On opto-thermally excited parametric oscillations of microbeam resonators. II

Authors

  • Nikita F. Morozov St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation; Institute of Problems in Mechanical Engineering of the Russian Academy of Sciences, 61, Bolshoi pr. V. O., St. Petersburg, 199178, Russian Federation
  • Dmitriy A. Indeitsev Institute of Problems in Mechanical Engineering of the Russian Academy of Sciences, 61 Bolshoi pr. V. O., St. Petersburg 199178, Russian Federation; Peter the Great St. Petersburg Polytechnic University, 29 ul. Politekhnicheskaia, St. Petersburg 195251, Russian Federation.
  • Alexey V. Lukin Peter the Great St. Petersburg Polytechnic University, 29, ul. Politekhnicheskaia, St. Petersburg, 195251, Russian Federation
  • Ivan A. Popov Peter the Great St. Petersburg Polytechnic University, 29, ul. Politekhnicheskaia, St. Petersburg, 195251, Russian Federation
  • Lev V. Shtukin Institute of Problems in Mechanical Engineering of the Russian Academy of Sciences, 61, Bolshoi pr. V. O., St. Petersburg, 199178, Russian Federation; Peter the Great St. Petersburg Polytechnic University, 29, ul. Politekhnicheskaia, St. Petersburg, 195251, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2023.404

Abstract

This article is the second part of the work devoted to the investigation of the nonlinear dynamics of parametrically excited flexural vibrations of a clamped-clamped microbeam - the basic sensitive element of a promising class of microsensors of various physical quantities - under laser thermooptical action in the form of periodically generated pulses acting on a certain part of the surface of the beam element. The fundamental technical feasibility of laser generation of parametric oscillations of high-Q microresonators without the implementation of scenarios for the loss of elastic stability of the sensitive element or its unacceptable heating is shown. The nature of the zone of the main parametric resonance is analyzed analytically. The resonant characteristics of the system are constructed in a geometrically non-linear formulation corresponding to the Bernoulli - Euler beam model.

Keywords:

nonlinear dynamics, parametric oscillations, Bernoulli - Euler beam, modal interaction, laser-induced opto-thermal excitation

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References

Литература

1. Vorobyev R. I., Sergeichev I. V., Karabutov A. A., Mironova E. A., Savateeva E. V., Akhatov I. Sh. Application of the Optoacoustic Method to Assess the Effect of Voids on the Crack Resistance of Structural Carbon Plastics. Acoust. Phys. 66, 132-136 (2020). https://doi.org/10.1134/S1063771020020153

2. Yan G., Raetz S., Chigarev N., Blondeau Ja., Gusev V. E., Tournat V. Cumulative fatigue damage in thin aluminum films evaluated non-destructively with lasers via zero-group-velocity Lamb modes. NDT & E International 116, 102323 (2020). https://doi.org/10.1016/j.ndteint.2020.102323

3. Pan Yu., Rossignol C., Audoin B. Acoustic waves generated by a laser line pulse in cylinders; Application to the elastic constants measurement. J. Acoust. Soc. Am. 115 (4), 1537-1545 (2004). https://doi.org/10.1121/1.1651191

4. Chow G., Uchaker E., Cao G., Wang Ju. Laser-induced surface acoustic waves: An alternative method to nanoindentation for the mechanical characterization of porous nanostructured thin lm electrode media. Mechanics of Materials 91, 333-342 (2015). https://doi.org/10.1016/J.MECHMAT.2015.10.005

5. Champion A., Bellouard Y. Direct volume variation measurements in fused silica specimens exposed to femtosecond laser. Optical Materials Express 2, 789-798 (2012). https://doi.org/10.1364/OME.2.000789

6. Otsuka P. H., Mezil S., Matsuda O., Tomoda M., Maznev A. A., Gan T., Fang N., Boechler N., Gusev V. E., Wright O. B. Time-domain imaging of gigahertz surface waves on an acoustic metamaterial. New Journal of Physics 20, 013026 (2018). https://doi.org/10.1088/1367-2630/AA9298

