Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2025, Cilt: 17 Sayı: 1, 61 - 72, 01.05.2025

Mustafa Şeker , Ömer Civalek

https://doi.org/10.24107/ijeas.1650748

Öz

Kaynakça

  • Moosavi, H., Mohammadi, M., Farajpour, A. and Shahidi, S., Vibration analysis of nanorings using nonlocal continuum mechanics and shear deformable ring theory. Physica E Low-dimensional Systems and Nanostructures, 44(1),135–140. 2011.
  • Wang, C. M., and Duan, W. H., Free vibration of nanorings/arches based on nonlocal elasticity. Journal of Applied Physics, 104(1) 2008.
  • Ebrahimi F., Daman M., An investigation of radial vibration modes of embedded double-curved-nanobeam system. Çankaya University Journal of Science and Engineering, 13(1), 058-079, 2016.
  • Lellep J., Mubasshar S., Natural vibrations of circular nanoarches of piecewise constant thickness. Acta Et CommentatıonesUnıversıtatısTartuensıs de Mathematıca, 27(2), 2023.
  • Kelf T.A., Tanaka Y., Matsuda O., Larsson E.M., Sutherland D.S., Wright O.B., Ultrafast vibrations of gold nanorings. Nano Letters, 11(9), 3893-3898, 2011.
  • Shi, M., Li, Q., Liu, B., Feng, X., and Huang, Y., Atomic-scale finite element analysis of vibration mode transformation in carbon nanorings and single-walled carbon nanotubes. International Journal of Solids and Structures, 46(25–26), 4342–4360, 2009.
  • Plaut, R. H. and Virgin, L. N., Deformation and vibration of upright loops on a foundation and of hanging loops. International Journal of Solids and Structures, 51(18), 3067–3075, 2014.
  • Nuhu, A. A. and Safaei, B. A., Comprehensive review on the vibration analyses of small-scaled plate based structures by utilizing the nonclassical continuum elasticity theories. Thin-Walled Structures, 179,109622, 2022.
  • Numanoğlu, H. M. and Civalek, Ö., On shear-dependent vibration of nano frames. International Journal of Engineering Science, 195, 103992, 2023.
  • Farajpour, A., Ghayesh, M. H. and Farokhi, H. A., Review on the mechanics of nanostructures. International Journal of Engineering Science, 133, 231-263, 2018.
  • Assadi, A. and Farshi, B., Size dependent vibration of curved nanobeams and rings including surface energies. Physica E Low-dimensional Systems and Nanostructures, 43(4), 975–978, 2011.
  • Murmu, T. and Adhikari, S., Nonlocal effects in the longitudinal vibration of double-nanorod systems. Physica E Low-dimensional Systems and Nanostructures, 43(1), 415–422, 2010.
  • Mohammadi, M., Farajpour, A., Goodarzi, M. and Pour, H. S. N., Numerical study of the effect of shear in-plane load on the vibration analysis of graphene sheet embedded in an elastic medium. Computational Materials Science, 82, 510–520, 2014.
  • Danesh, M., Farajpour, A. and Mohammadi, M., Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method. Mechanics Research Communications, 39(1), 23–27, 2012.
  • Li, H., Wang, X., Wang, H. and Chen, J., The nonlocal frequency behavior of nanomechanical mass sensors based on the multi-directional vibrations of a buckled nanoribbon. Applied Mathematical Modelling, 77(2), 1780–1796, 2020.
  • Fotouhi, M., Firouz-Abadi, R. and Haddadpour, H., Free vibration analysis of nanocones embedded in an elastic medium using a nonlocal continuum shell model. International Journal of Engineering Science, 64, 14–22, 2013.
  • Chakraverty, S. and Behera, L., Free vibration of rectangular nanoplates using Rayleigh–Ritz method. Physica E Low-dimensional Systems and Nanostructures, 56, 357–363, 2014.
  • Arpanahi, R. A., Hosseini-Hashemi, S., Rahmanian, S., Hashemi, S. H., and Ahmadi-Savadkoohi, A., Nonlocal surface energy effect on free vibration behavior of nanoplates submerged in incompressible fluid. Thin-Walled Structures, 143, 106212, 2019.
  • Fernandes, R., El-Borgi, S., Mousavi, S., Reddy, J. and Mechmoum, A., Nonlinear size-dependent longitudinal vibration of carbon nanotubes embedded in an elastic medium. Physica E Low-dimensional Systems and Nanostructures, 88, 18–25, 2017.
  • Pradhan, S. and Murmu, T., Application of nonlocal elasticity and DQM in the flapwise bending vibration of a rotating nanocantilever. Physica E Low-dimensional Systems and Nanostructures, 42(7), 1944–1949, 2010.
  • Mohammadi, M., Ghayour, M. and Farajpour, A., Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model. Composites Part B Engineering, 45(1), 32–42, 2013.
