Skip to main content
SpringerLink
Log in

Analysis of the quality factor of micromechanical resonators using memory-dependent derivative under different models

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

In the present work, the quality factor (and thermoelastic damping) of a microbeam resonator is analyzed by employing the three-phase-lag thermoelasticity theory with memory-dependent derivative. We compare our results with different heat conduction models. An explicit formula of thermoelastic damping has been derived, and effects of the normalized frequency and the beam height on thermoelastic damping of the microbeam resonator have been studied. We presented our work numerically by taking Silicon. The effects of normalized frequency, beam height, and different kernel of memory-dependent derivative on thermoelastic damping has been presented with the numerical data of Silicon.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Mohanty, P., Harrington, D.A., Ekinci, K.L., Yang, Y.T., Murphy, M.J., Roukes, M.L.: Intrinsic dissipation in high-frequency micromechanical resonators. Phys. Rev. B—Condens. Matter Mater. Phys. 66, 085146 (2002). https://doi.org/10.1103/PhysRevB.66.085416

    Article  Google Scholar 

  2. Reid, S., Cagnoli, G., Crooks, D.R.M., Hough, J., Murray, P., Rowan, S., Fejer, M.M.: Mechanical dissipation in silicon flexures. Phys. Lett. A 351, 205–211 (2006). https://doi.org/10.1016/j.physleta.2005.10.103

    Article  Google Scholar 

  3. Biot, M.A.: Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 27, 240 (1956). https://doi.org/10.1063/1.1722351

    Article  MathSciNet  MATH  Google Scholar 

  4. Lord, H.W., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15, 299–309 (1967). https://doi.org/10.1016/0022-5096(67)90024-5

    Article  MATH  Google Scholar 

  5. Green, A.E., Lindsay, K.A.: Thermoelasticity. J. Elast. 2, 1–7 (1972)

    Article  Google Scholar 

  6. Tzou, D.Y.: A unified field approach for heat conduction from macro- to micro-scales. J. Heat Transf. 117, 8–16 (1995). https://doi.org/10.1115/1.2822329

    Article  Google Scholar 

  7. Tzou, D.Y.: The generalized lagging response in small-scale and high-rate heating. Int. J. Heat Mass Transf. 38, 3231–3240 (1995). https://doi.org/10.1016/0017-9310(95)00052-B

    Article  Google Scholar 

  8. Tzou, D.Y.: Experimental support for the lagging behavior in heat propagation. J. Thermophys. Heat Transf. 9, 686–693 (1995). https://doi.org/10.2514/3.725

    Article  Google Scholar 

  9. Green, A.E., Naghdi, P.M.: A re-examination of the basic postulates of thermomechanics. Proc. R. Soc. A Math. Phys. Eng. Sci. 432, 171–194 (1991). https://doi.org/10.1098/rspa.1991.0012

    Article  MathSciNet  MATH  Google Scholar 

  10. Green, A.E., Naghdi, P.M.: On undamped heat waves in an elastic solid. J. Therm. Stress 15, 253–264 (1992)

    Article  MathSciNet  Google Scholar 

  11. Green, A.E., Naghdi, P.M.: Thermoelasticity without energy dissipation. J. Elast. 31, 189–208 (1993). https://doi.org/10.1007/BF00044969

    Article  MathSciNet  MATH  Google Scholar 

  12. Choudhuri, S.K.R.: On a thermoelastic three-phase-lag model. J. Therm. Stress 30, 231–238 (2007). https://doi.org/10.1080/01495730601130919

    Article  Google Scholar 

  13. Zener, C.: Internal friction in solids. I. Theory of internal friction in reeds. Phys. Rev. (1937). https://doi.org/10.1103/PhysRev.52.230

    Article  MATH  Google Scholar 

  14. Zener, C.: Internal friction in solids II. General theory of thermoelastic internal friction. Phys. Rev. (1938). https://doi.org/10.1103/PhysRev.53.90

    Article  MATH  Google Scholar 

  15. Kinra, V.K., Milligan, K.B.: A second-law analysis of thermoelastic damping. J. Appl. Mech. Trans. ASME 61, 71 (1994). https://doi.org/10.1115/1.2901424

    Article  Google Scholar 

  16. Lifshitz, R., Roukes, M.: Thermoelastic damping in micro- and nanomechanical systems. Phys. Rev. B—Condens. Matter Mater. Phys. 61, 5600–5609 (2000). https://doi.org/10.1103/PhysRevB.61.5600

    Article  Google Scholar 

  17. Vahdat, A.S., Rezazadeh, G., Ahmadi, G.: Thermoelastic damping in a micro-beam resonator tunable with piezoelectric layers. Acta Mech. Solida Sin. (2012). https://doi.org/10.1016/S0894-9166(12)60008-1

    Article  Google Scholar 

  18. Zuo, W., Li, P., Zhang, J., Fang, Y.: Analytical modeling of thermoelastic damping in bilayered microplate resonators. Int. J. Mech. Sci. (2016). https://doi.org/10.1016/j.ijmecsci.2015.12.009

    Article  Google Scholar 

  19. Zenkour, A.M.: Nonlocal thermoelasticity theory without energy dissipation for nano-machined beam resonators subjected to various boundary conditions. Microsyst. Technol. 23, 55–65 (2017). https://doi.org/10.1007/s00542-015-2703-4

