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Year 2020, Volume: 12 Issue: 2, 78 - 87, 14.10.2020

Büşra Uzun Mustafa Özgür Yaylı

https://doi.org/10.24107/ijeas.782419
Cited By: 7

Abstract

References

  • [1] Lü, C.F., Lim, C.W., Chen, W.Q., Size-dependent elastic behavior of FGM ultra-thin films based on generalized refined theory. International Journal of Solids and Structures, 46(5), 1176-1185, 2009.
  • [2] Lanhe, W., Thermal buckling of a simply supported moderately thick rectangular FGM plate. Composite Structures, 64(2), 211-218, 2004.
  • [3] Belkorissat, I., Houari, M.S.A., Tounsi, A., Bedia, E.A., Mahmoud, S.R., On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model. Steel Compos. Struct, 18(4), 1063-1081, 2015.
  • [4] Żur, K.K., Arefi, M., Kim, J., Reddy, J.N. Free vibration and buckling analyses of magneto-electro-elastic FGM nanoplates based on nonlocal modified higher-order sinusoidal shear deformation theory. Composites Part B: Engineering, 182, 107601, 2020.
  • [5] Ebrahimi, F., Ehyaei, J., Babaei, R. Thermal buckling of FGM nanoplates subjected to linear and nonlinear varying loads on Pasternak foundation. Advances in materials Research, 5(4), 245, 2016.
  • [6] Yuan, Y., Zhao, K., Sahmani, S., Safaei, B. Size-dependent shear buckling response of FGM skew nanoplates modeled via different homogenization schemes. Applied Mathematics and Mechanics, 1-18, 2020.
  • [7] Karami, B., Shahsavari, D., Janghorban, M., Li, L. On the resonance of functionally graded nanoplates using bi-Helmholtz nonlocal strain gradient theory. International Journal of Engineering Science, 144, 103143, 2019.
  • [8] Uzun, B., Yaylı, M.Ö. Nonlocal vibration analysis of Ti-6Al-4V/ZrO2 functionally graded nanobeam on elastic matrix. Arabian Journal of Geosciences, 13(4), 1-10, 2020.
  • [9] 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.
  • [10] Uzun, B., Yaylı, M. Ö., Finite element model of functionally graded nanobeam for free vibration analysis. International Journal of Engineering and Applied Sciences, 11(2), 387-400, 2019.
  • [11] Hosseini, S.A.H., Rahmani, O., Free vibration of shallow and deep curved FG nanobeam via nonlocal Timoshenko curved beam model. Applied Physics A, 122(3), 169, 2016.
  • [12] Jalaei, M.H., Civalek, Ӧ., On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam. International Journal of Engineering Science, 143, 14-32, 2019.
  • [13] Saffari, S., Hashemian, M., Toghraie, D., Dynamic stability of functionally graded nanobeam based on nonlocal Timoshenko theory considering surface effects. Physica B: Condensed Matter, 520, 97-105, 2017.
  • [14] Aydogdu, M., Arda, M., Filiz, S., Vibration of axially functionally graded nano rods and beams with a variable nonlocal parameter. Advances in nano research, 6(3), 257, 2018.
  • [15] Arda, M., Axial dynamics of functionally graded Rayleigh-Bishop nanorods. Microsystem Technologies, 1-14, 2020.
  • [16] Kiani, K., Free dynamic analysis of functionally graded tapered nanorods via a newly developed nonlocal surface energy-based integro-differential model. Composite Structures, 139, 151-166, 2016.
  • [17] Arefi, M., Zenkour, A. M., Employing the coupled stress components and surface elasticity for nonlocal solution of wave propagation of a functionally graded piezoelectric Love nanorod model. Journal of Intelligent Material Systems and Structures, 28(17), 2403-2413, 2017.
  • [18] Narendar, S., Wave dispersion in functionally graded magneto-electro-elastic nonlocal rod. Aerospace Science and Technology, 51, 42-51 2016.
  • [19] Demir, Ç., Civalek, Ö., A new nonlocal FEM via Hermitian cubic shape functions for thermal vibration of nano beams surrounded by an elastic matrix. Composite Structures, 168, 872-884, 2017.
  • [20] Adhikari, S., Murmu, T., McCarthy, M.A., Dynamic finite element analysis of axially vibrating nonlocal rods. Finite Elements in Analysis and Design, 63, 42-50, 2013.
  • [21] Hemmatnezhad, M., Ansari, R., Finite element formulation for the free vibration analysis of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory. Journal of theoretical and applied physics, 7(1), 6, 2013.
  • [22] Civalek, Ö., Uzun, B., Yaylı, M.Ö., Akgöz, B. Size-dependent transverse and longitudinal vibrations of embedded carbon and silica carbide nanotubes by nonlocal finite element method. The European Physical Journal Plus, 135(4), 381, 2020.
  • [23] Ghannadpour, S. A. M. (2019). A variational formulation to find finite element bending, buckling and vibration equations of nonlocal Timoshenko beams. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 43(1), 493-502.
  • [24] Akbaş, Ş.D., Static, Vibration, and Buckling Analysis of Nanobeams. Nanomechanics, 123, 2017.
  • [25] Anjomshoa, A., Shahidi, A. R., Hassani, B., Jomehzadeh, E. Finite element buckling analysis of multi-layered graphene sheets on elastic substrate based on nonlocal elasticity theory. Applied Mathematical Modelling, 38(24), 5934-5955, 2014.
  • [26] Taghizadeh, M., Ovesy, H.R., Ghannadpour, S.A.M. Beam buckling analysis by nonlocal integral elasticity finite element method. International Journal of Structural Stability and Dynamics, 16(06), 1550015, 2016.
  • [27] Demir, C., Mercan, K., Numanoglu, H.M., Civalek, O., Bending response of nanobeams resting on elastic foundation. Journal of Applied and Computational Mechanics, 4(2), 105-114, 2018.
  • [28] Taghizadeh, M., Ovesy, H.R., Ghannadpour, S.A.M., Nonlocal integral elasticity analysis of beam bending by using finite element method. Structural Engineering and Mechanics, 54(4), 755-769, 2015.
  • [29] 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.
  • [30] Reddy, J.N., Energy Principles and Variational Methods in Applied Mechanics (2nd ed.)’ (John Wiley & Sons, New York, 2002).
  • [31] 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.
  • [32] Xu, X.J., Zheng, M.L., Wang, X.C. On vibrations of nonlocal rods: Boundary conditions, exact solutions and their asymptotics. International Journal of Engineering Science, 119, 217-231, 2017.
  • [33] Numanoğlu, H.M., Akgöz, B., Civalek, Ö. On dynamic analysis of nanorods. International Journal of Engineering Science, 130, 33-50, 2018.
  • [34] Asghari, M., Rahaeifard, M., Kahrobaiyan, M.H., Ahmadian, M.T., The modified couple stress functionally graded Timoshenko beam formulation. Materials & Design, 32(3), 1435-1443, 2011.