  • Analooei, H., Azhari, M. and Heidarpour, A., Elastic buckling and vibration analyses of orthotropic nanoplates using nonlocal continuum mechanics and spline finite strip method. Applied Mathematical Modelling, 37(10–11), 6703–6717, 2013.
  • Sarrami-Foroushani, S. and 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, 85, 168–178, 2014.
  • Mohammadi, M., Goodarzi, M., Ghayour, M. and Farajpour, A., Influence of in-plane pre-load on the vibration frequency of circular graphene sheet via nonlocal continuum theory. Composites Part B Engineering, 51, 121–129, 2013.
  • Murmu, T. and Adhikari, S., Nonlocal elasticity based vibration of initially pre-stressed coupled nanobeam systems. European Journal of Mechanics - a/Solids, 34, 52–62, 2012.
  • Civalek, Ö., Akbaş, Ş.D., Akgöz B. and Dastjerdi S., Forced vibration analysis of composite beams reinforced by carbon nanotubes. Nanomaterials, 11(3),571, 2021.
  • Sobhani, E., Masoodi, A. R., Civalek, Ö. and Ahmadipar, A. R., Agglomerated impact of CNT vs. GNP nanofillers on hybridization of polymer matrix for vibration of coupled hemispherical-conical-conical shells. Aeorospace Science and Tecnology, 120, 107257, 2022.
  • Mercan, K., Baltacıoğlu, A. K. and Civalek, Ö., Free vibration of laminated and FGM/CNT composites annular thick plates with shear deformation by discrete singular convolution method. Composite Structures, 186, 139-153, 2018.
  • Khorasani, M., Soleimani-Javid, Z., Arshid, E., Lampani, L. and Civalek, Ö., Thermo-elastic buckling of honeycomb microplates integrated with FG-GNPs reinforced Epoxy skins with scretching effect. Composite Structures, 258, 113430, 2021.
  • Civalek, Ö., Şeker, M. and Numanoğlu, H. M., In-plane free vibration analysis of nonlocal nanorings embedded in elastic medium. Applied Physics A, 131, 69, 2025.
  • Numanoğlu, H. M., Nano Ölçekli Sürekli ve Ayrık Sistemlerin Yerel Olmayan Sonlu Elemanlar Formülasyonu (NL-FEM) ile Dinamik Analizi. Master Thesis, Akdeniz Univercity, Antalya, 252 s. 2019.
  • Eringen, A. C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied physics, 54(9), 4703-4710, 1983.
  • Jalaei, M. H. and Civalek, Ö., A nonlocal strain gradient refined plate theory for dynamic instability of embedded graphene sheet including thermal effects. Composite Structures, 220, 209-220, 2019.
  • Uzun, B., Civalek, Ö. and Yaylı, M.Ö., Vibration of FG nano-sized beams embedded in Winkler elastic foundation and with various boundary conditions. Mechanics Based Design of Structures and Machines, 51(1), 481-500, 2023.
  • Civalek, Ö. and Baltacıoğlu, A. K., Vibration of carbon nanotube reinforced composite (CNTRC) annular sector plates by discrete singular convolution method. Composite Structures, 203, 458-465, 2018.
  • Civalek, Ö. and Jalaei, M. H., Shear buckling analysis of functionally gradded (FG) carbon nanotube reinforced skew plates with different boundary conditions. Aerospace Science and Tecnology, 99, 105753, 2020.
  • Hadji, L., Avcar, M. and Civalek, Ö., An analytical solution for the free vibration of FG nanoplates. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 43, 418, 2021.
  • Abouelregal, A. E., Akgöz, B. and Civalek, Ö., Magneto-thermoelastic interactions in an unbounded orthotropic viscoelastic solid under the Hall current effect by the fourth-order Moore-Gibson-Thompson equation. Computers and Mathematics with Applications, 141, 102-115, 2023.
  • Akbaş, Ş. D., Dastjerdi, S., Akgöz, B. and Civalek, Ö., Dynamic analysis of functionally graded porous microbeams under moving load. Transport in Porous Media, 142, 209-227, 2022.
  • Dastjerdi, S., Akgöz, B., and Civalek, Ö., On the shell model for human eye in Glaucoma disease. International Journal of Engineering Science, 158, 103414, 2021.
  • Abouelregal, A.E., Akgöz, B. and Civalek, Ö., Nonlocal thermoelastic vibration of a solid medium subjected to a pulsed heat flux via Caputo-Fabrizio fractional derivative heat conduction. Applied Physics A, 128(8), 660, 2022.
  • Dastjerdi, S., Alibakhshi, A., Akgöz, B. and Civalek, Ö., On a comprehensive analysis for mechanical problems of spherical structures. International Journal of Engineering Science, 183,103796, 2023.
  • Dastjerdi, S., Malikan, M., Akgöz, B., Civalek, Ö., Wiczenbach, T., and Eremeyev, V.A., On the deformation and frequency analyses of SARS-CoV-2 at nanoscale. International Journal of Engineering Science, 170, 103604, 2022.