    Article  Google Scholar 

  20. Kumar, R., Kumar, R., Kumar, H.: Effects of phase-lag on thermoelastic damping in micromechanical resonators. J. Therm. Stress. (2018). https://doi.org/10.1080/01495739.2018.1469061

    Article  Google Scholar 

  21. Ezzat, M.A.: Fundamental solution in generalized magneto-thermoelasticity with two relaxation times for perfect conductor cylindrical region. Int. J. Eng. Sci. 42, 1503–1519 (2004)

    Article  MathSciNet  Google Scholar 

  22. Ezzat, M.A., Awad, E.S.: Constitutive relations, uniqueness of solution, and thermal shock application in the linear theory of micropolar generalized thermoelasticity involving two temperatures. J. Therm. Stress. 33, 226–250 (2010)

    Article  Google Scholar 

  23. El-Karamany, A.S., Ezzat, M.A.: On the three-phase-lag linear micropolar thermoelasticity theory. Eur. J. Mech.—A/Solids 40, 198–208 (2013)

    Article  MathSciNet  Google Scholar 

  24. El-Karamany, A.S., Ezzat, M.A.: On the dual-phase-lag thermoelasticity theory. Meccanica 49, 79–89 (2014)

    Article  MathSciNet  Google Scholar 

  25. Kaur, I., Lata, P., Singh, K.: Study of transversely isotropic nonlocal thermoelastic thin nano-beam resonators with multi-dual-phase-lag theory. Arch. Appl. Mech. 91, 1–25 (2020)

    Google Scholar 

  26. Wang, J.L., Li, H.F.: Surpassing the fractional derivative: concept of the memory-dependent derivative. Comput. Math. Appl. 62, 1562–1567 (2011). https://doi.org/10.1016/j.camwa.2011.04.028

    Article  MathSciNet  MATH  Google Scholar 

  27. Yu, Y.J., Hu, W., Tian, X.G.: A novel generalized thermoelasticity model based on memory-dependent derivative. Int. J. Eng. Sci. 81, 123–134 (2014). https://doi.org/10.1016/j.ijengsci.2014.04.014

    Article  MathSciNet  MATH  Google Scholar 

  28. Ezzat, M.A., El-Karamany, A.S., El-Bary, A.A.: Generalized thermo-viscoelasticity with memory-dependent derivatives. Int. J. Mech. Sci. 89, 470–475 (2014)

    Article  Google Scholar 

  29. Ezzat, M.A., El-Bary, A.A.: Memory-dependent derivatives theory of thermo-viscoelasticity involving two-temperature. J. Mech. Sci. Technol. 29, 4273–4279 (2015)

    Article  Google Scholar 

  30. Ezzat, M.A., El-Karamany, A.S., El-Bary, A.A.: Modeling of memory-dependent derivative in generalized thermoelasticity. Eur. Phys. J. Plus. 131, 372 (2016). https://doi.org/10.1140/epjp/i2016-16372-3

    Article  Google Scholar 

  31. Ezzat, M.A., El Karamany, A.S., El-Bary, A.A.: Electro-thermoelasticity theory with memory-dependent derivative heat transfer. Int. J. Eng. Sci. 99, 22–38 (2016)

    Article  MathSciNet  Google Scholar 

  32. Al-jamel, A., Al-jamal, M.F., El-karamany, A.: A memory-dependent derivative model for damping in oscillatory systems. J. Vib. Control 24, 2221–2229 (2018). https://doi.org/10.1177/1077546316681907

    Article  MathSciNet  Google Scholar 

  33. Mondal, S., Sur, A., Kanoria, M.: A memory response in the vibration of a microscale beam induced by laser pulse. J. Therm. Stress (2019). https://doi.org/10.1080/01495739.2019.1629854

    Article  MATH  Google Scholar 

  34. Mondal, S., Othman, M.I.A.: Memory dependent derivative effect on generalized piezo-thermoelastic medium under three theories. Waves Random Complex Media (2020). https://doi.org/10.1080/17455030.2020.1730480

    Article  Google Scholar 

  35. Lata, P., Singh, S.: Thermomechanical interactions in a non local thermoelastic model with two temperature and memory dependent derivatives. Coupled Syst. Mech. 9, 397–410 (2020)

    Google Scholar 

  36. Kaur, I., Lata, P., Singh, K.: Memory-dependent derivative approach on magneto-thermoelastic transversely isotropic medium with two temperatures. Int. J. Mech. Mater. Eng. 15, 1–13 (2020)

    Article  Google Scholar 

  37. Kumar, R., Tiwari, R., Kumar, R.: Significance of memory-dependent derivative approach for the analysis of thermoelastic damping in micromechanical resonators. Mech. Time-Depend. Mat. 8, 1–18 (2020)

    Google Scholar 

  38. Youssef, H.M., Alghamdi, N.A.: Thermoelastic damping in nanomechanical resonators based on two-temperature generalized thermoelasticity theory. J. Therm. Stress 38, 1347–1361 (2015). https://doi.org/10.1080/01495739.2015.1073541

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Central University of South Bihar, Gaya, 824236, India

    Ravi Kumar

Authors
  1. Ravi Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ravi Kumar.

Ethics declarations

Conflict of interest

The author declares that there is no any conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kumar, R. Analysis of the quality factor of micromechanical resonators using memory-dependent derivative under different models. Arch Appl Mech 91, 2735–2745 (2021). https://doi.org/10.1007/s00419-021-01920-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-021-01920-6

Keywords

Search

Navigation