A Solution Method for Longitudinal Vibrations of Functionally Graded Nanorods

Year 2020, Volume: 12 Issue: 2, 78 - 87, 14.10.2020

Büşra Uzun Mustafa Özgür Yaylı

https://doi.org/10.24107/ijeas.782419
Cited By: 7

Abstract

In the present study, a nonlocal finite element formulation of free longitudinal vibration is derived for functionally graded nano-sized rods. Size dependency is considered via Eringen’s nonlocal elasticity theory. Material properties, Young’s modulus and mass density, of the nano-sized rod change in the thickness direction according to the power-law. For the examined FG nanorod finite element, the axial displacement is specified with a linear function. The stiffness and mass matrices of functionally graded nano-sized rod are found by means of interpolation functions. Functionally graded nanorod is considered with clamped-free boundary condition and its longitudinal vibration analysis is performed.

Keywords

Nonlocal elaticity theory Functionally graded materials Nanorod Finite element method Vibration

References

  • [1] Lü, C.F., Lim, C.W., Chen, W.Q., Size-dependent elastic behavior of FGM ultra-thin films based on generalized refined theory. International Journal of Solids and Structures, 46(5), 1176-1185, 2009.
  • [2] Lanhe, W., Thermal buckling of a simply supported moderately thick rectangular FGM plate. Composite Structures, 64(2), 211-218, 2004.
  • [3] Belkorissat, I., Houari, M.S.A., Tounsi, A., Bedia, E.A., Mahmoud, S.R., On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model. Steel Compos. Struct, 18(4), 1063-1081, 2015.
  • [4] Żur, K.K., Arefi, M., Kim, J., Reddy, J.N. Free vibration and buckling analyses of magneto-electro-elastic FGM nanoplates based on nonlocal modified higher-order sinusoidal shear deformation theory. Composites Part B: Engineering, 182, 107601, 2020.
  • [5] Ebrahimi, F., Ehyaei, J., Babaei, R. Thermal buckling of FGM nanoplates subjected to linear and nonlinear varying loads on Pasternak foundation. Advances in materials Research, 5(4), 245, 2016.
  • [6] Yuan, Y., Zhao, K., Sahmani, S., Safaei, B. Size-dependent shear buckling response of FGM skew nanoplates modeled via different homogenization schemes. Applied Mathematics and Mechanics, 1-18, 2020.
  • [7] Karami, B., Shahsavari, D., Janghorban, M., Li, L. On the resonance of functionally graded nanoplates using bi-Helmholtz nonlocal strain gradient theory. International Journal of Engineering Science, 144, 103143, 2019.
  • [8] Uzun, B., Yaylı, M.Ö. Nonlocal vibration analysis of Ti-6Al-4V/ZrO2 functionally graded nanobeam on elastic matrix. Arabian Journal of Geosciences, 13(4), 1-10, 2020.
  • [9] 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.
  • [10] Uzun, B., Yaylı, M. Ö., Finite element model of functionally graded nanobeam for free vibration analysis. International Journal of Engineering and Applied Sciences, 11(2), 387-400, 2019.
  • [11] Hosseini, S.A.H., Rahmani, O., Free vibration of shallow and deep curved FG nanobeam via nonlocal Timoshenko curved beam model. Applied Physics A, 122(3), 169, 2016.
  • [12] Jalaei, M.H., Civalek, Ӧ., On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam. International Journal of Engineering Science, 143, 14-32, 2019.
  • [13] Saffari, S., Hashemian, M., Toghraie, D., Dynamic stability of functionally graded nanobeam based on nonlocal Timoshenko theory considering surface effects. Physica B: Condensed Matter, 520, 97-105, 2017.
  • [14] Aydogdu, M., Arda, M., Filiz, S., Vibration of axially functionally graded nano rods and beams with a variable nonlocal parameter. Advances in nano research, 6(3), 257, 2018.
