Vibration of layered nanobeams with periodic nanostructures

References

• Aifantis, E. C. 1992. On the role of gradients in the localization of deformation and fracture. International Journal of Engineering Science 30 (10):1279–99. doi:10.1016/0020-7225(92)90141-3.
   Web of Science ®Google Scholar
• Alimirzaei, S., M. Mohammadimehr, and A. Tounsi. 2019. Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions. Structural Engineering and Mechanics 71 (5):485–502. doi:10.12989/SEM.2019.71.5.485.
   Web of Science ®Google Scholar
• Altan, B. S., and E. C. Aifantis. 1997. On some aspects in the special theory of gradient elasticity. Journal of the Mechanical Behavior of Materials 8 (3):231–82. doi:10.1515/JMBM.1997.8.3.231.
   Google Scholar
• Arefi, M., and A. M. Zenkour. 2017a. 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. doi:10.1177/1099636217723186.
   Web of Science ®Google Scholar
• Arefi, M., and A. M. Zenkour. 2017b. Effect of thermos-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. doi:10.1177/1099636217697497.
   Web of Science ®Google Scholar
• Arefi, M., and A. M. Zenkour. 2018. Free vibration analysis of a three-layered microbeam based on strain gradient theory and three-unknown shear and normal deformation theory. Steel and Composite Structures 26 (4):421–37. doi:10.12989/scs.2018.26.4.421.
   Web of Science ®Google Scholar
• Asghar, S., M. N. Naeem, M. Hussain, M. Taj, and A. Tounsi. 2020. Prediction and assessment of nonlocal natural frequencies of DWCNTs: Vibration analysis. Computers and Concrete 25 (2):133–44. doi:10.12989/CAC.2020.25.2.133.
   Web of Science ®Google Scholar
• Awrejcewicz, J., V. A. Krysko, S. P. Pavlov, M. V. Zhigalov, and A. V. Krysko. 2017. Mathematical model of a three-layer micro- and nano-beams based on the hypotheses of the Grigolyuk–Chulkov and the modified couple stress theory. International Journal of Solids and Structures 117:39–50. doi:10.1016/j.ijsolstr.2017.04.011.
   Web of Science ®Google Scholar
• Awrejcewicz, J., A. V. Krysko, M. V. Zhigalov, O. A. Saltykova, and V. A. Krysko. 2008. Chaotic vibrations in flexible multilayered Bernoulli–Euler and Timoshenko type beams. Latin American Journal of Solids and Structures 5 (4):319–63.
   Web of Science ®Google Scholar
• Aydogdu, M., and U. Gul. 2018. Buckling analysis of double nanofibers embeded in an elastic medium using doublet mechanics theory. Composite Structures 202:355–63. doi:10.1016/j.compstruct.2018.02.015.
   Web of Science ®Google Scholar
• Balubaid, M., A. Tounsi, B. Dakhel, and S. R. Mahmoud. 2019. Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory. Computers and Concrete 24 (6):579–86. doi:10.12989/CAC.2019.24.6.579.
   Web of Science ®Google Scholar
• Barati, A., A. Hadi, M. Z. Nejad, and R. Noroozi. 2020. On vibration of bi-directional functionally graded nanobeams under magnetic field. Mechanics Based Design of Structures and Machines. doi:10.1080/15397734.2020.1719507.
   Web of Science ®Google Scholar
• Bedia, W. A., M. S. A. Houari, A. Bessaim, A. A. Bousahla, A. Tounsi, T. Saeed, and M. S. Alhodaly. 2019. A new hyperbolic two-unknown beam model for bending and buckling analysis of a nonlocal strain gradient nanobeams. Journal of Nano Research 57:175–91. doi:10.4028/www.scientific.net/jnanor.57.175.
   Web of Science ®Google Scholar
• Berghouti, H., E. A. Adda Bedia, A. Benkhedda, and A. Tounsi. 2019. Vibration analysis of nonlocal porous nanobeams made of functionally graded material. Advances in Nano Research 7 (5):351–64. doi:10.12989/ANR.2019.7.5.351.
   Web of Science ®Google Scholar
• Boutaleb, S., K. H. Benrahou, A. Bakora, A. Algarni, A. A. Bousahla, A. Tounsi, A. Tounsi, and S. R. Mahmoud. 2019. Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT. Advances in Nano Research 7 (3):191–208. doi:10.12989/ANR.2019.7.3.191.