Free Vibration Analysis of Nanorings Using The Nonlocal Elasticity

Yıl 2025, Cilt: 17 Sayı: 1, 61 - 72, 01.05.2025

Mustafa Şeker , Ömer Civalek

https://doi.org/10.24107/ijeas.1650748

Öz

In this research article, a free vibration analysis study of nanorings using nonlocal elasticity has been attempted. Nanorings are involved in many areas of our lives. It is seen that nanorings are frequently used, especially in technological tools. In this study, firstly the studies carried out by scientists on nanorings are discussed comprehensively. In particular, these studies are related to the theory of nonlocal elasticity and the vibration of nanorings. In this context, after a literature review, an attempt was made to express the theory of nonlocal elasticity. By using the simplest equations of the nonlocal elasticity theory, the main equation of this theory was obtained. While obtaining the main equation, a number of mathematical functions are used from the simplest equations. It has been seen that the main equation obtained in the nonlocal elasticity theory for nanorings has been used in many studies. After the theory of nonlocal elasticity, the free vibration of nanorings is discussed. Here, mathematical equations are used in the environment embedded in elastic soil. In addition, new mathematical equations are crated by taking the ''"k" _"m" '' value to zero in order to get rid of the elastic embedded environment, that is, the ground effect. Here, the free vibration dimensionless frequency equation of nanorings is obtained. As a result, mathematical equations regarding the theory of nonlocal elasticity and the free vibration of nanorings are derived.

