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Articles

Vibration of FG nano-sized beams embedded in Winkler elastic foundation and with various boundary conditions

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Pages 481-500 | Received 01 Oct 2020, Accepted 02 Nov 2020, Published online: 11 Nov 2020

References

  • Akbaş, Ş. D. 2018. Fonksiyonel derecelendirilmişortotropik bir kirişin statik ve titreşim davranışlarının incelenmesi. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20 (1):69–82.
  • Akgöz, B., and Ö. Civalek. 2013a. Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory. Composite Structures 98:314–22.
  • Akgöz, B., and Ö. Civalek. 2013b. Buckling analysis of functionally graded microbeams based on the strain gradient theory. Acta Mechanica 224 (9):2185–201.
  • Akgöz, B., and Ö. Civalek. 2015. A microstructure-dependent sinusoidal plate model based on the strain gradient elasticity theory. Acta Mechanica 226 (7):2277–94.
  • Alshorbagy, A. E., M. A. Eltaher, and F. F. Mahmoud. 2011. Free vibration characteristics of a functionally graded beam by finite element method. Applied Mathematical Modelling 35 (1):412–25. doi:10.1016/j.apm.2010.07.006.
  • Ansari, R., J. Torabi, and A. Norouzzadeh. 2018. Bending analysis of embedded nanoplates based on the integral formulation of Eringen’s nonlocal theory using the finite element method. Physica B: Condensed Matter 534:90–7.
  • Arefi, M. 2018. Analysis of a doubly curved piezoelectric nano shell: Nonlocal electro-elastic bending solution. European Journal of Mechanics-A/Solids 70:226–37.
  • Arefi, M. 2019. Third-order electro-elastic analysis of sandwich doubly curved piezoelectric micro shells. Mechanics Based Design of Structures and Machines. doi:10.1080/15397734.2019.1698435.
  • Arefi, M., S. Firouzeh, E. M. R. Bidgoli, and Ö. Civalek. 2020. Analysis of porous micro-plates reinforced with FG-GNPs based on Reddy plate theory. Composite Structures 247:112391.
  • Arefi, M., E. Mohammad-Rezaei Bidgoli, and Ö. Civalek. 2020. Bending response of FG composite doubly curved nanoshells with thickness stretching via higher-order sinusoidal shear theory. Mechanics Based Design of Structures and Machines. doi:10.1080/15397734.2020.1777157.
  • Arefi, M., and A. H. Soltan Arani. 2018. Higher order shear deformation bending results of a magnetoelectrothermoelastic functionally graded nanobeam in thermal, mechanical, electrical, and magnetic environments. Mechanics Based Design of Structures and Machines 46 (6):669–92.
  • Arefi, M., and A. M. Zenkour. 2017. Transient analysis of a three-layer microbeam subjected to electric potential. International Journal of Smart and Nano Materials 8 (1):20–40.
  • Arefi, M., and A. M. Zenkour. 2019a. Influence of magneto-electric environments on size-dependent bending results of three-layer piezomagnetic curved nanobeam based on sinusoidal shear deformation theory. Journal of Sandwich Structures & Materials 21 (8):2751–78.
  • Arefi, M., and A. M. Zenkour. 2019b. Effect of thermo-magneto-electro-mechanical fields on the bending behaviors of a three-layered nanoplate based on sinusoidal shear-deformation plate theory. Journal of Sandwich Structures & Materials 21 (2):639–69.
  • Asrari, R., F. Ebrahimi, M. M. Kheirikhah, and K. H. Safari. 2020. Buckling analysis of heterogeneous magneto-electro-thermo-elastic cylindrical nanoshells based on nonlocal strain gradient elasticity theory. Mechanics Based Design of Structures and Machines. doi:10.1080/15397734.2020.1728545.
  • Avcar, M. 2019. Free vibration of imperfect sigmoid and power law functionally graded beams. Steel and Composite Structures 30 (6):603–15.