   Web of Science ®Google Scholar
• Challamel, N., and C. M. Wang. 2008. The small length scale effect for a non-local cantilever beam: A paradox solved. Nanotechnology 19 (34):345703. doi:10.1088/0957-4484/19/34/345703.
   PubMed Web of Science ®Google Scholar
• Ebrahimi, F., M. Karimiasl, Ö. Civalek, and M. Vinyas. 2019. Surface effects on scale-dependent vibration behavior of flexoelectric sandwich nanobeams. Advances in Nano Research 7 (2):77–88. doi:10.12989/anr.2019.7.2.077.
   Web of Science ®Google Scholar
• Emdadi, M., M. Mohammadimehr, and B. R. Navi. 2019. Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using Ritz method. Advances in Nano Research 7 (2):109–23. doi:10.12989/anr.2019.7.2.109.
   Web of Science ®Google Scholar
• Eringen, A. C. 1972a. Nonlocal polar elastic continua. International Journal of Engineering Science 10 (1):1–16. doi:10.1016/0020-7225(72)90070-5.
   Web of Science ®Google Scholar
• Eringen, A. C. 1972b. Linear theory of nonlocal elasticity and dispersion of plane waves. International Journal of Engineering Science 10 (5):425–35. doi:10.1016/0020-7225(72)90050-X.
   Web of Science ®Google Scholar
• Fernando, D., C. M. Wang, and A. N. Roy Chowdhury. 2018. Vibration of laminated-beams on reference-plane formulation: Effect of end supports at different heights of the beam. Engineering Structures 159:245–51. doi:10.1016/j.engstruct.2018.01.004.
   Web of Science ®Google Scholar
• Ferrari, M., V. T. Granik, A. Imam, and J. Nadeau. 1997. Advances in doublet mechanics. Germany: Springer. doi:10.1007/978-3-540-49636-6.
   Google Scholar
• Ghorbani, K., A. Rajabpour, and M. Ghadiri. 2019. Determination of carbon nanotubes size-dependent parameters: Molecular dynamics simulation and nonlocal strain gradient continuum shell model. Mechanics Based Design of Structures and Machines 1–18. doi:10.1080/15397734.2019.1671863.
   Google Scholar
• Ghorbanpour, A. A., M. Pourjamshidian, and M. Arefi. 2017. Influence of electro-magneto-thermal environment on the wave propagation analysis of sandwich nano-beam based on nonlocal strain gradient theory and shear deformation theories. Smart Structures and Systems 20 (3):329–42. doi:10.12989/sss.2017.20.3.329.
   Web of Science ®Google Scholar
• Granik, V. T. 1978. Microstructural mechanics of granular media. Technique report IM/MGU, Institute of Mechanics of Moscow State University, 78–241.
   Google Scholar
• Granik, V. T., and M. Ferrari. 1993. Microstructural mechanics of granular media. Mechanics of Materials 15 (4):301–22. doi:10.1016/0167-6636(93)90005-C.
   Web of Science ®Google Scholar
• Gul, U., and M. Aydogdu. 2017. Wave propagation in double walled carbon nanotubes by using doublet mechanics theory. Physica E: Low-Dimensional Systems and Nanostructures 93:345–57. doi:10.1016/j.physe.2017.07.003.
   Web of Science ®Google Scholar
• Gul, U., and M. Aydogdu. 2018a. Structural modelling of nanorods and nanobeams using doublet mechanics theory. International Journal of Mechanics and Materials in Design 14 (2):195–212. doi:10.1007/s10999-017-9371-8.
   Web of Science ®Google Scholar
• Gul, U., and M. Aydogdu. 2018b. Noncoaxial vibration and buckling analysis of embedded double-walled carbon nanotubes by using doublet mechanics. Composites Part B: Engineering 137:60–73. doi:10.1016/j.compositesb.2017.11.005.
   Web of Science ®Google Scholar
• Gul, U., M. Aydogdu, and G. Gaygusuzoglu. 2017. Axial dynamics of a nanorod embedded in an elastic medium using doublet mechanics. Composite Structures 160:1268–78. doi:10.1016/j.compstruct.2016.11.023.
