- PII
- 10.31857/S2686740024030086-1
- DOI
- 10.31857/S2686740024030086
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 516 / Issue number 1
- Pages
- 51-58
- Abstract
- We study the nonlinear dynamics of a rectangular atomically thin nanostrip under conditions of internal combinational resonance between two transverse and one longitudinal modes of mechanical vibrations. Conditions have been analytically found for the initial pretension of the layer required to realize resonance between eigenforms with given indices of variability along the length. It is shown that under conditions of internal resonance, a nonlinear mode of free oscillations is excited in the system, the spectrum of which has the form of a frequency comb. Two qualitatively different types of oscillations of this kind are identified – those caused by the initial excitation in the working longitudinal form of oscillations and in two transverse forms. A significant dependence of the spectral composition of the generated frequency combs on the relationships between the amplitudes of the initial disturbance for the three interacting modes and on the value of the internal frequency detuning parameter of the system is shown.
- Keywords
- наноэлектромеханические системы НЭМС нелинейная динамика двумерные материалы нанослой лазерное термо-оптическое воздействие фононные частотные гребенки
- Date of publication
- 16.09.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 12
References
- 1. Xiao X., Li C., Fan S.-C., Liu Y.-J., Liu Y. Optical-thermally actuated graphene mechanical resonator for humidity sensing. Sensors and Actuators B.: Chemical, 2023. 374, 132851. https://doi.org/10.1016/j.snb.2022.132851
- 2. Roslon I., Steeneken P.G., Alijani F., Roslon I.E., Japaridze A., Naarden L., Smeets L., Dekker C., van Belkum A., Alijani F. Prospects and Challenges for Graphene Drums as Sensors of Individual Bacteria. 2023. https://doi.org/10.1101/2023.11.20.567863
- 3. Xu B., Zhang P., Zhu J., Liu Z., Eichler A., Zheng X.Q., Lee J., Dash A., More S., Wu S., Wang Y., Jia H., Naik A., Bachtold A., Yang R., Feng P. X. L., Wang Z. Nanomechanical Resonators: Toward Atomic Scale // ACS Nano. 2022. V. 16, Iss. 10. P. 15545–15585. American Chemical Society. https://doi.org/10.1021/acsnano.2c01673
- 4. Sajadi B., van Hemert S., Arash B., Belardinelli P., Steeneken P.G., Alijani F. Size- and temperature-dependent bending rigidity of graphene using modal analysis // Carbon. 2018. V. 139. P. 334–341. https://doi.org/10.1016/j.carbon.2018.06.066
- 5. Ferrari P.F., Kim S.P., van der Zande A.M. Nanoelectromechanical systems from two-dimensional materials // Appl. Physics Reviews. 2023. V. 10. Iss. 3. American Institute of Physics Inc. https://doi.org/10.1063/5.0106731
- 6. Steeneken P.G., Dolleman R.J., Davidovikj D., Alijani F., van der Zant H.S.J. Dynamics of 2D material membranes // 2D Materials. 2021. V. 8. Iss. 4. IOP Publishing Ltd. https://doi.org/10.1088/2053-1583/ac152c
- 7. Cupertino A., Shin D., Guo L., Steeneken P.G., Bessa M.A., Norte R.A. Centimeter-scale nanomechanical resonators with low dissipation. 2023. http://arxiv.org/abs/2308.00611
- 8. Dolleman R.J., Houri S., Chandrashekar A., Alijani F., van der Zant H.S.J., Steeneken P.G. Opto-thermally excited multimode parametric resonance in graphene membranes // Scientific Reports, 2018. 8(1). https://doi.org/10.1038/s41598-018-27561-4
- 9. Yang F., Rochau F., Huber J.S., Brieussel A., Rastelli G., Weig E.M., Scheer E. Spatial Modulation of Nonlinear Flexural Vibrations of Membrane Resonators // Physical Review Letters. 2019. V. 122(15). https://doi.org/10.1103/PhysRevLett.122.154301
- 10. Zega V., Nitzan S., Li M., Ahn C.H., Ng E., Hong V., Yang Y., Kenny T., Corigliano A., Horsley D.A. Predicting the closed-loop stability and oscillation amplitude of nonlinear parametrically amplified oscillators // Appl. Physics Letters. 2015. V. 106(23). https://doi.org/10.1063/1.4922533