  • Aydogdu, M. 2009. A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration. Physica E: Low-Dimensional Systems and Nanostructures 41 (9):1651–5.
  • Aydogdu, M., and V. Taskin. 2007. Free vibration analysis of functionally graded beams with simply supported edges. Materials & Design 28 (5):1651–6.
  • Barati, M. R. 2018. Vibration analysis of porous FG nanoshells with even and uneven porosity distributions using nonlocal strain gradient elasticity. Acta Mechanica 229 (3):1183–96.
  • Barati, M. R., and A. M. Zenkour. 2019. Analysis of postbuckling behavior of general higher-order functionally graded nanoplates with geometrical imperfection considering porosity distributions. Mechanics of Advanced Materials and Structures 26 (12):1081–8.
  • Cao, D., Y. Gao, M. Yao, and W. Zhang. 2018. Free vibration of axially functionally graded beams using the asymptotic development method. Engineering Structures 173:442–8.
  • Civalek, Ö., and Ç. Demir. 2011. Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory. Applied Mathematical Modelling 35 (5):2053–67.
  • Civalek, Ö., and Ç. Demir. 2016. A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method. Applied Mathematics and Computation 289:335–52.
  • Civalek, Ö., B. Uzun, M. Ö. Yaylı, and B. Akgöz. 2020. 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.
  • Crone, W. C. 2008. A brief introduction to MEMS and NEMS, 203–28. New York, NY: Springer.
  • Dabbagh, A., A. Rastgoo, and F. Ebrahimi. 2020. Thermal buckling analysis of agglomerated multiscale hybrid nanocomposites via a refined beam theory. Mechanics Based Design of Structures and Machines. doi:10.1080/15397734.2019.1692666.
  • Demir, Ç. 2016. Nonlocal vibration analysis for micro/nano beam on Winkler foundation via DTM. International Journal of Engineering & Applied Sciences 8 (4):108–18.
  • Ebrahimi, F., and M. R. Barati. 2018. Vibration analysis of piezoelectrically actuated curved nanosize FG beams via a nonlocal strain-electric field gradient theory. Mechanics of Advanced Materials and Structures 25 (4):350–9.
  • Ebrahimi, F., M. R. Barati, and Ö. Civalek. 2020. Application of Chebyshev–Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures. Engineering with Computers 36 (3):953–64. doi:10.1007/s00366-019-00742-z.
  • Ebrahimi, F., A. Dabbagh, and A. Rastgoo. 2019. Free vibration analysis of multi-scale hybrid nanocomposite plates with agglomerated nanoparticles. Mechanics Based Design of Structures and Machines. doi:10.1080/15397734.2019.1692665.
  • Ebrahimi, F., M. Ghadiri, E. Salari, S. A. H. Hoseini, and G. R. Shaghaghi. 2015. Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams. Journal of Mechanical Science and Technology 29 (3):1207–15.
  • Ebrahimi, F., M. Nouraei, and A. Dabbagh. 2020. Modeling vibration behavior of embedded graphene-oxide powder-reinforced nanocomposite plates in thermal environment. Mechanics Based Design of Structures and Machines 48 (2):217–40. doi:10.1080/15397734.2019.1660185.
  • Ebrahimi, F., and E. Salari. 2015. Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment. Acta Astronautica 113:29–50.
  • Ebrahimi, F., G. R. Shaghaghi, and E. Salari. 2014. Vibration analysis of size-dependent nano beams basedon nonlocal Timoshenko beam theory. Journal of Mechanical Engineering and Technology (JMET) 6 (2).
  • Elmeiche, A., A. Megueni, and A. Lousdad. 2016. Free vibration analysis of functionally graded nanobeams based on different order beam theories using Ritz method. Periodica Polytechnica Mechanical Engineering 60 (4):209–19.
  • Eltaher, M. A., S. A. Emam, and F. F. Mahmoud. 2012. Free vibration analysis of functionally graded size-dependent nanobeams. Applied Mathematics and Computation 218 (14):7406–20.
