Nanotube-Reinforced Composite Microbeams. Mathematical Methods in the Applied Sciences, 11(3), 571, 2020.
  • Civalek, Ö., Avcar, M., Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method. Engineering with Computers, 1-33, 2020.
  • Hadji, L., Avcar, M., Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory, Advances in Nano Research, 10(3), 281-293, 2021.
  • Akgöz, B., Linear and nonlinear analyses of micro and nano structures based on higher-order elasticity theories, Doktora Tezi, Akdeniz Üniversitesi, 2010.
  • Yaylı, M.Ö, Çerçevik, E.A., Axial vibration analysis of cracked nanorods with arbitrary boundary conditions, Journal of Vibroengineering, 17(6), 2907-2921, 2015.
  • Uzun, B., Yaylı, M.Ö., Deliktaş, B., Free vibration of FG nanobeam using a finite-element method, Micro & Nano Letters, 15(1), 35-40, 2020.
  • 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., Stability analysis of a gradient elasticbeam using finite element method, International Journal of the Physical Sciences, 6(12), 2844-2851, 2011.
  • Yayli, M.Ö., Free Vibration Behavior of a Gradient Elastic Beam with Varying Cross Section, Shock and Vibration, vol. 2014, Article ID 801696, 11 pages, 2014.
  • Yayli, M.Ö., Torsional vibration analysis of nanorods with elastic torsional restraints using non-local elasticity theory, Micro & Nano Letters, 13(5), 595-599, 2018.
  • Yayli, M.Ö., A compact analytical method for vibration of micro-sized beams with different boundary conditions, Mechanics of Advanced Materials and Structures, 24(6), 496-508, 2017.
  • Yayli, M.Ö., Torsion of nonlocal bars with equilateral triangle cross sections, Journal of Computational and Theoretical Nanoscience, 10(2), 376-379, 2013.
  • Yaylı, M.Ö., Buckling analysis of a rotationally restrained single walled carbon nanotube embedded in an elastic medium using nonlocal elasticity, International Journal of Engineering and Applied Sciences, 8(2), 40-50, 2016.
  • Yayli, M.Ö., Weak formulation of finite element method for nonlocal beams using additional boundary conditions, Journal of Computational and Theoretical Nanoscience, 8(11), 2173-2180, 2011.
  • Yaylı, M. Ö., An analytical solution for free vibrations of a cantilever nanobeam with a spring mass system, International Journal of Engineering and Applied Sciences, 7(4), 10-18, 2016.
  • Kadıoğlu, H. & Yaylı, M. Ö., Buckling analysis of non-local Timoshenko beams by using Fourier series, International Journal of Engineering and Applied Sciences, 9(4), 89-99, 2017.
  • Uzun, B, & Yaylı, M. Ö., Nonlocal vibration analysis of Ti-6Al-4V/ZrO 2 functionally graded nanobeam on elastic matrix, Arabian Journal of Geosciences, 13(4), 1-10, 2020.

Weighted Residual Approach for Bending Analysis of Nanobeam Using by Modified Couple Stress Theory

Year 2021, Volume: 13 Issue: 2, 43 - 55, 05.09.2021
https://doi.org/10.24107/ijeas.932580

Abstract

With the development of nanotechnology, interest in nanomaterials has increased significantly in recent years.
This study examines the bending analysis of a nanobeam with modified couple stress theory and weighted
residual methods. The formulas derived for calculating bending analysis results in the article has been found by
using Weighted Residual Method. The results have compared to show effects on nanobeam and the calculated
values are shown in the graphs and tables. The results obtained are compared with the results already found in
the literature and it was observed that they are consistent.