Anahtar Kelimeler

Free Vibration Nanorings Nonlocal Elasticity Theory

Kaynakça

  • Moosavi, H., Mohammadi, M., Farajpour, A. and Shahidi, S., Vibration analysis of nanorings using nonlocal continuum mechanics and shear deformable ring theory. Physica E Low-dimensional Systems and Nanostructures, 44(1),135–140. 2011.
  • Wang, C. M., and Duan, W. H., Free vibration of nanorings/arches based on nonlocal elasticity. Journal of Applied Physics, 104(1) 2008.
  • Ebrahimi F., Daman M., An investigation of radial vibration modes of embedded double-curved-nanobeam system. Çankaya University Journal of Science and Engineering, 13(1), 058-079, 2016.
  • Lellep J., Mubasshar S., Natural vibrations of circular nanoarches of piecewise constant thickness. Acta Et CommentatıonesUnıversıtatısTartuensıs de Mathematıca, 27(2), 2023.
  • Kelf T.A., Tanaka Y., Matsuda O., Larsson E.M., Sutherland D.S., Wright O.B., Ultrafast vibrations of gold nanorings. Nano Letters, 11(9), 3893-3898, 2011.
  • Shi, M., Li, Q., Liu, B., Feng, X., and Huang, Y., Atomic-scale finite element analysis of vibration mode transformation in carbon nanorings and single-walled carbon nanotubes. International Journal of Solids and Structures, 46(25–26), 4342–4360, 2009.
  • Plaut, R. H. and Virgin, L. N., Deformation and vibration of upright loops on a foundation and of hanging loops. International Journal of Solids and Structures, 51(18), 3067–3075, 2014.
  • Nuhu, A. A. and Safaei, B. A., Comprehensive review on the vibration analyses of small-scaled plate based structures by utilizing the nonclassical continuum elasticity theories. Thin-Walled Structures, 179,109622, 2022.
  • Numanoğlu, H. M. and Civalek, Ö., On shear-dependent vibration of nano frames. International Journal of Engineering Science, 195, 103992, 2023.
  • Farajpour, A., Ghayesh, M. H. and Farokhi, H. A., Review on the mechanics of nanostructures. International Journal of Engineering Science, 133, 231-263, 2018.
  • Assadi, A. and Farshi, B., Size dependent vibration of curved nanobeams and rings including surface energies. Physica E Low-dimensional Systems and Nanostructures, 43(4), 975–978, 2011.
  • Murmu, T. and Adhikari, S., Nonlocal effects in the longitudinal vibration of double-nanorod systems. Physica E Low-dimensional Systems and Nanostructures, 43(1), 415–422, 2010.
  • Mohammadi, M., Farajpour, A., Goodarzi, M. and Pour, H. S. N., Numerical study of the effect of shear in-plane load on the vibration analysis of graphene sheet embedded in an elastic medium. Computational Materials Science, 82, 510–520, 2014.
  • Danesh, M., Farajpour, A. and Mohammadi, M., Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method. Mechanics Research Communications, 39(1), 23–27, 2012.
  • Li, H., Wang, X., Wang, H. and Chen, J., The nonlocal frequency behavior of nanomechanical mass sensors based on the multi-directional vibrations of a buckled nanoribbon. Applied Mathematical Modelling, 77(2), 1780–1796, 2020.
  • Fotouhi, M., Firouz-Abadi, R. and Haddadpour, H., Free vibration analysis of nanocones embedded in an elastic medium using a nonlocal continuum shell model. International Journal of Engineering Science, 64, 14–22, 2013.
  • Chakraverty, S. and Behera, L., Free vibration of rectangular nanoplates using Rayleigh–Ritz method. Physica E Low-dimensional Systems and Nanostructures, 56, 357–363, 2014.
  • Arpanahi, R. A., Hosseini-Hashemi, S., Rahmanian, S., Hashemi, S. H., and Ahmadi-Savadkoohi, A., Nonlocal surface energy effect on free vibration behavior of nanoplates submerged in incompressible fluid. Thin-Walled Structures, 143, 106212, 2019.
  • Fernandes, R., El-Borgi, S., Mousavi, S., Reddy, J. and Mechmoum, A., Nonlinear size-dependent longitudinal vibration of carbon nanotubes embedded in an elastic medium. Physica E Low-dimensional Systems and Nanostructures, 88, 18–25, 2017.
  • Pradhan, S. and Murmu, T., Application of nonlocal elasticity and DQM in the flapwise bending vibration of a rotating nanocantilever. Physica E Low-dimensional Systems and Nanostructures, 42(7), 1944–1949, 2010.
  • Mohammadi, M., Ghayour, M. and Farajpour, A., Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model. Composites Part B Engineering, 45(1), 32–42, 2013.
  • Analooei, H., Azhari, M. and Heidarpour, A., Elastic buckling and vibration analyses of orthotropic nanoplates using nonlocal continuum mechanics and spline finite strip method. Applied Mathematical Modelling, 37(10–11), 6703–6717, 2013.
