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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Design optimization of graphene laminates for maximum fundamental frequency; pp. 354–362

(Full article in PDF format) https://doi.org/10.3176/proc.2017.4.08


Authors

Jüri Majak, Maarjus Kirs, Martin Eerme, Ernst Tungel, Toomas Lepikult

Abstract

Design optimization of nanostructures is a new challenging research area. The modelling of multilayer graphene sheets has a similar character as the modelling of composite laminates. However, the traditional laminate plate theories are revised in order to incorporate nonlocal elasticity. The main aim of the current study is to point out the crotchet features arising in the design optimization of graphene laminates based on the theoretical analysis performed and numerical results obtained. The study is focused on the improvement of the mechanical performance of graphene and nanostructures, particularly vibration properties of multilayer graphene laminates.

Keywords

graphene laminates, design optimization, genetic algorithms.

References

    1. Elishakoff , I. , Dujat , K. , Muscolino , G. , Bucas , S. , Narsuki , T. , Wand , C. M. , et al. Carbon Nanotubes and Nanosensors: Vibration , Buckling and Ballistic Impact. ISTE/Wiley , Portland , 2012.

    2. Eringen , A. C. and Edelen , D. G. B. On nonlocal elasticity. Int. J. Eng. Sci. , 1972 , 10 , 233–248.
https://doi.org/10.1016/0020-7225(72)90039-0
https://doi.org/10.1016/0020-7225(72)90070-5

    3. Eringen , A. C. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. , 1983 , 54 , 4703–4710.
https://doi.org/10.1063/1.332803

    4. Aydogdu , M. A general nonlocal beam theory: its application to nanobeam bending , buckling and vibration. Physica E , 2009 , 41 , 1651–1655.
https://doi.org/10.1016/j.physe.2009.05.014

    5. Aydogdu , M. and Elishakoff , I. On the vibration of nanorods restrained by a linear spring in-span. Mech. Res. Comm. , 2014 , 57 , 90–96.
https://doi.org/10.1016/j.mechrescom.2014.03.003

    6. Murmu , T. and Pradhan , S. C. Small-scale effect on the free in-plane vibration of nanoplates by nonlocal continuum model. Physica E , 2009 , 41 , 1628–1633.
https://doi.org/10.1016/j.physe.2009.05.013

    7. Emam , S. A. A general nonlocal nonlinear model for buckling of nanobeams. Appl. Math. Model. , 2013 , 37 , 6929–6939.
https://doi.org/10.1016/j.apm.2013.01.043

    8. 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. Compos. Part B-Eng. , 2013 , 45 , 32–42.
https://doi.org/10.1016/j.compositesb.2012.09.011

    9. Ansari , R. , Sahmani , S. , and Arash , B. Nonlocal plate model for free vibrations of single-layered graphene sheets. Phys. Lett. A , 2010 , 375 , 53– 62.
https://doi.org/10.1016/j.physleta.2010.10.028

 10. Ansari , R. and Sahmani , S. Surface stress effects on the free vibration behavior of nanoplates. Int. J. Eng. Sci. , 2011 , 49 , 1204–1215.
https://doi.org/10.1016/j.ijengsci.2011.06.005

 11. Malekzadeh , P. and Shojaee , M. Free vibration of nanoplates based on a nonlocal two-variable refined plate theory. Compos. Struct. , 2013 , 95 , 443–452.
https://doi.org/10.1016/j.compstruct.2012.07.006

 12. Hosseini-Hashemi , S. , Zare , M. , and Nazemnezhad , R. An exact analytical approach for free vibration of Mindlin rectangular nano-plates via nonlocal elasticity. Compos. Struct. , 2013 , 100 , 290–299.
https://doi.org/10.1016/j.compstruct.2012.11.035

 13. Wang , Y. , Li , F. , Jing , X. , and Wang , Y. Nonlinear vibration analysis of double-layered nanoplates with different boundary conditions. Phys. Lett. A , 2015 , 379 , 1532–1537.
https://doi.org/10.1016/j.physleta.2015.04.002

 14. Jomehzadeh , E. and Saidi , A. R. A study on large amplitude vibration of multilayered sheets. Comput. Mater. Sci. , 2011 , 50 , 1043–1051.
https://doi.org/10.1016/j.commatsci.2010.10.045

 15. Natarajan , S. , Chakraborty , S. , Thangavel , M. , Bordas , S. , and Rabczuk , T. Size-dependent free flexural vibration behavior of functionally graded nanoplates. Comput. Mater. Sci. , 2012 , 65 , 74–80.
https://doi.org/10.1016/j.commatsci.2012.06.031

 16. Liu , J. C. , Zhang , Y. Q. , and Fan , L. F. Nonlocal vibration and biaxial buckling of double-viscoelastic-FGM-nanoplate system with viscoelastic Pasternak medium in between. Compos. Part B-Eng. , 2017 , 118 , 125–134.
https://doi.org/10.1016/j.physleta.2017.01.056

 17. Zhang , L. W. , Zhang , Y. , and Liew , K. M. Modeling of nonlinear vibration of graphene sheets using a meshfree method based on nonlocal elasticity theory. Appl. Math. Model. , 2017 , 49 , 691–704.
https://doi.org/10.1016/j.apm.2017.02.053