References

  • Ecsedi, I., Baksa, A., Free axial vibration of nanorods with elastic medium interaction based on nonlocal elasticity, Mechanics Research Communications, 86, 2017.
  • Simsek, M., Nonlocal effects in the free longitudinal vibration of axially functionally graded tapered nanorods, Computational Materials Science, 61, 257–265, 2012.
  • Yaylı, M.Ö., Buckling Analysis of a Rotationally Restrained Single Walled Carbon Nanotube Embedded in an Elastic Medium Using Nonlocal Elasticity, International Journal of Engineering & Applied Sciences, 8(2), 40-50, 2016.
  • Aydogdu, 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.
  • Danesh, M., Farajpour, A., Mohammadi, M., Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications, 39, 23–27, 2012.
  • Guo, S.Q, Yang, S.P., Axial vibration analysis of nanocones based on nonlocal elasticity theory, Acta Mech. Sin., 28(3), 801–807, 2012.
  • Murmu, T., Pradhan, S.C., Vibration analysis of nanoplates under uniaxial prestressed conditions via nonlocal elasticity, J. Appl. Phys., 106, 104301, 2009.
  • Berrabah, H.M., Tounsi, A., Semmah, A., Adda Bedia, E.A., Structural Engineering and Mechanics, 48(3), 351-365, 2013.
  • Faker, M., Bending and free vibration analysis of nanobeams by differential and integral forms of nonlocal strain gradient with Rayleigh–Ritz method, Mater. Res. Express, 2053-1591, 2017.
  • Akgöz, B., Civalek, Ö., Buckling analysis of functionally graded microbeams based on the strain gradient theory, Acta Mechanica, 224, 2185–201, 2013.
  • Attia, M.A., Mahmoud, F.F., Modeling and Analysis of Nanobeams Based on Nonlocal Couple-Stress Elasticity and Surface Energy Theories, International Journal of Mechanical Sciences, 105, 126-134, 2016.
  • Mahmoud, F.F., Eltaher, M.A., Alshorbagy, A.E, Meletis, E.I., Static analysis of nanobeams including surface effects by nonlocal finite element, Journal of Mechanical Science and Technology, 26(11), 3555-3563, 2012.
  • Norouzzadeh, A., Ansari, R., Rouhi, H., Nonlinear Bending Analysis of Nanobeams Based on the Nonlocal Strain Gradient Model Using an Isogeometric Finite Element Approach, Iran J Sci Technol Trans Civ Eng, 43(1), 533-547, 2018.
  • Amal, A.E., Eltaher, M.A., Mahmoud, F.F., Static analysis of nanobeams using nonlocal FEM, Journal of Mechanical Science and Technology, 27(7), 2035-2041, 2013.
  • Eltaher, M.A., Mahmoud, F.F., Assie, A.E., Meletis, E.I., Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams, Applied Mathematics and Computation 224, 760–774, 2013.
  • Arefi, M., Mohammad-Rezaei Bidgoli, E., Dimitri, R., Bacciocchi, M., Tornabene, F., Nonlocal bending analysis of curved nanobeams reinforced by graphene nanoplatelets, Composites Part B, 166, 1-12, 2018.
  • Lu, L., Guo, X., Zhao, J., Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory, International Journal of Engineering Science, 116, 12–24, 2017.
  • Nikam, R.D., Sayyad, A.S., A unified nonlocal formulation for bending buckling and free vibration analysis of nanobeams, Mechanics of Advanced Materials and Structures, 27, 807-815, 2018.
  • Shokrieh, M., Zibaei, I., Determination of the Appropriate Gradient Elasticity Theory for Bending Analysis of Nano-beams by Considering Boundary Conditions Effect, Latin American Journal of Solids and Structures, 12, 2208-2230, 2014.
  • Beni, Y., Size-dependent electromechanical bending, buckling, and free vibration analysis of functionally graded piezoelectric nanobeams, Journal of Intelligent Material Systems and Structures, 27(16), 2199-2215, 2016.
  • Ghadiri, M., Rajabpour, A., Akbarshahi, A., Non-linear forced vibration analysis of nanobeams subjected to moving concentrated load resting on a viscoelastic foundation considering thermal and surface effects, Applied Mathematical Modelling, 50, 676-694, 2017.
  • Behera, L., Chakraverty, S., Application of Differential Quadrature method in free vibration analysis of nanobeams based on various nonlocal theories, Computers and Mathematics with Applications, 69(12), 1444-1462, 2015.
  • Hadi, A., Nejad M., Hosseini, M., Vibrations of three-dimensionally graded nanobeams, International Journal of Engineering Science, 128, 12–23, 2018.
  • Ebrahimi, F., Salari, E., Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments, Composite Structures, 128, 363-380, 2015.
  • Lin, S.C., Hsiao, K.M., Vibration analysis of a rotating Timoshenko beam, Journal of Sound and Vibration, 240(2), 303-322, 2001.
  • Ebrahimi, F., Barati, M., Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment, Journal of Vibration and Control, 24(3), 549-564, 2016.
  • Ansari, R., Mohammadi, V., Faghih Shojaei, M., Gholami, R., Rouhi, H., Nonlinear vibration analysis of Timoshenko nanobeams based onsurface stress elasticity theory, European Journal of Mechanics, 45, 143-152, 2014.
  • Jena, S., Chakraverty, S., Free vibration analysis of Euler-Bernoulli Nano beam using differential transform method, International Journal of Computational Materials Science and Engineering, 7(3), 2018.
  • Akbas, S., Forced vibration analysis of functionallygraded nanobeams, International Journal of Applied Mechanics, 7(4), 736-743, 2017.
