STUDYING GRAPHENE ELECTROMECHANICAL BEHAVIOR BASED ON THE ELASTIC PLATES MOMENT-MEMBRANE THEORY

Author details

E.Yu. Krylova
Saratov State University, Saratov, Russian Federation
S.H. Sargsyan
M. Nalbandyan State University of Shirak, Gyumri, Armenia

https://doi.org/10.15593/perm.mech/2023.4.06

Graphene being a two-dimensional nanomaterial created a new research area – its use as a functional element in various modern technology nanodevices. To open the way for such an application, it is necessary, first of all, to study the mechanical properties and its behavior under various conditions and learn how to manipulate them in a controlled way. All this necessitates an adequate graphene deformation simulations, the construction of an appropriate continuum theory that takes into account scale effects, microstructure and graphene crystal lattice physical parameters. This work aims at studying a rectangular graphene sheet in an electric field. For graphene deformations, the application of the transverse bending model of the elastic plates of the moment-membrane linear theory is justified. Forces of the electrical origin are modeled by means of a normal load applied to the front plate surface. A study was made of the influence of boundary conditions, the gap between the plate and the gate, the potential difference, and linear dimensions on the graphene sheet static transverse bending. The problem of graphene sheet natural vibrations is also solved. The graphene sheet vibration frequency lies in the GHz range. In the clamped boundary conditions case, the natural oscillations frequency is much higher than in the hinged supported case. Even at small deflections, a change in the constant voltage value has a significant effect on the graphene sheet natural frequency.

Keywords

graphene deformation modelingmoment-membrane theory of elastic plateselectric fieldgraphene sheet mechanical behavior problemstatic deflectionnatural oscillation frequencies.

ИЗУЧЕНИЕ ЭЛЕКТРОМЕХАНИЧЕСКОГО ПОВЕДЕНИЯ ГРАФЕНА НА ОСНОВЕ МОМЕНТНО-МЕМБРАННОЙ ТЕОРИИ УПРУГИХ ПЛАСТИН

Создание графена как двумерного наноматериала открыло новую область исследований – применение его как функционального элемента в различных наноприборах современной техники. Чтобы открыть дорогу для такого применения, необходимо, прежде всего, изучить механические свойства и его поведение в различных условиях, под действием различных внешних факторов и научиться контролируемым образом манипулировать его поведением. Все это обусловливает необходимость и актуальность адекватного моделирования деформационных процессов графена, построение соответствующей континуальной теории, учитывающей не только эффекты масштаба, но и микроструктуру, и физические параметры кристаллической решетки графена. Изучено поведение прямоугольного листа графена в электрическом поле. В работе для деформаций графена обосновывается применение модели поперечного изгиба моментно-мембранной линейной теории упругих пластин. Силы электрического происхождения моделируются посредством нормальной нагрузки, приложенной к лицевой поверхности пластины. Проведено исследование влияния граничных условий, величины зазора между пластиной и затвором, разности потенциалов постоянного электрического поля, линейных размеров на статический поперечный изгиб графенового листа. Также решается задача о собственных колебаниях графенового листа. Показано, что частоты собственных линейных колебаний листа графена лежат в гигагерцевом диапазоне. В случае жесткой заделки частота собственных линейных колебаний значительно выше, чем в случае шарнирного закрепления торцов пластины. Установлено, что даже при малых прогибах изменение значения постоянного напряжения электрического поля оказывает существенное влияние на частоту собственных линейных колебаний графенового листа.

Ключевые слова

моделирование деформаций графенамоментно-мембранная теория упругих пластинэлектрическое полезадача механического поведения листа графенастатический прогибсобственные частоты колебаний.

Bibliography

1.Ghayesh M. H., Farokhi H. Nonlinear behaviour of electrically actuated microplate-based MEMS resonators. Mechanical Systems and Signal Processing, 2018, Vol. 109, pp. 220-234. doi: 10.1016/j.ymssp.2017.11.043 Scholar
2.Farokhi H., Ghayesh M. H. On the dynamics of imperfect shear deformable microplates. International Journal of Engineering Science, 2018, Vol. 133, pp. 264-283. doi: 10.1016/j.ijengsci.2018.04.011 Scholar