- 11. Keşkekler A., Shoshani O., Lee M., van der Zant H.S.J., Steeneken P.G., Alijani F. Tuning nonlinear damping in graphene nanoresonators by parametric–direct internal resonance // Nature Communications. 2021. V. 12(1). https://doi.org/10.1038/s41467-021-21334-w
- 12. Lee J., Shaw S.W., Feng P.X.L. Giant parametric amplification and spectral narrowing in atomically thin MoS2 nanomechanical resonators // Appl. Physics Reviews. 2022. V. 9(1). https://doi.org/10.1063/5.0045106
- 13. Liu C.H., Kim I.S., Lauhon L.J. Optical Control of Mechanical Mode-Coupling within a MoS2 Resonator in the Strong-Coupling Regime // Nano Letters. 2015. V. 15(10). P. 6727–6731. https://doi.org/10.1021/acs.nanolett.5b02586
- 14. Keskekler A., Bos V., Aragón A.M., Steeneken P.G., Alijani F. Characterizing multi-mode nonlinear dynamics of nanomechanical resonators. 2023. http://arxiv.org/abs/2304.01419
- 15. Wang M., Perez-Morelo D.J., Lopez D., Aksyuk V.A. Persistent Nonlinear Phase-Locking and Nonmonotonic Energy Dissipation in Micromechanical Resonators // Physical Review X. 2022. V. 12(4). https://doi.org/10.1103/PhysRevX.12.041025
- 16. de Jong M.H.J., Cupertino A., Shin D., Gröblacher S., Alijani F., Steeneken P.G., Norte R.A. Beating Ringdowns of Near-Degenerate Mechanical Resonances // Physical Review Applied. 2023. V. 20(2), 024053. https://doi.org/10.1103/PhysRevApplied.20.024053
- 17. Wei X., Zhang T., Jiang Z., Ren J., Huan R. Frequency latching in nonlinear micromechanical resonators // Appl. Physics Letters. 2017. 110(14). https://doi.org/10.1063/1.4979829
- 18. Gajo K., Rastelli G., Weig E.M. Tuning the nonlinear dispersive coupling of nanomechanical string resonators // Phys. Review B, 2020. V. 101(7). https://doi.org/10.1103/PhysRevB.101.075420
- 19. Ganesan A., Do C., Seshia A. Phononic Frequency Comb via Intrinsic Three-Wave Mixing. Physical Review Letters, (2017). 118(3). https://doi.org/10.1103/PhysRevLett.118.033903
- 20. Udem T., Holzwarth R., Hansch T.W. Optical frequency metrology // Nature. 2002. 416(6877). https://doi.org/10.1038/416233a. PMID: 11894107
- 21. Kolachevsky N.N., Khabarova K.Yu., Zalivako I.V., Semerikov I.A., Borisenko A.S., Sherstov I.V., Bagaev S.N., Lugovoy A.A., Prudnikov О.N., Taichenachev A.V., Chepurov S.V. Prospective Quantum-Optical Technologies for Satellite Navigation Challenges // Rocket-Space Device Engineering and Information Systems. 2018. V. 5(1). P. 13–27. https://doi.org/10.30894/issn2409-0239.2018.5.1.13.27
- 22. Mantsevich S.N., Kostyleva E.I., Danilin A.N., Khorkin V.S. Generation of dual and quad-optical frequency combs in the injected radiation free mode-locked frequency-shifted feedback laser // Frontiers of Optoelectronics. 2023. 16(1). https://doi.org/10.1007/s12200-023-00079-y
- 23. Lee J., Shaw S.W., Feng P.X.L. Phononic Frequency Comb Generation via 1:1 Mode Coupling in MoS2 2D Nanoelectromechanical Resonators // Proc. IEEE International Conference on Micro Electro Mechanical Systems (MEMS). 2022. January. P. 503–506. https://doi.org/10.1109/MEMS51670.2022.9699651
- 24. Sun J., Yu S., Zhang H., Chen D., Zhou X., Zhao C., Gerrard D.D., Kwon R., Vukasin G., Xiao D., Kenny T.W., Wu X., Seshia A. Generation and Evolution of Phononic Frequency Combs via Coherent Energy Transfer between Mechanical Modes // Phys. Review Applied. 2023. 19(1). https://doi.org/10.1103/PhysRevApplied.19.014031
- 25. Ganesan A., Seshia A. Resonance tracking in a micromechanical device using phononic frequency combs // Scientific Reports. 2019. 9(1). https://doi.org/10.1038/s41598-019-46003-3
- 26. Zhang T., Seshia A.AA MEMS Frequency Comb Energy Harvester // J. Microelectromechanical Systems. 2023. https://doi.org/10.1109/JMEMS.2023.3316436
- 27. Morozov N.F., Indeitsev D.A., Lukin A.V., Popov I.A., Shtukin L.V. Nonlinear interaction of longitudinal and transverse vibrations of a rod at an internal combinational resonance in view of opto-thermal excitation of N/MEMS // J. Sound and Vibration. 2021. 509. https://doi.org/10.1016/j.jsv.2021.116247