  • Shafiei, N., Kazemi, M., Safi, M., Ghadiri, M., Nonlinear vibration of axially functionally graded non-uniform nanobeams, International Journal of Engineering Science, 106, 77–94, 2016.
  • Wang, J., Shen, H., Zhang, B., Liu, J., Zhang, Y., Complex modal analysis of transverse free vibrations for axially moving nanobeams based on the nonlocal strain gradient theory, Physica E: Low-dimensional Systems and Nanostructures, 14(1),119-137, 2018.
  • 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.
  • Faraji Oskouie, M., Ansari, R., Linear and nonlinear vibrations of fractional viscoelastic Timoshenko nanobeams considering surface energy effects, Applied Mathematical Modelling, 43(3), 337-350, 2016.
  • Zhang, R., Pang, M., Fan, M., Analyses of transverse vibrations of axially pretensioned viscoelastic nanobeams with small size and surface effects, Physics Letters A, 380(29-30), 2294-2299, 2016.
  • Yang, T., Tang, Y., Li, Q., Yang, X-D., Nonlinear bending, buckling and vibration of bidirectional functionally graded nanobeams, Composite Structures, 156, 319-331, 2018.
  • Zheng, L., Liu, H., Nonlinear bending response of functionally graded nanobeams with material uncertainties, International Journal of Mechanical Sciences, 12, 134, 2017.
  • Yan, J.W., Tong, L.H., Li, C., Zhu, Y., Wang, Z.W., Exact Solutions of Bending Deflections for Nano-beams and Nano- plates Based on Nonlocal Elasticity Theory, Composite Structures, 125, 304-313, 2015.
  • Barretta, R., Sciarra, R., A new nonlocal bending model for Euler-Bernoulli nanobeams, Mechanics Research Communications, 62, 25-30, 2014.
  • Civalek, O., Finite Element analysis of plates and shells, Master thesis, Elazığ, Fırat University, 1998. (in Turkish) Civalek, O., Kiracioglu, O., Free vibration analysis of Timoshenko beams by DSC method, International Journal for Numerical Methods in Biomedical Engineering, 26(12), 1890-1898, 2010.
  • Mercan, K., Demir, Ç., Civalek, O., Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique, Curved and Layered Structures, 3(1), 82-90, 2016.
  • Demir, C., Civalek, O., On the analysis of microbeams, International Journal of Engineering Science, 121, 14-33, 2017.
  • Jalaei, M., Civalek, O., On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam, International Journal of Engineering Science, 143, 14-32, 2019.
  • Civalek, O., Dastjerdi, S., Akbaş, S.D., Akgöz, B., Vibration Analysis of Carbon Nanotube-Reinforced Composite Microbeams. Mathematical Methods in the Applied Sciences, 11(3), 571, 2020.
  • Civalek, Ö., Avcar, M., Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method. Engineering with Computers, 1-33, 2020.
  • Hadji, L., Avcar, M., Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory, Advances in Nano Research, 10(3), 281-293, 2021.
  • Akgöz, B., Linear and nonlinear analyses of micro and nano structures based on higher-order elasticity theories, Doktora Tezi, Akdeniz Üniversitesi, 2010.
  • Yaylı, M.Ö, Çerçevik, E.A., Axial vibration analysis of cracked nanorods with arbitrary boundary conditions, Journal of Vibroengineering, 17(6), 2907-2921, 2015.
  • Uzun, B., Yaylı, M.Ö., Deliktaş, B., Free vibration of FG nanobeam using a finite-element method, Micro & Nano Letters, 15(1), 35-40, 2020.
  • 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., Stability analysis of a gradient elasticbeam using finite element method, International Journal of the Physical Sciences, 6(12), 2844-2851, 2011.
  • Yayli, M.Ö., Free Vibration Behavior of a Gradient Elastic Beam with Varying Cross Section, Shock and Vibration, vol. 2014, Article ID 801696, 11 pages, 2014.
  • Yayli, M.Ö., Torsional vibration analysis of nanorods with elastic torsional restraints using non-local elasticity theory, Micro & Nano Letters, 13(5), 595-599, 2018.
  • Yayli, M.Ö., A compact analytical method for vibration of micro-sized beams with different boundary conditions, Mechanics of Advanced Materials and Structures, 24(6), 496-508, 2017.
  • Yayli, M.Ö., Torsion of nonlocal bars with equilateral triangle cross sections, Journal of Computational and Theoretical Nanoscience, 10(2), 376-379, 2013.
  • Yaylı, M.Ö., Buckling analysis of a rotationally restrained single walled carbon nanotube embedded in an elastic medium using nonlocal elasticity, International Journal of Engineering and Applied Sciences, 8(2), 40-50, 2016.
  • Yayli, M.Ö., Weak formulation of finite element method for nonlocal beams using additional boundary conditions, Journal of Computational and Theoretical Nanoscience, 8(11), 2173-2180, 2011.
  • Yaylı, M. Ö., An analytical solution for free vibrations of a cantilever nanobeam with a spring mass system, International Journal of Engineering and Applied Sciences, 7(4), 10-18, 2016.
  • Kadıoğlu, H. & Yaylı, M. Ö., Buckling analysis of non-local Timoshenko beams by using Fourier series, International Journal of Engineering and Applied Sciences, 9(4), 89-99, 2017.
  • Uzun, B, & Yaylı, M. Ö., Nonlocal vibration analysis of Ti-6Al-4V/ZrO 2 functionally graded nanobeam on elastic matrix, Arabian Journal of Geosciences, 13(4), 1-10, 2020.
There are 59 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mustafa Özgür Yaylı 0000-0003-2231-170X