  • Eringen, A. C. 1983. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics 54 (9):4703–10.
  • Faleh, N. M., R. A. Ahmed, and R. M. Fenjan. 2018. On vibrations of porous FG nanoshells. International Journal of Engineering Science 133:1–14.
  • Hamed, M. A., M. A. Eltaher, A. M. Sadoun, and K. H. Almitani. 2016. Free vibration of symmetric and sigmoid functionally graded nanobeams. Applied Physics A 122 (9):829.
  • Heireche, H., A. Tounsi, A. Benzair, M. Maachou, and E. A. Bedia. 2008. Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity. Physica E: Low-Dimensional Systems and Nanostructures 40 (8):2791–9.
  • Hosseini-Hashemi, S., R. Nazemnezhad, and M. Bedroud. 2014. Surface effects on nonlinear free vibration of functionally graded nanobeams using nonlocal elasticity. Applied Mathematical Modelling 38 (14):3538–53. doi:10.1016/j.apm.2013.11.068.
  • Jalaei, M. H., and H. T. Thai. 2019. Dynamic stability of viscoelastic porous FG nanoplate under longitudinal magnetic field via a nonlocal strain gradient quasi-3D theory. Composites Part B: Engineering 175:107164.
  • Jena, S. K., S. Chakraverty, and M. Malikan. 2020. Application of shifted Chebyshev polynomial-based Rayleigh–Ritz method and Navier’s technique for vibration analysis of a functionally graded porous beam embedded in Kerr foundation. Engineering with Computers. doi:10.1007/s00366-020-01018-7.
  • Jena, S. K., S. Chakraverty, M. Malikan, and H. Sedighi. 2020. Implementation of Hermite–Ritz method and Navier’s technique for vibration of functionally graded porous nanobeam embedded in Winkler–Pasternak elastic foundation using bi-Helmholtz nonlocal elasticity. Journal of Mechanics of Materials and Structures 15 (3):405–34.
  • Kahrobaiyan, M. H., M. Asghari, M. Rahaeifard, and M. T. Ahmadian. 2011. A nonlinear strain gradient beam formulation. International Journal of Engineering Science 49 (11):1256–67.
  • Li, C. 2017. Nonlocal thermo-electro-mechanical coupling vibrations of axially moving piezoelectric nanobeams. Mechanics Based Design of Structures and Machines 45 (4):463–78.
  • Li, L., and Y. Hu. 2015. Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory. International Journal of Engineering Science 97:84–94.
  • Li, X., L. Li, Y. Hu, Z. Ding, and W. Deng. 2017. Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory. Composite Structures 165:250–65.
  • Lu, L., X. Guo, and J. Zhao. 2017. Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory. International Journal of Engineering Science 116:12–24.
  • Malikan, M., V. B. Nguyen, and F. Tornabene. 2018. Damped forced vibration analysis of single-walled carbon nanotubes resting on viscoelastic foundation in thermal environment using nonlocal strain gradient theory. Engineering Science and Technology, an International Journal 21 (4):778–86.
  • Mercan, K., and Ö. Civalek. 2017. Buckling analysis of silicon carbide nanotubes (SiCNTs) with surface effect and nonlocal elasticity using the method of HDQ. Composites Part B: Engineering 114:34–45.
  • Nayak, P., S. Bhowmick, and K. N. Saha. 2020. Elasto-plastic analysis of thermo-mechanically loaded functionally graded disks by an iterative variational method. Engineering Science and Technology, an International Journal 23 (1):42–64.
  • Phadikar, J. K., and S. C. Pradhan. 2010. Variational formulation and finite element analysis for nonlocal elastic nanobeams and nanoplates. Computational Materials Science 49 (3):492–9.
  • Pradhan, K. K., and S. Chakraverty. 2013. Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh–Ritzmethod. Composites Part B: Engineering 51:175–84. doi:10.1016/j.compositesb.2013.02.027.
  • Reddy, J. N. 2002. Energy principles and variational methods in applied mechanics. 2nd ed. New York: John Wiley & Sons.
