Static Stability Analysis of Mass Sensors Consisting of Hygro-Thermally Activated Graphene Sheets Using a Nonlocal Strain Gradient Theory
Abstract
This paper develops a nonlocal strain gradient plate model for buckling analysis of graphene sheets under hygro-thermal environments with mass sensors. For a more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. The graphene sheet is modeled via a two-variable shear deformation plate theory that does not need shear correction factors. Governing equations of a nonlocal strain gradient graphene sheet on the elastic substrate are derived via Hamilton’s principle. Galerkin’s method is implemented to solve the governing equations for different boundary conditions. Effects of different factors, such as moisture concentration rise, temperature rise, nonlocal parameter, length scale parameter, nanoparticle mass and geometrical parameters, on buckling characteristics of graphene sheets are examined and presented as dispersion graphs.Keywords:
humid-thermal buckling, refined plate theory, graphene sheets, nonlocal strain gradient, mass sensorReferences
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3. Eringen A.C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, International Journal of Applied Physics, 54(9): 4703–4710, 1983, https://doi.org/10.1063/1.332803
4. Hashemi S.H., Samaei A.T., Buckling analysis of micro/nanoscale plates via nonlocal elasticity theory, Physica E: Low-dimensional Systems and Nanostructures, 43(7): 1400–1404, 2011, https://doi.org/10.1016/j.physe.2011.03.012
5. Kheroubi B., Benzair A., Tounsi A., Semmah A., A new refined nonlocal beam theory accounting for effect of thickness stretching in nanoscale beams, Advances in Nano Research, 4(4): 251–264, 2016, https://doi.org/10.12989/anr.2016.4.4.251
6. Ebrahimi F., Daman M., Analytical investigation of the surface effects on nonlocal vibration behavior of nanosize curved beams, Advances in Nano Research, 5(1): 35–47, 2017, https://doi.org/10.12989/anr.2017.5.1.035
7. Rakrak K., Zidour M., Heireche H., Bousahla A.A., Chemi A., Free vibration analysis of chiral double-walled carbon nanotube using non-local elasticity theory, Advances in Nano Research, 4(1): 31–44, 2016, https://doi.org/10.12989/anr.2016.4.1.031
8. 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): 257–278, 2018, https://doi.org/10.12989/anr.2018.6.3.257
9. Elmerabet A.H., Heireche H., Tounsi A., Semmah A., Buckling temperature of a single-walled boron nitride nanotubes using a novel nonlocal beam model, Advances in Nano Research, 5(1): 1–12, 2017, https://doi.org/10.12989/anr.2017.5.1.001
10. Pradhan S.C., Murmu T., Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics, Computational Materials Science, 47(1): 268–274, 2009, https://doi.org/10.1016/j.commatsci.2009.08.001
11. Pradhan S.C., Kumar A., Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method, Composite Structures, 93(2): 774–779, 2011, https://doi.org/10.1016/j.compstruct.2010.08.004
12. Aksencer T., Aydogdu M., Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory, Physica E: Low-dimensional Systems and Nanostructures, 43(4), 954–959, 2011, https://doi.org/10.1016/j.physe.2010.11.024
13. Mohammadi M., Farajpour A., Moradi A., Ghayour M., Shear buckling of orthotropic rectangular graphene sheet embedded in an elastic medium in thermal environment, Composites Part B: Engineering, 56: 629–637, 2014, https://doi.org/10.1016/j.compositesb.2013.08.060
14. Mohammadi M., Goodarzi M., Ghayour M., Farajpour A., Influence of in-plane pre-load on the vibration frequency of circular graphene sheet via nonlocal continuum theory, Composites Part B: Engineering, 51: 121–129, 2013, https://doi.org/10.1016/j.compositesb.2013.02.044
15. Ansari R., Arash B., Rouhi H., Vibration characteristics of embedded multi-layered graphene sheets with different boundary conditions via nonlocal elasticity, Composite Structures, 93(9): 2419–2429, 2011, https://doi.org/10.1016/j.compstruct.2011.04.006
16. Shen Z-B., Tang H-L., Li D-K., Tang G-J., Vibration of single-layered graphene sheet-based nanomechanical sensor via nonlocal Kirchhoff plate theory, Computational Materials Science, 61: 200–205, 2012, https://doi.org/10.1016/j.commatsci.2012.04.003
17. Farajpour A., Shahidi A.R., Mohammadi M., Mahzoon M., Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics, Composite Structures, 94(5): 1605–1615, 2012, https://doi.org/10.1016/j.compstruct.2011.12.032
18. Ansari R., Sahmani S., Prediction of biaxial buckling behavior of single-layered graphene sheets based on nonlocal plate models and molecular dynamics simulations, Applied Mathematical Modelling, 37(12–13): 7338–7351, 2013, https://doi.org/10.1016/j.apm.2013.03.004
19. Sobhy M., Thermomechanical bending and free vibration of single-layered graphene sheets embedded in an elastic medium, Physica E: Low-dimensional Systems and Nanostructures, 56: 400–409, 2014, https://doi.org/10.1016/j.physe.2013.10.017