 18. Pradhan , S. C. and Murmu , T. Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory. Physica E , 2010 , 42 , 1293–1301.
https://doi.org/10.1016/j.physe.2009.10.053

 19. Pradhan , S. C. and Phadikar , J. K. Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models. Phys. Lett. A , 2009 , 373 , 1062–1069.
https://doi.org/10.1016/j.physleta.2009.01.030

 20. Nazemnezhada , R. , Zarea , M. , and Hosseini-Hashemi , S. Sandwich plate model of multilayer graphene sheets for considering interlayer shear effect in vibration analysis via molecular dynamics simulations. Appl. Math. Model. , 2017 , 47 , 459–472.
https://doi.org/10.1016/j.apm.2017.03.033

 21. Lu , L. , Ru , C. Q. , and Guo , X. M. Vibration of a multilayer graphene sheet under layerwise tension forces. Int. J. Mech. Sci. , 2017 , 121 , 157–163.
https://doi.org/10.1016/j.ijmecsci.2017.01.007

 22. Behera , L. and Chakraverty , S. Application of Differential Quadrature method in free vibration analysis of nanobeams based on various nonlocal theories. Comput. Math. Appl. , 2015 , 69 , 1444–1462.
https://doi.org/10.1016/j.camwa.2015.04.010

 23. Malekzadeh , P. , Setoodeh , A. R. , and Beni , A. A. Small scale effect on the free vibration of orthotropic arbitrary straight sided quadrilateral nanoplates. Compos. Struct. , 2011 , 93 , 1631–1639.
https://doi.org/10.1016/j.compstruct.2011.01.008
https://doi.org/10.1016/j.compstruct.2011.02.013

 24. Ravari , M. R. K. and Shahidi , A. R. Axisymmetric buckling of the circular annular nanoplates using finite difference method. Meccanica , 2013 , 48(1) , 135–144.
https://doi.org/10.1007/s11012-012-9589-3

 25. Chakraverty , S. and Behera , L. Free vibration of rectangular nanoplates using Rayleigh–Ritz method. Physica E , 2014 , 56 , 357–363.
https://doi.org/10.1016/j.physe.2013.08.014

 26. Eltaher , M. A. , Emam , S. A. , and Mahmoud , F. F. Static and stability analysis of nonlocal functionally graded nanobeams. Compos. Struct. , 2013 , 96 , 82–88.
https://doi.org/10.1016/j.compstruct.2012.09.030

 27. Reddy , J. N. , El-Borgi , S. , and Romanoff , J. Non-linear analysis of functionally graded microbeams using Eringen’s non-local differential model. Int. J. Nonlin. Mech. , 2014 , 67 , 308–318.
https://doi.org/10.1016/j.ijnonlinmec.2014.09.014

 28. Kirs , M. , Mikola , M. , Haavajõe , A. , Õunapuu , E. , Shvartsman , B. , and Majak , J. Haar wavelet method for vibration analysis of nanobeams. WWFAA , 2016 , 2 , 20–28.
https://doi.org/10.1515/wwfaa-2016-0003

 29. Majak , J. , Shvartsman , B. , Kirs , M. , Pohlak , M. , and Herranen , H. Convergence theorem for the Haar wavelet based discretization method. Compos. Struct. , 2015 , 126 , 227–232.
https://doi.org/10.1016/j.compstruct.2015.02.050

 30. Majak , J. , Shvartsman , B. , Karjust , K. , Mikola , M. , Haavajõe , A. , and Pohlak , M. On the accuracy of the Haar wavelet discretization method. Compos. Part B-Eng. , 2015 , 80 , 321–327.
https://doi.org/10.1016/j.compositesb.2015.06.008

 31. Aruniit , A. , Kers , J. , Goljandin , D. , Saarna , M. , Tall , K. , Majak , J. , and Herranen , H. Particulate filled composite plastic materials from recycled glass fibre reinforced plastics. Mater. Sci. – Medzg. , 2011 , 17(3) , 276−281.

 32. Aruniit , A. , Kers , J. , Majak , J. , Krumme , A. , and Tall , K. Influence of hollow glass microspheres on the mechanical and physical properties and cost of particle reinforced polymer composites. Proc. Estonian Acad. Sci. , 2012 , 61 , 160–165.
https://doi.org/10.3176/proc.2012.3.03

 33. Lellep , J. and Majak , J. On optimal orientation of nonlinear elastic orthotropic materials. Struct. Optim. , 1997 , 14 , 116–120.
https://doi.org/10.1007/BF01812513

 34. Majak , J. and Hannus , S. Orientational design of anisotropic materials using the Hill and Tsai-Wu strength criteria. Mech. Compos. Mater. , 2003 , 39(6) , 509–520.
https://doi.org/10.1023/B:MOCM.0000010623.38596.3e

 35. Reddy , J. N. Mechanics of Composite Plates: Theory and Analysis. Chemical Rubber Company , Boca Raton , FL , 1997.

 
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Current Issue: Vol. 67, Issue 4 in Press, 2018




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December