7. Li C., Guan G., Zhang F., Nabi G., Wang R. K., Huang Z. Laser induced surface acoustic wave combined with phase sensitive optical coherence tomography for super cial tissue characterization: a solution for practical application. Biomedical Optics Express 5 (5), 1403-1418 (2014). https://doi.org/10.1364/BOE.5.001403

8. Phinney L. M., Klody K. A., Sackos Jo. T., Walraven Je. A. Damage of MEMS thermal actuators heated by laser irradiation. Reliability, Packaging, Testing and Characterization of MEMS/MOEMS IV. Proceedings of MOEMS-MEMS Micro and Nanofabrication, 2005, San Jose, 5716, 81-88 (2005). https://doi.org/10.1117/12.594408

9. Serrano J. R., Phinney L. M. Displacement and Thermal Performance of Laser-Heated Asymmetric MEMS Actuators. Journal of Microelectromechanical Systems 17 (1), 166-174 (2008). https://doi.org/10.1109/JMEMS.2007.911945

10. Mai A., Bunce C., Hu¨bner R., Pahner D., Dauderstadt U. A. In situ bow change of Al-alloy MEMS micromirrors during 248-nm laser irradiation. Journal of Micro/Nanolithography, MEMS and MOEMS 15 (3), 035502 (2016). https://doi.org/10.1117/1.JMM.15.3.035502

11. Zook J. D., Burns D. W., Herb W. R., Guckel H., Kang J. W., Ahn Y. Optically excited self-resonant microbeams. Sensors and Actuators A: Physical 52 (1), 92-98 (1996). https://doi.org/10.1016/0924-4247(96)80131-2

12. Yang T., Bellouard Y. Laser-induced transition between nonlinear and linear resonant behaviors of a micromechanical oscillator. Phys. Rev. Applied 7, 064002 (2017). https://doi.org/10.1103/PhysRevApplied.7.064002

13. 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. Sci. Rep. 8, 9366 (2018). https://doi.org/10.1038/s41598-018-27561-4

14. Zehnder A. T., Rand R. H., Krylov S. Locking of electrostatically coupled thermo-optically driven MEMS limit cycle oscillators. International Journal of Non-Linear Mechanics 102, 92-100 (2018). https://doi.org/10.1016/J.IJNONLINMEC.2018.03.009

15. Bhaskar A., Shayak B., Rand R. H., Zehnder A. T. Synchronization characteristics of an array of coupled MEMS limit cycle oscillators. International Journal of Non-Linear Mechanics 128, 103634 (2021). https://doi.org/10.1016/j.ijnonlinmec.2020.103634

16. Morozov N. F., Indeitsev D. A., Lukin A. V., Popov I. A., Privalova O. V., Shtukin L. V. Stability of the Bernoulli - Euler Beam in coupled electric and thermal fields. Dokl. Phys. 63, 342-347 (2018). https://doi.org/10.1134/S1028335818080086

17. Morozov N. F., Indeitsev D. A., Lukin A. V., Popov I. A., Privalova O. V., Semenov B. N., Shtukin L. V. Bernoulli - Euler beam under action of a moving thermal source: characteristics of the dynamic behavior. Dokl. Phys. 64, 185-188 (2019). https://doi.org/10.1134/S1028335819040050

18. Morozov N. F., Indeitsev D. A., Lukin A. V., Popov I. A., Privalova O. V., Shtukin L. V. Stability of the Bernoulli - Euler Beam under the action of a moving thermal source. Dokl. Phys. 65, 67-71 (2020). https://doi.org/10.1134/S102833582002007X

19. 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. Journal of Sound and Vibration 509, 116-247 (2021). https://doi.org/10.1016/j.jsv.2021.116247