3.Geim A.K., Novoselov K.S. The rise of graphene. Nature Materials, 2007, №6, pp. 183–191. doi: 10.1038/nmat1849 Scholar
4.Annin B.D., Baimova Y.A., Mulyukov R.R. Mechanical properties, stability, and buckling of graphene sheets and carbon nanotubes (review) // Journal of Applied Mechanics and Technical Physics, 2020, Vol. 61, № 5(363), pp. 175-189. doi: 10.15372/PMTF20200519 Scholar
5.Zaporotskova I.V.; Boroznina N.P.; Parkhomenko Y.N.; Kozhitov L.V. Carbon nanotubes: Sensor properties. A review. Mod. Electron. Mater, 2016, Vol. 2, pp. 95–105. doi:10.1016/j.moem.2017.02.002 Scholar
6.Meyyappan M. Carbon Nanotube-Based Chemical Sensor. Small J, 2016, Vol. 12, pp. 2118–2129. doi: 10.1002/smll.201502555 Scholar
7.Ionete E.I.; Spiridon S.-I.; Monea B.F.; Ebrasu-Ion D.; Vaseashta A. SWCNT-Pt-P2O5-Based Sensor for Humidity Measurements. IEEE Sens. J, 2016, Vol. 16, pp. 7593–7599. doi:10.1109/JSEN.2016.2603478 Scholar
8.Ionete E.I.; Spiridon S.-I.; Monea B.F.; Stratulat E.A Room Temperature Gas Sensor Based on Sulfonated SWCNTs for the Detection of NO and NO2. Sensors, 2019, Vol. 19, pp. 1116. doi:10.3390/s19051116 Scholar
9.Nazaria A., Faezb R., Shamlooa H. Modeling comparison of graphene nanoribbon field effect transistors with single vacancy defect. Superlattices and Microstructures, 2016, Vol. 97, pp. 28-45. doi: 10.1016/j.spmi.2016.06.008 Scholar
10.Wong K.L., Chuan M.W., Afiq Hamzah A., Rusli S., et. al. Performance metrics of current transport in pristine graphene nanoribbon field-effect transistors using recursive non-equilibrium Green's function approach. Superlattices and Microstructures, 2020, Vol. 145, pp. 106624. doi: 10.1016/j.spmi.2020.106624 Scholar
11.Chuan M.W., Riyadi M.A., Hamzah A., et. al. Impact of phonon scattering mechanisms on the performance of silicene nanoribbon field-effect transistors. Results in Physics, 2021, Vol. 29, pp. 104714. doi: 10.1016/j.rinp.2021.104714 Scholar
12.Kulakova I. I., Lisichkin G. V. Biosensors based on graphene nanomaterials. Moscow University Chemistry Bulletin, 2022, Vol. 63, № 6, pp. 375-394. Scholar
13.Yu C. et al. Epitaxial graphene gas sensors on SiC substrate with high sensitivity. Journal of Semiconductors, 2020, Vol. 41 (3), pp. 032101. doi:10.1088/1674-4926/41/3/032101 Scholar
14.Dong Q. et al. Recent progress of toxic gas sensors based on 3d graphene frameworks. Sensors, 2021, Vol. 21(10), pp. 3386. doi:10.3390/s21103386 Scholar
15.Wei L. et al. The recent progress of MEMS/NEMS resonators. Micromachines, 2021, Vol. 12 (6), pp. 724. doi: 10.3390/mi12060724 Scholar
16.Mozhgova N., Lukin A., Popov I. Model of a Micromechanical Modal-Localized Accelerometer with an Initially Curvedmicrobeam as a Sensitive Element. Microactuators, Microsensors and Micromechanisms: MAMM 2022. Cham : Springer International Publishing, 2022, pp. 94-118. doi: 10.1007/978-3-031-20353-4_7 Scholar
17.Morozov N. F. et al. Nonlinear dynamics of mode-localized MEMS accelerometer with two electrostatically coupled microbeam sensing elements. International Journal of Non-Linear Mechanics, 2022, Vol. 138, pp. 103852. doi: 10.1016/j.injonlimec.2021.103852 Scholar
18.Ilyas S., Younis M. I. Theoretical and experimental investigation of mode localization in electrostatically and mechanically coupled microbeam resonators. International Journal of Non-Linear Mechanics, 2020, Vol. 125, pp. 103516. doi:10.1016/j.injonlimec.2020.103516 Scholar
19.Indeitsev D. A. et al. Differential Resonant MEMS Accelerometer: Synchronization Characteristics of Weakly Coupled Microbeam Sensing Elements, 2022. doi: 10.13140/Pt.2.2.36579.84004 Scholar
20.Indeitev D. A. et al. Self-Oscillating Mode Of A Nanoresonator. Physical Mesomechanics, 2016, Vol. 19, No 5, pp.23-28. Scholar
21.Berinskii I.E., Indeitev D.I., Morozov N.F., Skubov D.Y., Shtukin L.V Differential Graphene Resonator As A Mass Detector. Mechanics of Solids. 2015, T. 50. No 2, pp. 127-134. Scholar
22.Karimipour I., Beni Y. T., Akbarzadeh A. H. Size-dependent nonlinear forced vibration and dynamic stability of electrically actuated micro-plates. Communications in Nonlinear Science and Numerical Simulation, 2019, Vol. 78, pp. 104856. doi:10.1016/j.cnsns.2019.104856 Scholar
