Vibration Analysis of an Imperfect Single-Layer Graphene Sheet using Quasi-3d Theory and Isogeometric Approach

ADMT Journal

دوره 16، شماره 1، خرداد 2023، صفحه 13-27   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30486/admt.2022.1951472.1338

نویسندگان

Heidar Fazeli¹؛ Armen Adamian^{* 2}؛ Ahmad Hosseini-Sianaki¹

¹Department of Mechanical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran

²Department of Mechanical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran.

چکیده

In this study, the size-dependent free vibration analysis of a geometrically imperfect single-layer graphene sheet (SLGS) is studied by an isogeometric approach along with the quasi-3D shear and normal deformation theory. Initial geometric imperfections alter the natural frequencies of the graphene sheets that may exist inherently or purposely created by researchers. The initial curvature is modelled by an analytical function in the governing Equations of the plate. A 4-variable quasi-3D theory with a seventh-order distribution function is used to include both shear deformation and thickness stretching influences. A weak form of a nonlocal plate for free vibration analysis is derived that requires the first-order continuity of the displacement fields. Inherent high-order continuity of non-uniform rational B-spline (NURBS) basis functions in isogeometric analysis can meet this condition. A comparison between the present study and other published works reveals the efficiency and accuracy of the proposed method in imperfect SLGS. The results of the present study show a significant effect of initial geometric imperfection on the natural frequency of single-layer graphene sheets.

کلیدواژه‌ها

Fundamental Frequency؛ Imperfection Sensitivity؛ Initial Geometric Imperfection؛ Isogeometric Analysis؛ Single-Layer Graphene