  • Sarrami-Foroushani, S. and 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, 85, 168–178, 2014.
  • Mohammadi, M., Goodarzi, M., Ghayour, M. and Farajpour, A., Influence of in-plane pre-load on the vibration frequency of circular graphene sheet via nonlocal continuum theory. Composites Part B Engineering, 51, 121–129, 2013.
  • Murmu, T. and Adhikari, S., Nonlocal elasticity based vibration of initially pre-stressed coupled nanobeam systems. European Journal of Mechanics - a/Solids, 34, 52–62, 2012.
  • Civalek, Ö., Akbaş, Ş.D., Akgöz B. and Dastjerdi S., Forced vibration analysis of composite beams reinforced by carbon nanotubes. Nanomaterials, 11(3),571, 2021.
  • Sobhani, E., Masoodi, A. R., Civalek, Ö. and Ahmadipar, A. R., Agglomerated impact of CNT vs. GNP nanofillers on hybridization of polymer matrix for vibration of coupled hemispherical-conical-conical shells. Aeorospace Science and Tecnology, 120, 107257, 2022.
  • Mercan, K., Baltacıoğlu, A. K. and Civalek, Ö., Free vibration of laminated and FGM/CNT composites annular thick plates with shear deformation by discrete singular convolution method. Composite Structures, 186, 139-153, 2018.
  • Khorasani, M., Soleimani-Javid, Z., Arshid, E., Lampani, L. and Civalek, Ö., Thermo-elastic buckling of honeycomb microplates integrated with FG-GNPs reinforced Epoxy skins with scretching effect. Composite Structures, 258, 113430, 2021.
  • Civalek, Ö., Şeker, M. and Numanoğlu, H. M., In-plane free vibration analysis of nonlocal nanorings embedded in elastic medium. Applied Physics A, 131, 69, 2025.
  • Numanoğlu, H. M., Nano Ölçekli Sürekli ve Ayrık Sistemlerin Yerel Olmayan Sonlu Elemanlar Formülasyonu (NL-FEM) ile Dinamik Analizi. Master Thesis, Akdeniz Univercity, Antalya, 252 s. 2019.
  • Eringen, A. C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied physics, 54(9), 4703-4710, 1983.
  • Jalaei, M. H. and Civalek, Ö., A nonlocal strain gradient refined plate theory for dynamic instability of embedded graphene sheet including thermal effects. Composite Structures, 220, 209-220, 2019.
  • Uzun, B., Civalek, Ö. and Yaylı, M.Ö., Vibration of FG nano-sized beams embedded in Winkler elastic foundation and with various boundary conditions. Mechanics Based Design of Structures and Machines, 51(1), 481-500, 2023.
  • Civalek, Ö. and Baltacıoğlu, A. K., Vibration of carbon nanotube reinforced composite (CNTRC) annular sector plates by discrete singular convolution method. Composite Structures, 203, 458-465, 2018.
  • Civalek, Ö. and Jalaei, M. H., Shear buckling analysis of functionally gradded (FG) carbon nanotube reinforced skew plates with different boundary conditions. Aerospace Science and Tecnology, 99, 105753, 2020.
  • Hadji, L., Avcar, M. and Civalek, Ö., An analytical solution for the free vibration of FG nanoplates. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 43, 418, 2021.
  • Abouelregal, A. E., Akgöz, B. and Civalek, Ö., Magneto-thermoelastic interactions in an unbounded orthotropic viscoelastic solid under the Hall current effect by the fourth-order Moore-Gibson-Thompson equation. Computers and Mathematics with Applications, 141, 102-115, 2023.
  • Akbaş, Ş. D., Dastjerdi, S., Akgöz, B. and Civalek, Ö., Dynamic analysis of functionally graded porous microbeams under moving load. Transport in Porous Media, 142, 209-227, 2022.
  • Dastjerdi, S., Akgöz, B., and Civalek, Ö., On the shell model for human eye in Glaucoma disease. International Journal of Engineering Science, 158, 103414, 2021.
  • Abouelregal, A.E., Akgöz, B. and Civalek, Ö., Nonlocal thermoelastic vibration of a solid medium subjected to a pulsed heat flux via Caputo-Fabrizio fractional derivative heat conduction. Applied Physics A, 128(8), 660, 2022.
  • Dastjerdi, S., Alibakhshi, A., Akgöz, B. and Civalek, Ö., On a comprehensive analysis for mechanical problems of spherical structures. International Journal of Engineering Science, 183,103796, 2023.
  • Dastjerdi, S., Malikan, M., Akgöz, B., Civalek, Ö., Wiczenbach, T., and Eremeyev, V.A., On the deformation and frequency analyses of SARS-CoV-2 at nanoscale. International Journal of Engineering Science, 170, 103604, 2022.
Toplam 43 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Katı Mekanik
Bölüm Makaleler
Yazarlar