23.Karimipour I., Tadi Beni Y., Zeighampour H. Vibration and dynamic behavior of electrostatic size-dependent micro-plates. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2020, Vol. 42, pp. 1-22. doi:10.1007/c40430-020-02490-4 Scholar
24.Karami M., Kazemi A., Vatankhah R., Khosravifard A. Adaptive fractional-order backstepping sliding mode controller design for an electrostatically actuated size-dependent microplate. JVC/Journal of Vibration and Control, 2021, Vol. 27(11-12), pp. 1353-1369. doi:10.1177/1077546320940916 Scholar
25.Ghayesh M.H., Farokhi H. Nonlinear behaviour of electrically actuated microplate-based MEMS resonators. Mechanical Systems and Signal Processing, 2018, Vol.109, pp. 220-234. doi:10.1016/j.ymssp.2017.11.043 Scholar
26.Saghir S., Younis M.I. An investigation of the mechanical behavior of initially curved microplates under electrostatic actuation. Acta Mechanica, 2018, Vol. 229(7), pp. 2909-2922. doi:10.1007/s00707-018-2141-3 Scholar
27.Stebunov Yu. V., Leiman V. G., Arsenin A. V. Detektor modulirovannogo teragercovogo izlucheniya na osnove grafenovyh nanolent. Zhurnal radioelektroniki, 2012, No 7, pp. 5 Scholar
28.Saghir S., Younis M. I. An investigation of the mechanical behavior of initially curved microplates under electrostatic actuation // Acta Mechanica. - 2018. - V. 229. - pp. 2909-2922. doi: 10.1007/s00707-018-2141-3. Scholar
29.Ghayesh M. H., Farokhi H. Nonlinear behaviour of electrically actuated microplate-based MEMS resonators. Mechanical Systems and Signal Processing, 2018, Vol. 109, - pp. 220-234. doi:10.1016/j.ymssp.2017.11.043 Scholar
30.Chen X. et al. Nonlinear forced vibration of in-plane bidirectional functionally graded materials rectangular plate with global and localized geometrical imperfections. Applied Mathematical Modelling, 2021, Vol. 93, pp 443-466. doi:10.1016/j.apm.2020.12.033 Scholar
31.Bulyarskiy S.V., Dudin A.A., Orlov A.P., Pavlov A.A., Leont'ev V.L. Forced vibration of a carbon nanotube with emission currents in an electromagnetic field. Technical Physics, 2017, Vol. 87, No 11, pp. 1624-1627. Scholar
32.Bulyarskiy S.V., Dudin A.A., Orlov A.P., Pavlov A.A., Shamanayev A.A., Leontiev V.L. Resonance of a carbon nanotube with a current in the electromagnetic field. Nano- and microsystem technology, 2017, Vol. 19, No 7, pp. 395-398. doi: 10.17587/nmst.19.395-398. Scholar
33.Dmitriev S.V., Sunagatova I.R., Ilgamov M.A., Pavlov I. S. Natural frequencies of bending vibrations of carbon nanotubes. Zhurnal tekhnicheskoj fiziki, 2021, Vol. 91, No 11, pp. 1732-1737. doi: 10.21883/JTF.2021.11.51536.127-21. Scholar
34.Xiao X. et al. Optical-Thermally Excited Graphene Resonant Mass Detection: A Molecular Dynamics Analysis // Nanomaterials. - 2021. - V. 11. - No. 8. - pp. 1924. doi:10.3390/nano11081924 Scholar
35.Gluhova, O.E., Savost'yanov, G.V., Slepchenkov, M.M., SHunaev, V.V. Novye grafenevye nanotekhnologii manipulirovaniya molekulyarnymi ob'ektami. Technical Physics Letters, 2016, Vol. 42, No 11. pp. 56-63. Scholar
36.Makwana M. et al. Effect of mass on the dynamic characteristics of single-and double-layered graphene-based nano resonators. Materials, 2022, Vol. 15, No. 16, pp. 5551. doi: 10.3390/ma15165551 Scholar
37.Xiao Y. et al. A review on graphene-based nanoelectromechanical resonators: Fabrication, performance, and applications. Micromachines, 2022, Vol. 13, No. 2, pp. 215. doi: 10.3390/mi13020215 Scholar
38.Fan S. C. et al. Research Progress of Graphene NanoElectromechanical Resonant Sensors—A Review. Micromachines, 2022, Vol. 13, No. 2, pp. 241. doi: 10.3390/mi13020241 Scholar
39.Allen M.P., Tildesley D.I. Computer simulation of liquids. Oxford Science Publications. 2000. 385 p. Scholar
40.Popov A. M. Vychislitel'nye nanotekhnologii. M.: «KNORUS». 2017. 312 p. Scholar
41.Kang J. W. et al. Molecular dynamics modeling and simulation of a graphene-based nanoelectromechanical resonator. Current Applied Physics, 2013, Vol. 13(4), pp. 789-794. doi: 10.1016/j.cap.2012.12.007 Scholar
42.Wang J., Li T. T. Molecular dynamics simulation of the resonant frequency of graphene nanoribbons. Ferroelectrics, 2019, Vol. 549, No. 1, pp. 87-95. doi: 10.1080/00150193.2019.1592547 Scholar
43.Korobeynikov S. N., Alyokhin V. V., Babichev A. V. Molecular mechanics of single layer graphene sheets. Vestnik Chuvashskogo gosudarstvennogo pedagogicheskogo universiteta im. I.YA. Yakovleva. Seriya: Mekhanika predel'nogo sostoyaniya, 2020, No 2(44), pp. 89-94. Scholar