   Web of Science ®Google Scholar
• Gul, U., M. Aydogdu, and G. Gaygusuzoglu. 2018. Vibration and buckling analysis of nanotubes (nanofibers) embedded in an elastic medium using doublet mechanics. Journal of Engineering Mathematics 109 (1):85–111. doi:10.1007/s10665-017-9908-8.
   Web of Science ®Google Scholar
• Hamidi, B. A., S. A. Hosseini, H. Hayati, and R. Hassannejad. 2020. Forced axial vibration of micro and nanobeam under axial harmonic moving and constant distributed forces via nonlocal strain gradient theory. Mechanics Based Design of Structures and Machines doi:10.1080/15397734.2020.1744003.
   Web of Science ®Google Scholar
• Hashemi, S. H., and H. B. Khaniki. 2017. Dynamic behavior of multi-layered viscoelastic nanobeam system embedded in a viscoelastic medium with a moving nanoparticle. Journal of Mechanics 33 (5):559–75. doi:10.1017/jmech.2016.91.
   Web of Science ®Google Scholar
• Hosseini Kordkheili, S. A., and H. Sani. 2013. Mechanical properties of double-layered graphene sheets. Computational Materials Science 69:335–43. doi:10.1016/j.commatsci.2012.11.027.
   Web of Science ®Google Scholar
• Hosseini, S. A. H., and O. Rahmani. 2016. Surface effects on buckling of double nanobeam system based on nonlocal Timoshenko model. International Journal of Structural Stability and Dynamics 16 (10):1550077. doi:10.1142/S0219455415500777.
   Web of Science ®Google Scholar
• Hosseini, S. A. H., and O. Rahmani. 2017. Exact solution for axial and transverse dynamic response of functionally graded nanobeam under moving constant load based on nonlocal elasticity theory. Meccanica 52 (6):1441–57. doi:10.1007/s11012-016-0491-2.
   Web of Science ®Google Scholar
• Hussain, M., M. N. Naeem, M. Taj, and A. Tounsi. 2020. Simulating vibration of single-walled carbon nanotube using Rayleigh–Ritz’s method. Advances in Nano Research 8 (3):215–28. doi:10.12989/ANR.2020.8.3.215.
   Web of Science ®Google Scholar
• Hussain, M., M. N. Naeem, A. Tounsi, and M. Taj. 2019. Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity. Advances in Nano Research 7 (6):431–42. doi:10.12989/ANR.2019.7.6.431.
   Web of Science ®Google Scholar
• Kammoun, N., H. Jrad, S. Bouaziz, M. Soula, and M. Haddar. 2017. Vibration analysis of three-layered nanobeams based on nonlocal elasticity theory. Journal of Theoretical and Applied Mechanics 55:1299–312. doi:10.15632/JTAM-PL.55.4.1299.
   Web of Science ®Google Scholar
• Karamanli, A., and M. Aydogdu. 2020. Structural dynamics and stability analysis of 2D-FG microbeams with two-directional porosity distribution and variable material length scale parameter. Mechanics Based Design of Structures and Machines 48 (2):164–91. doi:10.1080/15397734.2019.1627219.
   Web of Science ®Google Scholar
• Karami, B., M. Janghorban, and A. Tounsi. 2019a. Galerkin’s approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions. Engineering with Computers 35 (4):1297–316. doi:10.1007/s00366-018-0664-9.
   Web of Science ®Google Scholar
• Karami, B., M. Janghorban, and A. Tounsi. 2019b. On pre-stressed functionally graded anisotropic nanoshell in magnetic field. Journal of the Brazilian Society of Mechanical Sciences and Engineering 41 (11):495. doi:10.1007/s40430-019-1996-0.
   Web of Science ®Google Scholar
• Khorasani, M., A. Eyvazian, M. Karbon, A. Tounsi, L. Lampani, and T. A. Sebaey. 2020. Magneto-electro-elastic vibration analysis of modified couple stress-based three-layered micro rectangular plates exposed to multi-physical fields considering the flexoelectricity effects. Smart Structures and Systems 26 (3):331–43. doi:10.12989/SSS.2020.26.3.331.
   Web of Science ®Google Scholar
• Kiani, K. 2014. Longitudinal and transverse instabilities of moving nanoscale beam-like structures made of functionally graded materials. Composite Structures 107:610–69. doi:10.1016/j.compstruct.2013.07.035.