Togay Küpeli 0000-0002-5921-8667

Yakup Çavuş 0000-0002-6607-9650

Publication Date September 5, 2021
Acceptance Date June 18, 2021
Published in Issue Year 2021 Volume: 13 Issue: 2

Cite

APA Yaylı, M. Ö., Küpeli, T., & Çavuş, Y. (2021). Weighted Residual Approach for Bending Analysis of Nanobeam Using by Modified Couple Stress Theory. International Journal of Engineering and Applied Sciences, 13(2), 43-55. https://doi.org/10.24107/ijeas.932580
AMA Yaylı MÖ, Küpeli T, Çavuş Y. Weighted Residual Approach for Bending Analysis of Nanobeam Using by Modified Couple Stress Theory. IJEAS. September 2021;13(2):43-55. doi:10.24107/ijeas.932580
Chicago Yaylı, Mustafa Özgür, Togay Küpeli, and Yakup Çavuş. “Weighted Residual Approach for Bending Analysis of Nanobeam Using by Modified Couple Stress Theory”. International Journal of Engineering and Applied Sciences 13, no. 2 (September 2021): 43-55. https://doi.org/10.24107/ijeas.932580.
EndNote Yaylı MÖ, Küpeli T, Çavuş Y (September 1, 2021) Weighted Residual Approach for Bending Analysis of Nanobeam Using by Modified Couple Stress Theory. International Journal of Engineering and Applied Sciences 13 2 43–55.
IEEE M. Ö. Yaylı, T. Küpeli, and Y. Çavuş, “Weighted Residual Approach for Bending Analysis of Nanobeam Using by Modified Couple Stress Theory”, IJEAS, vol. 13, no. 2, pp. 43–55, 2021, doi: 10.24107/ijeas.932580.
ISNAD Yaylı, Mustafa Özgür et al. “Weighted Residual Approach for Bending Analysis of Nanobeam Using by Modified Couple Stress Theory”. International Journal of Engineering and Applied Sciences 13/2 (September 2021), 43-55. https://doi.org/10.24107/ijeas.932580.
JAMA Yaylı MÖ, Küpeli T, Çavuş Y. Weighted Residual Approach for Bending Analysis of Nanobeam Using by Modified Couple Stress Theory. IJEAS. 2021;13:43–55.
MLA Yaylı, Mustafa Özgür et al. “Weighted Residual Approach for Bending Analysis of Nanobeam Using by Modified Couple Stress Theory”. International Journal of Engineering and Applied Sciences, vol. 13, no. 2, 2021, pp. 43-55, doi:10.24107/ijeas.932580.
Vancouver Yaylı MÖ, Küpeli T, Çavuş Y. Weighted Residual Approach for Bending Analysis of Nanobeam Using by Modified Couple Stress Theory. IJEAS. 2021;13(2):43-55.

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