44.Korobeynikov, S.N., Alyokhin, V.V., Babichev, A.V. Simulation of mechanical parameters of graphene using the DREIDING force field. ActaMechanica. 2018, V. 229, No 6, pp. 2343-2378. DOI 10.1007/s00707-018-2115-5. Scholar
45.Korobeynikov S.N., Alyokhin V.V., Babichev A.V. On the molecular mechanics of single layer graphene sheets. International Journal of Engineering Science. 2018, V. 133, pp. 109-131. doi: 10.1016/j.ijengsci.2018.09.001. Scholar
46.Korobeynikov S.N., Alyokhin V.V., Babichev A.V. Advanced nonlinear buckling analysis of a compressed single layer graphene sheet using the molecular mechanics method. International Journal of Mechanical Sciences, 2021, Vol. 209, pp. 106703. Scholar
47.Korobeynikov S.N. Discussion on "Nonlinear buckling analysis of double-layered graphene nanoribbons based on molecular mechanics" by Namnabat et al. Carbon Letters, 2021, Vol. 31, No 6, pp. 1365-1366. Scholar
48.Kvashnin A.G., Sorokin P.B., Kvashnin D.G. Teoreticheskoe issledovanie mekhanicheskikh svoistv grafenovykh membran metodom molekulyarnoi mekhaniki [Theoretical study of the mechanical properties of graphene membranes by molecular mechanics]. Zhurnal Sibirskogo federal'nogo universiteta. Seriya: Matematika i fizika, 2009, T.2, No4, pp. 426-431. Scholar
49.Odegard G.M., Gates T.S., Nicholson L.M., Wise K.E. Equivalent Continuum Modeling of Nano-structured Materials. NASA Langley Research Center. Technical Memorandum NASA/TM, 2001, 210863-2001. Scholar
50.Li C.A., Chou T.W. A structural mechanics approach for the analysis of carbon nanotubes. Int. J. Solids Struct., 2003, Vol. 40, pp. 2487-2499. Scholar
51.Gol'dshtein R.V., Chentsov A.V. Diskretno-kontinual'naya model' nanotrubki [Discrete-continual model of a nanotube]. Izvestiya RAN. MTT, 2005, No4, pp. 57-74. Scholar
52.Wan, H, Delale, F. A structural mechanics approach for predicting the mechanical properties of carbon nanotubes. Mechanica. 2010, V. 45, Pp. 43-51. Scholar
53.Krylova E. Y. et al. Features of complex vibrations of flexible micropolar mesh panels. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, Vol. 21 (1), pp. 48-59. Scholar
54.Krylova E.Y. et al. Theory of vibrations of carbon nanotubes like flexible micropolar mesh cylindrical shells taking into account shift. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2019, Vol. 19(3), pp. 305-316. Scholar
55.Nuhu A. A., Safaei B. A comprehensive review on the vibration analyses of small-scaled plate-based structures by utilizing the nonclassical continuum elasticity theories. Thin-Walled Structures, 2022, Vol. 179, pp. 109622. Scholar
56.Ansari, R., Sahmani, S., Arash, B. Nonlocal plate model for free vibrations of single-layered graphene sheets. Physics Letters A. 2010, V. 375, pp. 53-62. Scholar
57.Mir Abbas Roudbari, Tahereh Doroudgar Jorshari, Chaofeng Lu, Reza Ansari, Abbas Z. Kouzani, Marco AmabiliA review of size-dependent continuum mechanics models for micro- and nano-structures. Thin-Walled Structures. 2022, V. 170, 108562. doi: 10.1016/j.tws.2021.108562 Scholar
58.Ivanova E.A., Krivtsov A.M., Morozov N.F. Derivation Of Macroscopic Relations Of The Elasticity Of Complex Crystal Lattices Taking Into Account The Moment Interactions At The Microlevel. Journal of Applied Mathematics and Mechanics, 2007, Vol. 71, № 4, pp. 595-615. Scholar
59.Ivanova E. A., Krivcov A. M., Morozov N. F. Derivation Of Macroscopic Relations Of The Elasticity Of Complex Crystal Lattices Taking Into Account The Moment Interactions At The Microlevel. Journal of Applied Mathematics and Mechanics. 2007, V. 71. № 4, pp. 543-561. Scholar
60.Berinskij I.E., Ivanova E.A., Krivcov A.M., Morozov N.F. Primenenie momentnogo vzaimodejstviva k postroeniyu ustojchivoj modeli kristallicheskoj reshetki grafita.[ Application of moment interaction to the construction of a graphite crystal latticestable model] Mechanics of Solids, 2007, № 5, pp. 6-16. Scholar
61.Berinskij I.E. et al. Sovremennye problemy mekhaniki. Mekhanicheskie svojstva kovalentnyh kristallov: ucheb. posobie pod obshch. red. A. M.Krivcova, O.S.Loboda. [Modern problems of mechanics. Mechanical properties of covalent crystals: textbook. allowance] SPb.: Izd-vo Politekhn. un-ta,2014. 160 p. Scholar