   Web of Science ®Google Scholar
• Koiter, W. T. 1964. Couple-stresses in the theory of elasticity: I and II. Philosophical Transactions of the Royal Society of London B 67:17–44.
   Google Scholar
• 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. doi:10.1080/15397734.2016.1242079.
   Web of Science ®Google Scholar
• Mastorakos, I. N., N. Abdolrahim, and H. M. Zbib. 2010. Deformation mechanisms in composite nano-layered metallic and nanowire structures. International Journal of Mechanical Sciences 52 (2):295–302. doi:10.1016/j.ijmecsci.2009.09.034.
   Web of Science ®Google Scholar
• Matouk, H., A. A. Bousahla, H. Heireche, F. Bourada, E. A. A. Bedia, A. Tounsi, S. R. Mahmoud, A. Tounsi, and K. H. Benrahou. 2020. Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory. Advances in Nano Research 8 (4):293–305. doi:10.12989/ANR.2020.8.4.293.
   Web of Science ®Google Scholar
• Matsunaga, H. 2001. Vibration and buckling of multilayered composite beams according to higher order deformation theories. Journal of Sound and Vibration 246 (1):47–62. doi:10.1006/jsvi.2000.3627.
   Web of Science ®Google Scholar
• Menasria, A., A. Bouhadra, A. Tounsi, A. A. Bousahla, and S. R. Mahmoud. 2017. A new and simple HSDT for thermal stability analysis of FG sandwich plates. Steel & Composite Structures 25 (2):157–75. doi:10.12989/SCS.2017.25.2.157.
   Web of Science ®Google Scholar
• Mindlin, R. D. 1963. Influences of couple-stresses on stress concentrations. Experimental Mechanics 3 (1):1–7. doi:10.1007/BF02327219.
   Google Scholar
• Mindlin, R. D. 1965. Second gradient of strain and surface-tension in linear elasticity. International Journal of Solids and Structures 1 (4):417–438. doi:10.1016/0020-7683(65)90006-5.
   Google Scholar
• Nejad, M. Z., A. Hadi, and A. Farajpour. 2017. Consistent couple-stress theory for free vibration analysis of Euler–Bernoulli nano-beams made of arbitrary bi-directional functionally graded materials. Structural Engineering and Mechanics 63 (2):161–9. doi:10.12989/sem.2017.63.2.161.
   Web of Science ®Google Scholar
• Ni, Z., and H. Hua. 2018. Axial-bending coupled vibration analysis of an axially-loaded stepped multi-layered beam with arbitrary boundary conditions. International Journal of Mechanical Sciences 138–139:187–98. doi:10.1016/j.ijmecsci.2018.02.006.
   Web of Science ®Google Scholar
• Pirmohammadi, A. A., M. Pourseifi, O. Rahmani, and S. A. H. Hoseini. 2014. Modeling and active vibration suppression of a single-walled carbon nanotube subjected to a moving harmonic load based on a nonlocal elasticity theory. Applied Physics A 117 (3):1547–55. doi:10.1007/s00339-014-8592-z.
   Web of Science ®Google Scholar
• Pourseifi, M., O. Rahmani, and S. A. H. Hoseini. 2015. Active vibration control of nanotube structures under a moving nanoparticle based on the nonlocal continuum theories. Meccanica 50 (5):1351–69. doi:10.1007/s11012-014-0096-6.
   Web of Science ®Google Scholar
• Rahmani, M. C., A. Kaci, A. A. Bousahla, F. Bourada, A. Tounsi, E. A. A. Bedia, S. R. Mahmoud, K. H. Benrahou, and A. Tounsi. 2020. Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory. Computers and Concrete 25 (3):225–44. doi:10.12989/CAC.2020.25.3.225.
   Web of Science ®Google Scholar
• Rahmani, O., S. Deyhim, and S. A. H. Hosseini. 2018. Size dependent bending analysis of micro/nano sandwich structures based on a nonlocal high order theory. Steel and Composite Structures 27 (3):371–88. doi:10.12989/SCS.2018.27.3.371.