Mustafa Şeker 0000-0003-4128-8891

Ömer Civalek 0000-0003-1907-9479

Yayımlanma Tarihi 1 Mayıs 2025
Gönderilme Tarihi 4 Mart 2025
Kabul Tarihi 10 Nisan 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 17 Sayı: 1

Kaynak Göster

APA Şeker, M., & Civalek, Ö. (2025). Free Vibration Analysis of Nanorings Using The Nonlocal Elasticity. International Journal of Engineering and Applied Sciences, 17(1), 61-72. https://doi.org/10.24107/ijeas.1650748
AMA Şeker M, Civalek Ö. Free Vibration Analysis of Nanorings Using The Nonlocal Elasticity. IJEAS. Mayıs 2025;17(1):61-72. doi:10.24107/ijeas.1650748
Chicago Şeker, Mustafa, ve Ömer Civalek. “Free Vibration Analysis of Nanorings Using The Nonlocal Elasticity”. International Journal of Engineering and Applied Sciences 17, sy. 1 (Mayıs 2025): 61-72. https://doi.org/10.24107/ijeas.1650748.
EndNote Şeker M, Civalek Ö (01 Mayıs 2025) Free Vibration Analysis of Nanorings Using The Nonlocal Elasticity. International Journal of Engineering and Applied Sciences 17 1 61–72.
IEEE M. Şeker ve Ö. Civalek, “Free Vibration Analysis of Nanorings Using The Nonlocal Elasticity”, IJEAS, c. 17, sy. 1, ss. 61–72, 2025, doi: 10.24107/ijeas.1650748.
ISNAD Şeker, Mustafa - Civalek, Ömer. “Free Vibration Analysis of Nanorings Using The Nonlocal Elasticity”. International Journal of Engineering and Applied Sciences 17/1 (Mayıs 2025), 61-72. https://doi.org/10.24107/ijeas.1650748.
JAMA Şeker M, Civalek Ö. Free Vibration Analysis of Nanorings Using The Nonlocal Elasticity. IJEAS. 2025;17:61–72.
MLA Şeker, Mustafa ve Ömer Civalek. “Free Vibration Analysis of Nanorings Using The Nonlocal Elasticity”. International Journal of Engineering and Applied Sciences, c. 17, sy. 1, 2025, ss. 61-72, doi:10.24107/ijeas.1650748.
Vancouver Şeker M, Civalek Ö. Free Vibration Analysis of Nanorings Using The Nonlocal Elasticity. IJEAS. 2025;17(1):61-72.
 Kapak Resmi İndir

21357