62.Sargsyan S.H. Beam and continuous-moment models of deformation of two-dimensional nanomaterials. Physical Mesomechanics, 2022, Vol. 25, № 2, pp. 109-121. Scholar
63.Sargsyan S.H. A thin shell model within the moment theory of elasticity with the concept of deformation by shear plus rotation. Physical Mesomechanics, 2020, Vol. 23, № 4,pp. 13-19. Scholar
64.Sargsyan S.H. Variational principles of the shell momentum-membrane theory. Moscow University Mathematics Bulletin, 2022, № 1, pp. 38-47. Scholar
65.Nowacki, W. Theory of Asymmetric Elasticity. Oxford: Perganon. 1986. 383 p. Scholar
66.Sargsyan S.H. Kraevye zadachi tonkih plastin v nesimmetrichnoj teorii uprugosti. [Boundary-value problems of non-symmetric elasticity for thin plates]. Journal of Applied Mathematics and Mechanics. 2008, V. 72., № 1, pp. 129-147. Scholar
67.Lukin, A. V. Popov I. A., Skubov D. YU. Issledovanie ustojchivosti i vetvleniya form ravnovesiya uprugih elementov mikrosistemnoj tekhniki. [Study of the Stability and Branching of Equilibrium Forms of Elastic Elements of Microsystem Technology] Nelinejnaya dinamika mashin – School-NDM 2017: sbornik IV Mezhdunarodnoj SHkoly-konferencii molodyh uchenyh, Moskva, 18–21 aprelya 2017 goda. – Moskva: Federal'noe gosudarstvennoe byudzhetnoe uchrezhdenie nauki Institut mashinovedeniya im. A.A. Blagonravova Rossijskoj akademii nauk, 2017, pp. 313-322. Scholar
68.Pelekh B. L. Koncentraciya napryazhenij okolo otverstij pri izgibe transversal'no-izotropnyh plastin.[ Stress concentration near holes during bending of transversally isotropic plates] Kiev: Naukova dumka, 1977. 183 p. Scholar
69.Baimova YU. A., Mulyukov R. R. Grafen, nanotrubki i drugie uglerodnye nanostruktury. [Graphene, nanotubes and other carbon nanostructures] M.: RAN, 2018. 212 p. Scholar
70.Vol'mir A. S Nelinejnaya dinamika plastinok i obolochek. [Nonlinear dynamics of plates and shells] M: Glavnaya redakciya fiziko-matematicheskoj literatury izd-va Nauka, 1972. 432 p. Scholar

1.Ghayesh M.H., Farokhi H. Nonlinear behaviour of electrically actuated microplate-based MEMS resonators // Mechanical Systems and Signal Processing. – 2018. – Vol. 109. – P. 220–234. DOI: 10.1016/j.ymssp.2017.11.043 Scholar
2.Farokhi H., Ghayesh M.H. On the dynamics of imperfect shear deformable microplates // International Journal of Engineering Science. – 2018. – Vol. 133. – P. 264–283. DOI: 10.1016/j.ijengsci.2018.04.011 Scholar
3.Geim A.K., Novoselov K.S. The rise of graphene // Nature Materials. – 2007. – № 6. – P. 183–191. DOI: 10.1038/nmat1849 Scholar
4.Аннин Б.Д., Баймова Ю.А., Мулюков Р.Р. Механические свойства, устойчивость, коробление графеновых листов и углеродных нанотрубок (обзор) // Прикладная механика и техническая физика. – 2020. – Т. 61, № 5(363). – С. 175–189. DOI: 10.15372/PMTF20200519 Scholar
5.Carbon nanotubes: Sensor properties. A review / I.V. Zaporotskova, N.P. Boroznina, Y.N. Parkhomenko, L.V. Kozhitov // Mod. Electron. Mater. - 2016. – Vol. 2. – P. 95– 105. DOI: 10.1016/j.moem.2017.02.002 Scholar
6.Meyyappan M. Carbon Nanotube-Based Chemical Sensor // Small J. – 2016. – Vol. 12. – P. 2118–2129. DOI: 10.1002/smll.201502555 Scholar
7.SWCNT-Pt-P2O5-Based Sensor for Humidity Measurements / E.I. Ionete, S.-I. Spiridon, B.F. Monea, D. Ebrasu-Ion, A. Vaseashta // IEEE Sens. J. – 2016. - Vol. 16. – P. 7593–7599. DOI: 10.1109/JSEN.2016.2603478 Scholar
8.A Room Temperature Gas Sensor Based on Sulfonated SWCNTs for the Detection of NO and NO2 / E.I. Ionete, S.- I. Spiridon, B.F. Monea, E. Stratulat // Sensors. – 2019. – Vol. 19. – P. 1116. DOI: 10.3390/s19051116 Scholar
9.Nazaria A., Faezb R., Shamlooa H. Modeling comparison of graphene nanoribbon field effect transistors with single vacancy defect // Superlattices and Microstructures. – 2016. – Vol. 97. – P. 28–45. DOI: 10.1016/j.spmi.2016.06.008 Scholar
10.Performance metrics of current transport in pristine graphene nanoribbon field-effect transistors using recursive non-equilibrium Green's function approach / K.L. Wong, M.W. Chuan, A. Afiq Hamzah, S. Rusli [et. al.] // Superlattices and Microstructures. – 2020. – Vol. 145. – P. 106624. DOI: 10.1016/j.spmi.2020.106624 Scholar
11.Impact of phonon scattering mechanisms on the performance of silicene nanoribbon field-effect transistors / M.W. Chuan, M.A. Riyadi, A. Hamzah [et. al.] // Results in Physics. – 2021. – Vol. 29. – P. 104714. DOI: 10.1016/j.rinp.2021.104714 Scholar