   Web of Science ®Google Scholar
• Rahmani, O., S. Norouzi, H. Golmohammadi, and S. A. H. Hosseini. 2017. Dynamic response of a double, single-walled carbon nanotube under a moving nanoparticle based on modified nonlocal elasticity theory considering surface effects. Mechanics of Advanced Materials and Structures 24 (15):1274–91. doi:10.1080/15376494.2016.1227504.
   Web of Science ®Google Scholar
• Rahmani, O., M. Shokrnia, H. Golmohammadi, and S. A. H. Hosseini. 2018. Dynamic response of a single-walled carbon nanotube under a moving harmonic load by considering modified nonlocal elasticity theory. The European Physical Journal Plus 133 (2):42. doi:10.1140/epjp/i2018-11868-4.
   Web of Science ®Google Scholar
• Saadatnia, Z., and E. Esmailzadeh. 2017. Nonlinear harmonic vibration analysis of fluid-conveying piezoelectric-layered nanotubes. Composites Part B: Engineering 123:193–209. doi:10.1016/j.compositesb.2017.05.012.
   Web of Science ®Google Scholar
• Saffari, P. R., M. Fakhraie, and M. R. Roudbari. 2020. Free vibration problem of fluid-conveying double-walled boron nitride nanotubes via nonlocal strain gradient theory in thermal environment. Mechanics Based Design of Structures and Machines doi:10.1080/15397734.2020.1819310.
   Web of Science ®Google Scholar
• Semmah, A., H. Heireche, A. A. Bousahla, and A. Tounsi. 2019. Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT. Advances in Nano Research 7 (2):89–98. doi:10.12989/ANR.2019.7.2.089.
   Web of Science ®Google Scholar
• Shariati, A., M. Habibi, A. Tounsi, H. Safarpour, and M. Safa. 2020. Application of exact continuum size-dependent theory for stability and frequency analysis of a curved cantilevered microtubule by considering viscoelastic properties. Engineering with Computers doi:10.1007/s00366-020-01024-9.
   Web of Science ®Google Scholar
• Şimşek, M. 2010. Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory. International Journal of Engineering Science 48 (12):1721–32. doi:10.1016/j.ijengsci.2010.09.027.
   Web of Science ®Google Scholar
• Şimşek, M. 2011. Nonlocal effects in the forced vibration of an elastically connected double-carbon nanotube system under a moving nanoparticle. Computational Materials Science 50 (7):2112–23. doi:10.1016/j.commatsci.2011.02.017.
   Web of Science ®Google Scholar
• Şimşek, M., M. Aydın, H. H. Yurtcu, and J. N. Reddy. 2015. Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory. Acta Mechanica 226 (11):3807–22. doi:10.1007/s00707-015-1437-9.
   Web of Science ®Google Scholar
• Tlidji, Y., M. Zidour, K. Draiche, A. Safa, M. Bourada, A. Tounsi, A. A. Bousahla, and S. R. Mahmoud. 2019. Vibration analysis of different material distributions of functionally graded microbeam. Structural Engineering and Mechanics 69 (6):637–49. doi:10.12989/SEM.2019.69.6.637.
   Web of Science ®Google Scholar
• Vajari, A. F. 2018. A new method for evaluating the natural frequency in radial breathing like mode vibration of double‐walled carbon nanotubes. ZAMM – Journal of Applied Mathematics and Mechanics 98 (2):255–69. doi:10.1002/zamm.201600234.
   Google Scholar
• Vajari, A. F., and A. Imam. 2016a. Axial vibration of single-walled carbon nanotubes using doublet mechanics. Indian Journal of Physics 90 (4):447–55. doi:10.1007/s12648-015-0775-8.
   Web of Science ®Google Scholar
• Vajari, A. F., and A. Imam. 2016b. Torsional vibration of single-walled carbon nanotubes using doublet mechanics. Zeitschrift für Angewandte Mathematik und Physik 67 (4):81. doi:10.1007/s00033-016-0675-6.
   Web of Science ®Google Scholar
• Yademellat, H., R. Ansari, A. Darvizeh, J. Torabi, and A. Zabihi. 2020. Nonlinear electromechanical analysis of micro/nanobeams based on the nonlocal strain gradient theory tuned by flexoelectric and piezoelectric effects. Mechanics Based Design of Structures and Machines doi:10.1080/15397734.2020.1836970.
   Web of Science ®Google Scholar