  • [15] Arda, M., Axial dynamics of functionally graded Rayleigh-Bishop nanorods. Microsystem Technologies, 1-14, 2020.
  • [16] Kiani, K., Free dynamic analysis of functionally graded tapered nanorods via a newly developed nonlocal surface energy-based integro-differential model. Composite Structures, 139, 151-166, 2016.
  • [17] Arefi, M., Zenkour, A. M., Employing the coupled stress components and surface elasticity for nonlocal solution of wave propagation of a functionally graded piezoelectric Love nanorod model. Journal of Intelligent Material Systems and Structures, 28(17), 2403-2413, 2017.
  • [18] Narendar, S., Wave dispersion in functionally graded magneto-electro-elastic nonlocal rod. Aerospace Science and Technology, 51, 42-51 2016.
  • [19] Demir, Ç., Civalek, Ö., A new nonlocal FEM via Hermitian cubic shape functions for thermal vibration of nano beams surrounded by an elastic matrix. Composite Structures, 168, 872-884, 2017.
  • [20] Adhikari, S., Murmu, T., McCarthy, M.A., Dynamic finite element analysis of axially vibrating nonlocal rods. Finite Elements in Analysis and Design, 63, 42-50, 2013.
  • [21] Hemmatnezhad, M., Ansari, R., Finite element formulation for the free vibration analysis of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory. Journal of theoretical and applied physics, 7(1), 6, 2013.
  • [22] Civalek, Ö., Uzun, B., Yaylı, M.Ö., Akgöz, B. Size-dependent transverse and longitudinal vibrations of embedded carbon and silica carbide nanotubes by nonlocal finite element method. The European Physical Journal Plus, 135(4), 381, 2020.
  • [23] Ghannadpour, S. A. M. (2019). A variational formulation to find finite element bending, buckling and vibration equations of nonlocal Timoshenko beams. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 43(1), 493-502.
  • [24] Akbaş, Ş.D., Static, Vibration, and Buckling Analysis of Nanobeams. Nanomechanics, 123, 2017.
  • [25] Anjomshoa, A., Shahidi, A. R., Hassani, B., Jomehzadeh, E. Finite element buckling analysis of multi-layered graphene sheets on elastic substrate based on nonlocal elasticity theory. Applied Mathematical Modelling, 38(24), 5934-5955, 2014.
  • [26] Taghizadeh, M., Ovesy, H.R., Ghannadpour, S.A.M. Beam buckling analysis by nonlocal integral elasticity finite element method. International Journal of Structural Stability and Dynamics, 16(06), 1550015, 2016.
  • [27] Demir, C., Mercan, K., Numanoglu, H.M., Civalek, O., Bending response of nanobeams resting on elastic foundation. Journal of Applied and Computational Mechanics, 4(2), 105-114, 2018.
  • [28] Taghizadeh, M., Ovesy, H.R., Ghannadpour, S.A.M., Nonlocal integral elasticity analysis of beam bending by using finite element method. Structural Engineering and Mechanics, 54(4), 755-769, 2015.
  • [29] 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.
  • [30] Reddy, J.N., Energy Principles and Variational Methods in Applied Mechanics (2nd ed.)’ (John Wiley & Sons, New York, 2002).
  • [31] 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.
  • [32] Xu, X.J., Zheng, M.L., Wang, X.C. On vibrations of nonlocal rods: Boundary conditions, exact solutions and their asymptotics. International Journal of Engineering Science, 119, 217-231, 2017.
  • [33] Numanoğlu, H.M., Akgöz, B., Civalek, Ö. On dynamic analysis of nanorods. International Journal of Engineering Science, 130, 33-50, 2018.
  • [34] Asghari, M., Rahaeifard, M., Kahrobaiyan, M.H., Ahmadian, M.T., The modified couple stress functionally graded Timoshenko beam formulation. Materials & Design, 32(3), 1435-1443, 2011.
There are 34 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Büşra Uzun 0000-0002-7636-7170