12.Кулакова И.И., Лисичкин Г.В. Биосенсоры на основе графеновых наноматериалов // Вестник Московского университета. Серия 2: Химия. – 2022. – Т. 63, № 6. – С. 375–394. Scholar
13.Epitaxial graphene gas sensors on SiC substrate with high sensitivity / C. Yu [et al.] // Journal of Semiconductors. – 2020. – Vol. 41 (3). – P. 032101. DOI: 10.1088/1674- 4926/41/3/032101 Scholar
14.Recent progress of toxic gas sensors based on 3d graphene frameworks / Q. Dong [et al.] // Sensors. – 2021. – Vol. 21(10). – P. 3386. DOI: 10.3390/s21103386 Scholar
15.The recent progress of MEMS/NEMS resonators / L. Wei [et al.] // Micromachines. – 2021. – Vol. 12 (6). – P. 724. DOI: 10.3390/mi12060724 Scholar
16.Mozhgova N., Lukin A., Popov I. Model of a Micromechanical Modal-Localized Accelerometer with an Initially Curvedmicrobeam as a Sensitive Element // Microactuators, Microsensors and Micromechanisms: MAMM 2022. – Cham: Springer International Publishing, – 2022. – P. 94–118. DOI: 10.1007/978-3-031-20353-4_7 Scholar
17.Nonlinear dynamics of mode-localized MEMS accelerometer with two electrostatically coupled microbeam sensing elements / N.F. Morozov [et al.] // International Journal of Non-Linear Mechanics. – 2022. – Vol. 138. – P. 103852. DOI: 10.1016/j.ijnonlinec.2021.103852 Scholar
18.Ilyas S., Younis M.I. Theoretical and experimental investigation of mode localization in electrostatically and mechanically coupled microbeam resonators // International Journal of Non-Linear Mechanics. – 2020. – Vol. 125. – P. 103516. DOI: 10.1016/j.ijnonlinemec.2020.103516 Scholar
19.Differential Resonant MEMS Accelerometer: Synchronization Characteristics of Weakly Coupled Microbeam Sensing Elements / D.A. Indeitsev [et al.]. – 2022. DOI: 10.13140/Pt.2.2.36579.84004 Scholar
20.Автоколебательный режим нанорезонатора / Д.А. Индейцев, О.С. Лобода, Н.Ф. Морозов, Л.В. Штукин // Физическая мезомеханика. 2016. – Т. 19, № 5. – С. 23–28. Scholar
21.Дифференциальный графеновый резонатор как детектор массы / И.Е. Берлинский, Д.А. Индейцев, Н.Ф. Морозов, Д.Ю. Скубов, Л.В. Штукин // Известия РАН. МТТ. – 2015. – № 2. – С. 20–29. Scholar
22.Karimipour I., Beni Y.T., Akbarzadeh A.H. Size-dependent nonlinear forced vibration and dynamic stability of electrically actuated micro-plates // Communications in Nonlinear Science and Numerical Simulation. – 2019. – Vol. 78. – P. 104856. DOI: 10.1016/j.cnsns.2019.104856 Scholar
23.Karimipour I., Tadi Beni Y., Zeighampour H. Vibration and dynamic behavior of electrostatic size-dependent micro-plates // Journal of the Brazilian Society of Mechanical Sciences and Engineering. – 2020. – Vol. 42. – P. 1–22. DOI: 10.1007/c40430-020-0490-4 Scholar
24.Adaptive fractional-order backstepping sliding mode controller design for an electrostatically actuated size-dependent microplate / Karami M., Kazemi A., Vatankhah R., Khosravifard A. // JVC/Journal of Vibration and Control. – 2021. – Vol. 27(11- 12). – P. 1353–1369. DOI: 10.1177/1077546320940916 Scholar
25.Ghayesh M.H., Farokhi H. Nonlinear behaviour of electrically actuated microplate-based MEMS resonators // Mechanical Systems and Signal Processing. – 2018. – Vol. 109. – P. 220–234. DOI: 10.1016/j.mssp.2017.11.043 Scholar
26.Saghir S., Younis M.I. An investigation of the mechanical behavior of initially curved microplates under electrostatic actuation // Acta Mechanica. – 2018. – Vol. 229(7). – P. 2909–2922. DOI: 10.1007/s00707-018-2141-3 Scholar
27.Детектор модулированного терагерцового излучения на основе графеновых нанолент / Ю.В. Стебунов, В.Г. Лейман, А.В. Арсенин // Журнал радиоэлектроники. – 2012. – № 7. – С. 5. Scholar
28.Saghir S., Younis M.I. An investigation of the mechanical behavior of initially curved microplates under electrostatic actuation // Acta Mechanica. – 2018. – Vol. 229. – P. 2909–2922. DOI: 10.1007/s00707-018-2141-3 Scholar
29.Ghayesh M.H., Farokhi H. Nonlinear behaviour of electrically actuated microplate-based MEMS resonators // Mechanical Systems and Signal Processing. – 2018. – Vol. 109. – P. 220–234. DOI: 10.1016/j.ymssp.2017.11.043 Scholar
30.Nonlinear forced vibration of in-plane bi-directional functionally graded materials rectangular plate with global and localized geometrical imperfections / X. Chen [et al.] // Applied Mathematical Modelling. – 2021. – Vol. 93. – P. 443–466. DOI: 10.1016/j.apm.2020.12.033 Scholar