  • Shafiei, N., and M. Kazemi. 2017. Buckling analysis on the bi-dimensional functionally graded porous tapered nano-/micro-scale beams. Aerospace Science and Technology 66:1–11. doi:10.1016/j.ast.2017.02.019.
  • Shi, X., J. Li, and M. Habibi. 2020. On the statics and dynamics of an electro-thermo-mechanically porous GPLRC nanoshell conveying fluid flow. Mechanics Based Design of Structures and Machines. doi:10.1080/15397734.2020.1772088.
  • Shokrgozar, A., A. Ghabussi, F. Ebrahimi, M. Habibi, and H. Safarpour. 2020. Viscoelastic dynamics and static responses of a graphene nanoplatelets-reinforced composite cylindrical microshell. Mechanics Based Design of Structures and Machines. doi:10.1080/15397734.2020.1719509.
  • Thai, H. T., and T. P. Vo. 2012. Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. International Journal of Mechanical Sciences 62 (1):57–66.
  • Togun, N. 2016. Nonlocal beam theory for nonlinear vibrations of a nanobeam resting on elastic foundation. Boundary Value Problems 2016 (1):57.
  • Togun, N., and S. Bağdatlı. 2016. Nonlinear vibration of a nanobeam on a Pasternak elastic foundation based on non-local Euler-Bernoulli beam theory. Mathematical and Computational Applications 21 (1):3.
  • Uzun, B., and Ö. Civalek. 2019a. Free vibration analysis silicon nanowires surrounded by elastic matrix by nonlocal finite element method. Advances in Nano Research 7 (2):99–108.
  • Uzun, B., and Ö. Civalek. 2019b. Nonlocal FEM formulation for vibration analysis of nanowires on elastic matrix with different materials. Mathematical and Computational Applications 24 (2):38.
  • Uzun, B., U. Kafkas, and M. Ö. Yaylı. 2020. Free vibration analysis of nanotube based sensors including rotary inertia based on the Rayleigh beam and modified couple stress theories. Microsystem Technologies. doi:10.1007/s00542-020-04961-z.
  • Uzun, B., and M. Ö. Yaylı. 2019. Finite element model of functionally graded nanobeam for free vibration analysis. International Journal of Engineering and Applied Sciences 11 (2):387–400.
  • Uzun, B., and M. Ö. Yaylı. 2020a. Nonlocal vibration analysis of Ti-6Al-4V/ZrO2 functionally graded nanobeam on elastic matrix. Arabian Journal of Geosciences 13 (4):1–10.
  • Uzun, B., and M. Ö. Yaylı. 2020b. A solution method for longitudinal vibrations of functionally graded nanorods. International Journal of Engineering and Applied Sciences 12 (2):78–87.
  • Yayli, M. Ö. 2015. Buckling analysis of a rotationally restrained single walled carbon nanotube. Acta Physica Polonica A 127 (3):678–83.
  • Yayli, M. Ö. 2017. Buckling analysis of a cantilever single-walled carbon nanotube embedded in an elastic medium with an attached spring. Micro & Nano Letters 12 (4):255–9.
  • Yayli, M. Ö. 2018. Free vibration analysis of a single-walled carbon nanotube embedded in an elastic matrix under rotational restraints. Micro & Nano Letters 13 (2):202–6.
  • Yayli, M. Ö. 2019. Effects of rotational restraints on the thermal buckling of carbon nanotube. Micro & Nano Letters 14 (2):158–62.
  • Zenkour, A. M., and A. E. Abouelregal. 2014. Vibration of FG nanobeams induced by sinusoidal pulse-heating via a nonlocal thermoelastic model. Acta Mechanica 225 (12):3409–21.
  • Zenkour, A. M., and M. Arefi. 2017. Nonlocal transient electrothermomechanical vibration and bending analysis of a functionally graded piezoelectric single-layered nanosheet rest on visco-Pasternak foundation. Journal of Thermal Stresses 40 (2):167–84.

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