Mustafa Özgür Yaylı 0000-0003-2231-170X

Publication Date October 14, 2020
Acceptance Date October 6, 2020
Published in Issue Year 2020 Volume: 12 Issue: 2

Cite

APA Uzun, B., & Yaylı, M. Ö. (2020). A Solution Method for Longitudinal Vibrations of Functionally Graded Nanorods. International Journal of Engineering and Applied Sciences, 12(2), 78-87. https://doi.org/10.24107/ijeas.782419
AMA Uzun B, Yaylı MÖ. A Solution Method for Longitudinal Vibrations of Functionally Graded Nanorods. IJEAS. October 2020;12(2):78-87. doi:10.24107/ijeas.782419
Chicago Uzun, Büşra, and Mustafa Özgür Yaylı. “A Solution Method for Longitudinal Vibrations of Functionally Graded Nanorods”. International Journal of Engineering and Applied Sciences 12, no. 2 (October 2020): 78-87. https://doi.org/10.24107/ijeas.782419.
EndNote Uzun B, Yaylı MÖ (October 1, 2020) A Solution Method for Longitudinal Vibrations of Functionally Graded Nanorods. International Journal of Engineering and Applied Sciences 12 2 78–87.
IEEE B. Uzun and M. Ö. Yaylı, “A Solution Method for Longitudinal Vibrations of Functionally Graded Nanorods”, IJEAS, vol. 12, no. 2, pp. 78–87, 2020, doi: 10.24107/ijeas.782419.
ISNAD Uzun, Büşra - Yaylı, Mustafa Özgür. “A Solution Method for Longitudinal Vibrations of Functionally Graded Nanorods”. International Journal of Engineering and Applied Sciences 12/2 (October 2020), 78-87. https://doi.org/10.24107/ijeas.782419.
JAMA Uzun B, Yaylı MÖ. A Solution Method for Longitudinal Vibrations of Functionally Graded Nanorods. IJEAS. 2020;12:78–87.
MLA Uzun, Büşra and Mustafa Özgür Yaylı. “A Solution Method for Longitudinal Vibrations of Functionally Graded Nanorods”. International Journal of Engineering and Applied Sciences, vol. 12, no. 2, 2020, pp. 78-87, doi:10.24107/ijeas.782419.
Vancouver Uzun B, Yaylı MÖ. A Solution Method for Longitudinal Vibrations of Functionally Graded Nanorods. IJEAS. 2020;12(2):78-87.

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