31.Вынужденные колебания углеродной нанотрубки с током эмиссии в электромагнитном поле (01) / С.В. Булярский, А.А. Дудин, А.П. Орлов [и др.] // Журнал технической физики. – 2017. – Т. 87, № 11. – С. 1624–1627. Scholar
32.Резонанс углеродной нанотрубки с током в электромагнитном поле / С.В. Булярский, А.А. Дудин, А.П. Орлов [и др.] // Нано- и микросистемная техника. – 2017. – Т. 19, № 7. – С. 395–398. DOI: 10.17587/nmst.19.395-398 Scholar
33.Собственные частоты изгибных колебаний углеродных нанотрубок / С.В. Дмитриев, И.Р. Сунагатова, М.А. Ильгамов, И.С. Павлов // Журнал технической физики. – 2021. – Т. 91, № 11. – С. 1732–1737. DOI: 10.21883/JTF.2021.11.51536.127-21 Scholar
34.Optical-Thermally Excited Graphene Resonant Mass Detection: A Molecular Dynamics Analysis / X. Xiao [et al.] // Nanomaterials. – 2021. – Vol. 11, № 8. – P. 1924. DOI: 10.3390/nano11081924 Scholar
35.Новые графеновые нанотехнологии манипулирования молекулярными объектами / О.Е. Глухова, Г.В. Савостьянов, М.М. Слепченков, В.В. Шунаев // Письма в Журнал технической физики. – 2016. – Т. 42, № 11. – С. 56–63. Scholar
36.Effect of mass on the dynamic characteristics of single- and double-layered graphene-based nano resonators / M. Makwana [et al.] // Materials. – 2022. – Vol. 15, № 16. – P. 5551. DOI: 10.3390/ma15165551 Scholar
37.A review on graphene-based nano-electromechanical resonators: Fabrication, performance, and applications / Y. Xiao [et al.] // Micromachines. – 2022. – Vol. 13, № 2. – P. 215. DOI: 10.3390/mi13020215 Scholar
38.Research Progress of Graphene Nano-Electromechanical Resonant Sensors – A Review / S.C. Fan [et al.] // Micromachines. – 2022. – Vol. 13, № 2. – P. 241. DOI: 10.3390/mi13020241 Scholar
39.Allen M.P., Tildesley D.I. Computer simulation of liquids. – Oxford Science Publications, 2000. – 385 p. Scholar
40.Попов А.М. Вычислительные нанотехнологии. – М.: КНОРУС, 2017. – 312 с. Scholar
41.Molecular dynamics modeling and simulation of a graphene-based nanoelectromechanical resonator / J.W. Kang [et al.] // Current Applied Physics. – 2013. – Vol. 13(4). – P. 789–794. DOI: 10.1016/j.cap.2012.12.007 Scholar
42.Wang J., Li T.T. Molecular dynamics simulation of the resonant frequency of graphene nanoribbons // Ferroelectrics. – 2019. – Vol. 549, № 1. – P. 87–95. DOI: 10.1080/00150193.2019.1592547 Scholar
43.Коробейников С.Н., Алехин В.В, Бабичев А.В. Молекулярная механика однослойных графеновых листов // Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния. – 2020. – № 2(44). – С. 89–94. DOI: 10.37972/chgpu.2020.44.2.009 Scholar
44.Korobeynikov S.N., Alyokhin V.V., Babichev A.V. Simulation of mechanical parameters of graphene using the DREIDING force field // ActaMechanica. – 2018. – Vol. 229, № 6. – P. 2343–2378. DOI: 10.1007/s00707-018-2115-5 Scholar
45.Korobeynikov S.N., Alyokhin V.V., Babichev A.V. On the molecular mechanics of single layer graphene sheets // International Journal of Engineering Science. – 2018. – Vol. 133. – P. 109–131. DOI: 10.1016/j.ijengsci.2018.09.001 Scholar
46.Korobeynikov S.N., Alyokhin V.V., Babichev A.V. Advanced nonlinear buckling analysis of a compressed single layer graphene sheet using the molecular mechanics method // International Journal of Mechanical Sciences. – 2021. – Vol. 209. – P. 106703 (30 pages). DOI: 10.1016/j.ijmecsci.2021.106703 Scholar
47.Korobeynikov S.N. Discussion on “Nonlinear buckling analysis of double-layered graphene nanoribbons based on molecular mechanics” by Namnabat et al. // Carbon Letters. – 2021. – Vol. 31, № 6. – P. 1365–1366. DOI: 10.1007/s42823-021-00233-6 Scholar
48.Квашнин А.Г., Сорокин П.Б., Квашнин Д.Г. Теоретическое исследование механических свойств графеновых мембран методом молекулярной механики // Журнал Сибирского федерального университета. Серия: Математика и физика. – 2009. – Т. 2, № 4. – С. 426–431. Scholar
49.Equivalent Continuum Modeling of Nano-structured Mstierials / G.M. Odegard, T.S. Gates, L.M. Nicholson, K.E. Wise // NASA Langley Research Center. Technical Memorandum NASA / TM. – 2001. – 210863–2001. Scholar
50.Li C.A., Chou T.W. A structural mechanics approach for the analysis of carbon nanotubes // Int. J. Solids Struct. – 2003. – Vol. 40. – P. 2487–2499. Scholar
51.Гольдштейн Р.В., Ченцов А.В. Дискретно-континуальная модель нанотрубки // Известия РАН. МТТ. – 2005. – № 4. – С. 57–74. Scholar