20. Ebrahimi F., Barati M.R., An exact solution for buckling analysis of embedded piezo-electro-magnetically actuated nanoscale beams, Advances in Nano Research, 4(2): 65–84, 2016, https://doi.org/10.12989/anr.2016.4.2.065
21. Ehyaei J., Daman M., Free vibration analysis of double walled carbon nanotubes embedded in an elastic medium with initial imperfection, Advances in Nano Research, 5(2): 179–192, 2017, https://doi.org/10.12989/anr.2017.5.2.179
22. Narendar S., Gopalakrishnan S., Scale effects on buckling analysis of orthotropic nanoplates based on nonlocal two-variable refined plate theory, Acta Mechanica, 223(2): 395–413, 2012, https://doi.org/10.1007/s00707-011-0560-5
23. Murmu T., Mccarthy M. A., Adhikari S., In-plane magnetic field affected transverse vibration of embedded single-layer graphene sheets using equivalent nonlocal elasticity approach, Composite Structures, 96: 57–63, 2013, https://doi.org/10.1016/j.compstruct.2012.09.005
24. Bessaim A., Houari M.S.A., Bernard F., Tounsi A., A nonlocal quasi-3D trigonometric plate model for free vibration behaviour of micro/nanoscale plates, Structural Engineering and Mechanics, 56(2): 223–240, 2015, https://doi.org/10.12989/sem.2015.56.2.223
25. Hashemi S.H., Mehrabani H., Ahmadi-Savadkoohi A., Exact solution for free vibration of coupled double viscoelastic graphene sheets by viscoPasternak medium, Composites Part B: Engineering, 78: 377–383, 2015, https://doi.org/10.1016/j.compositesb.2015.04.008
26. Ebrahimi F., Shafiei N., Influence of initial shear stress on the vibration behavior of single-layered graphene sheets embedded in an elastic medium based on Reddy's higher-order shear deformation plate theory, Mechanics of Advanced Materials and Structures, 24(9): 761–772, 2016, https://doi.org/10.1080/15376494.2016.1196781
27. Jiang R. W., Shen Z. B., Tang G. J., Vibration analysis of a single-layered graphene sheet-based mass sensor using the Galerkin strip distributed transfer function method, Acta Mechanica, 227(10): 2899–2910, 2016, https://doi.org/10.1007/s00707-016-1649-7
28. Arani A.G., Haghparast E., Zarei H.B., Nonlocal vibration of axially moving graphene sheet resting on orthotropic visco-Pasternak foundation under longitudinal magnetic field, Physica B: Condensed Matter, 495: 35–49, 2016, https://doi.org/10.1016/j.physb.2016.04.039
29. Aslanyan N.S., Sargsyan S.H., Applied theories of thermoelasticity of micropolar thin beams, Journal of Thermal Stresses, 41(6): 687–705, 2018, https://doi.org/10.1080/01495739.2018.1426066
30. Bachiri A., Bourada M., Mahmoudi A., Benyoucef S., Tounsi A., Thermodynamic effect on the bending response of elastic foundation FG plate by using a novel four variable refined plate theory, Journal of Thermal Stresses, 41(8): 1042–1062, 2018, https://doi.org/10.1080/01495739.2018.1452169
31. Cinefra M., Petrolo M., Li G., Carrera E., Variable kinematic shell elements for composite laminates accounting for hygrothermal effects, Journal of Thermal Stresses, 40(12): 1523–1544, 2017, https://doi.org/10.1080/01495739.2017.1360165
32. Jaiani G., Bitsadze L., Basic problems of thermoelasticity with microtemperatures for the half-space, Journal of Thermal Stresses, 41(9): 1101–1114, 2018, https://doi.org/10.1080/01495739.2018.1464415
33. Khdeir A.A., Thermoelastic response of cross-ply laminated shells based on a rigorous shell theory, Journal of Thermal Stresses, 35(11): 1000–1017, 2012, https://doi.org/10.1080/01495739.2012.720219
34. Mirzaei M., Thermal buckling of temperature-dependent composite super elliptical plates reinforced with carbon nanotubes, Journal of Thermal Stresses, 41(7): 920–935, 2018, https://doi.org/10.1080/01495739.2018.1429969
35. Vinyas M., Kattimani S.C., Joladarashi S., Hygrothermal coupling analysis of magneto-electroelastic beams using finite element methods, Journal of Thermal Stresses, 41(8): 1063–1079, 2018, https://doi.org/10.1080/01495739.2018.1447856
36. Kurtinaitiene M., Mazeika K., Ramanavicius S., Pakstas V., Jagminas A., Effect of additives on the hydrothermal synthesis of manganese ferrite nanoparticles, Advances in Nano Research, 4(1): 1–14, 2016, https://doi.org/10.12989/anr.2016.4.1.001
37. Ebrahimi F., Babaei R., Shaghaghi G.R., Vibration analysis thermally affected viscoelastic nanosensors subjected to linear varying loads, Advances in Nano Research, 6(4): 399–422, 2018, https://doi.org/10.12989/anr.2018.6.4.399
38. Ebrahimi F., Habibi S., Low-velocity impact response of laminated FG-CNT reinforced composite plates in thermal environment, Advances in Nano Research, 5(2): 69–97, 2017, https://doi.org/10.12989/anr.2018.6.4.399
39. Sobhy M., Hygrothermal vibration of orthotropic double-layered graphene sheets embedded in an elastic medium using the two-variable plate theory, Applied Mathematical Modelling, 40(1): 85–99, 2016, https://doi.org/10.1016/j.apm.2015.04.037
40. Zenkour A.M., Nonlocal transient thermal analysis of a single-layered graphene sheet embedded in viscoelastic medium, Physica E: Low-dimensional Systems and Nanostructures, 79: 87–97, 2016, https://doi.org/10.1016/j.physe.2015.12.003
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