مراجع

• Terrones, M., Botello-Méndez, A. R., and Campos-Delgado, J, et al., Graphene and Graphite Nano Ribbons: Morphology, Properties, Synthesis, Defects and Applications, Nano Today, Vol. 5, 2010, pp. 351-372.
• Hierold, Ch., Jungen, A., Stampfer, C. , and Helbling, T., Nano Electromechanical Sensors Based on Carbon Nanotubes, Sensors and Actuators A, Vol. 136, 2007, pp. 51-61.
• Wang, C. G., Lan, L., Liu, Y. P., and Tan, H. F., Defect-Guided Wrinkling in Graphene, Computational Materials Science, Vol. 77, 2013, pp. 250–253.
• Jalali, S. K., Pugno, N. M., and Jomehzadeh, E., Influence of Out-Of-Plane Defects on Vibration Analysis of Graphene Sheets: molecular and Continuum Approaches, Superlattices and Microstructures, Vol. 91, 2016, pp. 331-344.
• Lehtinen, O., Kurasch, S., Krasheninnikov, A. V., and Kaiser, U., Atomic Scale Study of The Life Cycle of a Dislocation in Graphene from Birth to Annihilation, Nat Commun, Vol. 4, 2013, 2098.
• Robertson, A. W., Allen, C. S., Wu, Y. A., He, K., Olivier, J., Neethling, J., Kirkland, A. I., and Warner, J. H., Spatial Control of Defect Creation in Graphene at The Nanoscale, Nat Commun, Vol. 3, 2012, 1144.
• Berthe, M., Yoshida, S., Ebine, Y., Kanazawa, K., Okada, A., Taninaka A., and et al, Reversible Defect Engineering of Single-Walled Carbon Nanotubes Using Scanning Tunneling Microscopy, Nano Lett, Vol. 7, 2007, pp. 3623–3627.
• Suleimani, A., Naei, M. H., and Mashhadi, M. M., Nonlocal Post Buckling Analysis of Graphene Sheets with Initial Imperfection Based on First Order Shear Deformation Theory, Results in Physics, Vol. 7, 2017, pp. 1299-1307.
• Jomehzadeh, E., Afshar, M. K., Galiotis, C., Shi, X., and Pugno, M. N., Nonlinear Softening and Hardening Nonlocal Bending Stiffness of An Initially Curved Monolayer Graphene, Compos Part B: Eng, Vol. 56, 2017, pp. 123-131.
• Eringen, A. C., Nonlocal Continuum Field Theories, Springer, NewYork.
• Sarrami-Foroushani, S., Azhari M., Nonlocal Buckling and Vibration Analysis of Thick Rectangular Nanoplates Using Finite Strip Method Based on Refined Plate Theory, Acta Mechanica, Vol. 227, 2016, pp. 721-742.
• Malekzadeh, P., Shojaee, M., Free Vibration of Nanoplates Based on A Nonlocal Two-Variable Refined Plate Theory, Compos. Struct, Vol. 95, 2013, pp. 443–452.
• Arash, B., Wang, Q., A Review on The Application of Nonlocal Elastic Models in Modeling of Carbon Nanotubes and Graphenes, Comp Mater Sci, Vol. 51, 2012, pp. 303–313.
• Bayati Chaleshtori, B., Hajiahmad, A., and Mohtasebi, S. S., Vibration Analysis of Rectangular Kirchhoff Nano-Plate using Modified Couple Stress Theory and Navier Solution Method, Int J of Advanced Design and Manufacturing Technology, Vol. 14, No. 2, 2021, pp. 85–92.
• Nourbakhsh, S. H., Botshekanan Dehkordi, M., and Atrian, A., Free Vibration Analysis of Nanoplates using Differential Transformation Method, Int J of Advanced Design and Manufacturing Technology, Vol. 10, No. 1, 2017, pp. 39-49.
• Thai, C. H., Ferreira A. J. M., and Phung-Van, P., Free Vibration Analysis of Functionally Graded Anisotropic Microplates Using Modified Strain Gradient Theory, Engineering Analysis with Boundary Elements, Vol. 117, 2020, pp. 284–298
• Senthilnathan, N. R., Lim, S. P., Lee, K. H., and Chow, S. T., Buckling of Shear-Deformable Plates, AIAA J, Vol. 25, 1987, pp. 1268–1271.
• Narendar, S., Buckling Analysis of Micro-/Nano-Scale Plates Based on Two-Variable Refined Plate Theory Incorporating Nonlocal Scale Effects, Compos, Struct, Vol. 93, 2011, pp. 3093–3103.
• Shimpi, R. P., Refined Plate Theory and Its Variants, AIAA J, Vol. 40, 2002, pp. 137–146.
• Nguyen, N. T., Hui, D., Lee, J., and Nguyen-Xuan, H., An Efficient Computational Approach for Size-Dependent Analysis of Functionally Graded Nanoplates, Comput. Methods Appl. Mech. Engrg, Vol. 297, 2015, pp. 191–218.
• Zenkour, A. M., Bending Analysis of Functionally Graded Sandwich Plates Using a Simple Four Unknown Shear and Normal Deformations Theory, J. Sandwich Struct. Mater, Vol. 15, 2013, pp. 629–656.
• Zenkour, A. M., A Simple Four-Unknown Refined Theory for Bending Analysis of Functionally Graded Plates, Appl. Math. Model, Vol. 37, 2013, pp. 9041–9051.
• Nguyen, H. X., Nguyen, T. N., Abdel-Wahab, M., Bordas, S. P. A., Nguyen-Xuan, H., and Vo, T. P., A Refined Quasi-3D Isogeometric Analysis for Functionally Graded Microplates Based on The Modified Couple Stress Theory, Comput. Methods Appl. Mech. Engrg, Vol. 313, 2017, pp. 904–940.
• Gupta, A., Talha, M., An Assessment of a Non-Polynomial Based Higher Order Shear and Normal Deformation Theory for Vibration Response of Gradient Plates with Initial Geometric Imperfections, Composites Part B, Vol. 107, 2016, pp. 141-161.
• Van Do, V. N., Lee, C. H., Free Vibration Analysis of Fgm Plates with Complex Cutouts by Using Quasi-3d Isogeometric Approach, International Journal of Mechanical Sciences, Vol. 159, 2019, pp. 213–233
• Phung-Van, P., Ferreira, A. J. M., Nguyen-Xuan, H., and Wahab, M. A., An Isogeometric Approach for Size-Dependent Geometrically Nonlinear Transient Analysis of Functionally Graded Nanoplates, Composites Part B, Vol. 118, 2017, pp. 125-134.
• Hughes, T. J. R., Cottrell, J. A., and Bazilevs, Y., Isogeometricanalysis: CAD, Finite Elements, Nurbs, Exact Geometry and Mesh Refinement, Comput Methods Appl Mech Eng, Vol. 194, 2005, pp. 4135–4195.
• Fazeli, H., Adamian, A., and Hosseini‑Sianaki, A., Influence of Initial Geometric Imperfection on Static and Free Vibration Analyses of Porous Fg Nanoplate Using an Isogeometric Approach, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 43, No. 4, 2021, pp. 200.
• Soldatos, K. P., A Transverse Shear Deformation Theory for Homogeneous Monoclinic Plates, Acta Mech, Vol. 94, 1992, pp. 195–220.
• Nguyen-Xuan, H., Thai, C. H., and Nguyen-Thoi, T., Isogeometric Finite Element Analysis of Composite Sandwich Plates Using a Higher Order Shear Deformation Theory, Composites Part B, Vol. 55, 2013, pp. 558–574.
• Nguyen-Xuan, H., Tran, L. V., Thai, C. H., Kulasegaram, S., and Bordas S., Isogeometric Analysis of Functionally Graded Plates Using a Refined Plate Theory, Composites Part B, Vol. 64, 2014, pp. 222–234.
• Thai, H. T., Kim, S. E., A Simple Quasi-3D Sinusoidal Shear Deformation Theory for Functionally Graded Plates, Composite Structures, Vol. 99, 2013, pp. 172–180.
• Auricchio, F., Da Veiga, L. B., Buffa, A., Lovadina, C., Reali, and A., Sangalli, G., A Fully Locking-Free Isogeometric Approach for Plane Linear Elasticity Problems: A Stream Function Formulation, Comput. Methods Appl. Mech. Engrg, Vol. 197, 2007, pp. 160–172.
• Sarrami-Foroushani, S., Azhari M., Nonlocal Vibration and Buckling Analysis of Single and Multi-Layered Graphene Sheets Using Finite Strip Method Including van Der Waals Effects, Phys. E Low Dimens. Syst. Nanostruct, Vol. 57, 2014, pp. 83–95.
• Gupta, A., Talha, M., Nonlinear Flexural and Vibration Response of Geometrically Imperfect Gradient Plates Using Hyperbolic Higher-Order Shear and Normal Deformation Theory, Composites Part B, Vol. 123, 2017, pp. 241-261.
• Ansari, R., Sahmani, S., and Arash B., Nonlocal Plate Model for Free Vibrations of Single-Layered Graphene Sheets, Physics Letters A, Vol. 375, 2010, pp. 53–62.