20. Морозов Н. Ф., Индейцев Д. А., Лукин А. В., Попов И. А., Штукин Л. В. Нелинейное модальное взаимодействие продольных и изгибных колебаний балочного резонатора при периодическом тепловом нагружении. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия 9 (67), вып. 2, 317-337 (2022). https://doi.org/10.21638/spbu01.2022.212

21. Морозов Н. Ф., Индейцев Д. А., Лукин А. В., Попов И. А., Штукин Л. В. О термооптическом возбуждении параметрических колебаний микробалочных резонаторов. I. Вестник Санкт- Петербургского университета. Математика. Механика. Астрономия 10 (2), 315-333 (2023). https://doi.org/10.21638/spbu01.2023.212

References

1. Vorobyev R. I., Sergeichev I.V., Karabutov A.A., Mironova E.A., Savateeva E.V., Akhatov I. Sh. Application of the Optoacoustic Method to Assess the Effect of Voids on the Crack Resistance of Structural Carbon Plastics. Acoust. Phys. 66, 132-136 (2020). https://doi.org/10.1134/S1063771020020153

2. Yan G., Raetz S., Chigarev N., Blondeau Ja., Gusev V. E., Tournat V. Cumulative fatigue damage in thin aluminum films evaluated non-destructively with lasers via zero-group-velocity Lamb modes. NDT & E International 116, 102323 (2020). https://doi.org/10.1016/j.ndteint.2020.102323

3. Pan Yu., Rossignol C., Audoin B. Acoustic waves generated by a laser line pulse in cylinders; Application to the elastic constants measurement. J. Acoust. Soc. Am. 115 (4), 1537-1545 (2004). https://doi.org/10.1121/1.1651191

4. Chow G., Uchaker E., Cao G., Wang Ju. Laser-induced surface acoustic waves: An alternative method to nanoindentation for the mechanical characterization of porous nanostructured thin film electrode media. Mechanics of Materials 91, 333-342 (2015). https://doi.org/10.1016/J.MECHMAT.2015.10.005

5. Champion A., Bellouard Y. Direct volume variation measurements in fused silica specimens exposed to femtosecond laser. Optical Materials Express 2, 789-798 (2012). https://doi.org/10.1364/OME.2.000789

6. Otsuka P.H., Mezil S., Matsuda O., Tomoda M., Maznev A.A., Gan T., Fang N., Boechler N., Gusev V.E., Wright O.B. Time-domain imaging of gigahertz surface waves on an acoustic metamaterial. New Journal of Physics 20, 013026 (2018). https://doi.org/10.1088/1367-2630/AA9298

7. Li C., Guan G., Zhang F., Nabi G., Wang R.K., Huang Z. Laser induced surface acoustic wave combined with phase sensitive optical coherence tomography for superficial tissue characterization: a solution for practical application. Biomedical Optics Express 5 (5), 1403-1418 (2014). https://doi.org/10.1364/BOE.5.001403

8. Phinney L.M., Klody K.A., Sackos Jo.T., Walraven Je.A. Damage of MEMS thermal actuators heated by laser irradiation. Reliability, Packaging, Testing and Characterization of MEMS/MOEMS IV. Proceedings of MOEMS-MEMS Micro and Nanofabrication, 2005, San Jose, 5716, 81-88 (2005). https://doi.org/10.1117/12.594408

9. Serrano J. R., Phinney L.M. Displacement and Thermal Performance of Laser-Heated Asymmetric MEMS Actuators. Journal of Microelectromechanical Systems 17 (1), 166-174 (2008). https://doi.org/10.1109/JMEMS.2007.911945

10. Mai A., Bunce C., H¨ubner R., Pahner D., Dauderstadt U.A. In situ bow change of Al-alloy MEMS micromirrors during 248-nm laser irradiation. Journal of Micro/Nanolithography, MEMS and MOEMS 15 (3), 035502 (2016). https://doi.org/10.1117/1.JMM.15.3.035502