52.Wan H, Delale F. A structural mechanics approach for predicting the mechanical properties of carbon nanotubes // Mechanica. – 2010. – Vol. 45. – P. 43–51. Scholar
53.Особенности сложных колебаний гибких микрополярных сетчатых панелей / Е.Ю. Крылова, И.В. Папкова, О.А. Салтыкова, В.А. Крысько // Известия Саратовского университета. Новая серия. Серия: Математика. Механика. Информатика. – 2021. – Vol. 21 (1). – P. 48–59. DOI: 10.18500/1816-9791-2021-21-1-48-59 Scholar
54.Теория колебаний углеродных нанотрубок как гибких микрополярных сетчатых цилиндрических оболочек с учетом сдвига / Е.Ю. Крылова, И.В. Папкова, Т.В. Яковлева, В.А. Крысько // Известия Саратовского университета. Новая серия. Серия: Математика. Механика. Информатика. – 2019. – Vol. 19 (3). – P. 305–316. DOI: 10.18500/1816-9791-2019-19-3-305-316 Scholar
55.Nuhu A.A., Safaei B. A comprehensive review on the vibration analyses of small-scaled plate-based structures by utilizing the nonclassical continuum elasticity theories // Thin- Walled Structures. – 2022. – Vol. 179. – P. 109622. DOI: 10.1016/j.tws.2022.109622 Scholar
56.Ansari R., Sahmani S., Arash B. Nonlocal plate model for free vibrations of single-layered graphene sheets // Physics Letters A. – 2010. – Vol. 375. – P. 53–62. Scholar
57.A review of size-dependent continuum mechanics models for micro- and nano-structures / Mir Abbas Roudbari, Tahereh Doroudgar Jorshari, Chaofeng Lu, Reza Ansari, Abbas Z. Kouzani, Marco Amabili // Thin-Walled Structures. – 2022. – Vol. 170. – P. 108562. DOI: 10.1016/j.tws.2021.108562 Scholar
58.Об определении упругих модулей наноструктур, теоретический расчет и методика экспериментов / Е.А. Иванова, Н.Ф. Морозов, Б.Н. Семенов, А.Д. Фирсова // Известия РАН. МТТ. – 2005. – № 4. – С. 75–84. Scholar
59.Иванова Е.А, Кривцов А.М., Морозов Н.Ф. Получение макроскопических соотношений упругости сложных кристаллических решеток при учете моментных взаимодействий на микроуровне // Прикладная математика и механика. – 2007. – Т. 71, № 4. – С. 595–615. Scholar
60.Применение моментного взаимодействия к построению устойчивой модели кристаллической решетки графита / И.Е. Беринский, Е.А. Иванова, А.М. Кривцов, Н.Ф. Морозов // Известия Российской академии наук. Механика твердого тела. – 2007. – № 5. – С. 6–16. Scholar
61.Современные проблемы механики. Механические свойства ковалентных кристаллов: учеб. пособие / И.Е. Беринский [и др.]; под общ. ред. А.М. Кривцова, О.С. Лобода. – СПб.: Изд-во Политехн. ун-та, 2014. – 160 с. Scholar
62.Саркисян С.О. Стержневая и континуально-моментная модели деформаций двумерных наноматериалов // Физическая мезомеханика. – 2022. – Т. 25, № 2. – С. 109–121. DOI: 10.55652/1683-805X_2022_25_2_109 Scholar
63.Саркисян С.О. Модель тонких оболочек в моментной теории упругости с деформационной концепцией «сдвиг плюс поворот» // Физическая мезомеханика. – 2020. – Т. 23, № 4. – С. 13–19. DOI: 10.24411/1683-805X-2020-14002 Scholar
64.Саркисян С.О. Вариационные принципы моментно-мембранной теории оболочек // Вестник Московского университета. Серия 1: Математика. Механика. – 2022. – № 1. – С. 38–47. Scholar
65.Nowacki W. Theory of Asymmetric Elasticity. – Oxford: Perganon, 1986. – 383 p. Scholar
66.Саркисян С.О. Краевые задачи тонких пластин в несимметричной теории упругости // Прикладная математика и механика (ПММ). – 2008. – Т. 72, № 1. – С. 129–147. Scholar
67.Лукин А.В., Попов И.А., Скубов Д.Ю. Исследование устойчивости и ветвления форм равновесия упругих элементов микросистемной техники // Нелинейная динамика машин – School-NDM 2017: сборник IV Международной Школы-конференции молодых ученых, Москва, 18–21 апреля 2017 года. – М.: Федеральное государственное бюджетное учреждение науки Институт машиноведения им. А.А. Благонравова Российской академии наук, 2017. – С. 313–322. Scholar
68.Пелех Б.Л. Концентрация напряжений около отверстий при изгибе трансверсально-изотропных пластин. – Киев: Наукова думка, 1977. – 183 с. Scholar
69.Баимова Ю.А., Мулюков Р.Р. Графен, нанотрубки и другие углеродные наноструктуры. – М.: РАН, 2018. – 212 с. Scholar
70.Вольмир А.С Нелинейная динамика пластинок и оболочек. – М.: Главная редакция физико-математической литературы изд-ва «Наука», 1972. – 432 с. Scholar

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Published: 5 October 2023
Issue date: 5 October 2023
Issue: No. 4 (2023)