11. Zook J.D., Burns D.W., Herb W. R., Guckel H., Kang J.W., Ahn Y. Optically excited self-resonant microbeams. Sensors and Actuators A: Physical 52 (1), 92-98 (1996). https://doi.org/10.1016/0924-4247(96)80131-2

12. Yang T., Bellouard Y. Laser-induced transition between nonlinear and linear resonant behaviors of a micromechanical oscillator. Phys. Rev. Applied 7, 064002 (2017). https://doi.org/10.1103/PhysRevApplied.7.064002

13. 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. Sci. Rep. 8, 9366 (2018). https://doi.org/10.1038/s41598-018-27561-4

14. Zehnder A.T., Rand R.H., Krylov S. Locking of electrostatically coupled thermo-optically driven MEMS limit cycle oscillators. International Journal of Non-Linear Mechanics 102, 92-100 (2018). https://doi.org/10.1016/J.IJNONLINMEC.2018.03.009

15. Bhaskar A., Shayak B., Rand R.H., Zehnder A.T. Synchronization characteristics of an array of coupled MEMS limit cycle oscillators. International Journal of Non-Linear Mechanics 128, 103-634 (2021). https://doi.org/10.1016/j.ijnonlinmec.2020.103634

16. Morozov N.F., Indeitsev D.A., Lukin A.V., Popov I.A., Privalova O.V., Shtukin L.V. Stability of the Bernoulli-Euler Beam in coupled electric and thermal fields. Dokl. Phys. 63, 342-347 (2018). https://doi.org/10.1134/S1028335818080086

17. Morozov N.F., Indeitsev D.A., Lukin A.V., Popov I.A., Privalova O.V., Semenov B.N., Shtukin L.V. Bernoulli- Euler beam under action of a moving thermal source: characteristics of the dynamic behavior. Dokl. Phys. 64, 185-188 (2019). https://doi.org/10.1134/S1028335819040050

18. Morozov N.F., Indeitsev D.A., Lukin A.V., Popov I.A., Privalova O.V., Shtukin L.V. Stability of the Bernoulli-Euler Beam under the action of a moving thermal source. Dokl. Phys. 65, 67-71 (2020). https://doi.org/10.1134/S102833582002007X

19. 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. Journal of Sound and Vibration 509, 116247 (2021). https://doi.org/10.1016/j.jsv.2021.116247

20. Morozov N.F., Indeitsev D.A., Lukin A.V., Popov I.A., Shtukin L.V. Nonlinear modal interaction between longitudinal and bending vibrations of a beam resonator underperiodic thermal loading. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 9 (67), iss. 2, 317-337 (2022). https://doi.org21638/spbu01.2022.212 (In Russian) [Engl. trans.: Vestnik St. Petersburg University, Mathematics 55, iss. 2, 212-228 (2022). https://doi.org/10.1134/S106345412202008X].

21. Morozov N.F., Indeitsev D.A., Lukin A.V., Popov I.A., Shtukin L.V. On optothermally excited parametric oscillations of microbeam resonators. I. Vestnik of Saint Petersburg Universitу Mathematics. Mechanics. Astronomy 10 (68), iss. 2, 315-333 (2023). https://doi.org/10.21638/spbu01.2023.212 (In Russian) [Engl. trans.: Vestnik St. Petersburg University, Mathematics 56, iss. 2, 231-244 (2023) https://doi.org/10.1134/S1063454123020127].

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Published

2023-12-23

How to Cite

Morozov, N. F., Indeitsev, D. A., Lukin, A. V., Popov, I. A., & Shtukin, L. V. (2023). On opto-thermally excited parametric oscillations of microbeam resonators. II. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10(4), 632–649. https://doi.org/10.21638/spbu01.2023.404

Issue

Vol. 10 No. 4 (2023)

Section

On the anniversary of A. K. Belyaev

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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.

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