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Research Article

Analytical solutions for thermo-elastic damping of rotational ring resonators incorporating thermal relaxations and elastic small scales

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Pages 321-346 | Received 21 Jul 2023, Accepted 08 Nov 2023, Published online: 09 Jan 2024

References

  • J. Söderkvist, “Micromachined gyroscopes,” Sens. Actuators A, vol. 43, no. 1-3, pp. 65–71, 1994. DOI: 10.1016/0924-4247(93)00667-S.
  • P. Mohanty, D. A. Harrington, K. L. Ekinci, Y. T. Yang, M. J. Murphy and M. L. Roukes, “Intrinsic dissipation in high-frequency micromechanical resonators,” Phys. Rev. B, vol. 66, no. 8, pp. 085416, 2002. DOI: 10.1103/PhysRevB.66.085416.
  • F. L. Guo and G. A. Rogerson, “Thermoelastic coupling effect on a micro-machined beam resonator,” Mech. Res. Commun., vol. 30, no. 6, pp. 513–518, 2003. DOI: 10.1016/S0093-6413(03)00061-2.
  • A. M. Fennimore, T. D. Yuzvinsky, W.-Q. Han, M. S. Fuhrer, J. Cumings and A. Zettl, “Rotational actuators based on carbon nanotubes,” Nature, vol. 424, no. 6947, pp. 408–410, 2003. DOI: 10.1038/nature01823.
  • F. L. Ekinci and M. K. Roukes, “Nanoelectromechanical systems,” Rev. Sci. Instrum., vol. 76, no. 6, pp. 061101, 2005. DOI: 10.1063/1.1927327.
  • V. Sazonova, Y. Yaish, H. Ustünel, D. Roundy, T. A. Arias and P. L. McEuen, “A tunable carbon nanotube electromechanical oscillator,” Nature, vol. 431, no. 7006, pp. 284–287, 2004. DOI: 10.1038/nature02905.
  • R. Raiteri, M. Grattarola, H.-J. Butt and P. Skládal, “Micromechanical cantilever based biosensors,” Sens. Actuators B Chem., vol. 79, no. 2-3, pp. 115–126, 2001. DOI: 10.1016/S0925-4005(01)00856-5.
  • Z. Hao, Y. Xu and S. K. Durgam, “A thermal-energy method for calculating thermoelastic damping in micromechanical resonators,” J. Sound Vib., vol. 322, no. 4–5, pp. 870–882, 2009. DOI: 10.1016/j.jsv.2008.12.005.
  • C. Zener, “Internal friction in solids-I: theory of internal friction in reeds,” Phys. Rev., vol. 52, no. 3, pp. 230–235, 1937. DOI: 10.1103/PhysRev.52.230.
  • C. Zener, “Internal friction in solids-II: general theory of thermoelastic internal friction,” Phys. Rev., vol. 53, no. 1, pp. 90–99, 1938. DOI: 10.1103/PhysRev.53.90.
  • R. Lifshitz and M. L. Roukes, “Thermoelastic damping in micro-and nanomechanical systems,” Phys. Rev. B, vol. 61, no. 8, pp. 5600–5609, 2000. DOI: 10.1103/PhysRevB.61.5600.
  • F. Zangeneh-Nejad and R. Safian, “A Graphene-based THz ring resonator for label-free sensing,” IEEE Sens. J., vol. 16, no. 11, pp. 4338–4344, 2016. DOI: 10.1109/JSEN.2016.2548784.
  • M. M. Ariannejad, I. S. Amiri, S. R. B. Azzuhri, R. Zakaria and P. Yupapin, “Polarization dependence of SU-8 micro ring resonator,” Results Phys., vol. 11, pp. 515–522, 2018. DOI: 10.1016/j.rinp.2018.09.048.
  • W. Zhou, et al., “A piezoelectric micro ultrasonic motor with high Q and good mode match,” IEEE/ASME Trans. Mechatron., vol. 26, no. 4, pp. 1773–1781, 2021. DOI: 10.1109/TMECH.2021.3067774.
  • Y. Ding, et al., “Effective electro-optical modulation with high extinction ratio by a graphene–silicon microring resonator,” Nano Lett., vol. 15, no. 7, pp. 4393–4400, 2015. DOI: 10.1021/acs.nanolett.5b00630.
  • B. Walter, et al., “Design and operation of a silicon ring resonator for force sensing applications above 1 MHz,” J. Micromech. Microeng., vol. 19, no. 11, pp. 115009, 2009. DOI: 10.1088/0960-1317/19/11/115009.
  • H. W. Lord and Y. Shulman, “A generalized dynamical theory of thermoelasticity,” J. Mech. Phys. Solids, vol. 15, no. 5, pp. 299–309, 1967. DOI: 10.1016/0022-5096(67)90024-5.
  • D. Y. Tzou, Macro-to Microscale Heat Transfer: The Lagging Behavior, 2nd ed., John Wiley & Sons, West Sussex, 2015.
  • S. R. Choudhuri, “On a thermoelastic three-phase-lag model,” J. Therm. Stresses, vol. 30, no. 3, pp. 231–238, 2007. DOI: 10.1080/01495730601130919.
  • A. E. Green and P. M. Naghdi, “Thermoelasticity without energy dissipation,” J. Elast., vol. 31, no. 3, pp. 189–208, 1993. DOI: 10.1007/BF00044969.
  • S. J. Wong, C. H. J. Fox, S. McWilliam, C. P. Fell and R. Eley, “A preliminary investigation of thermo-elastic damping in silicon rings,” J. Micromech. Microeng., vol. 14, no. 9, pp. 108–113, 2004.
  • S. J. Wong, C. H. J. Fox and S. McWilliam, “Thermoelastic damping of the in-plane vibration of thin silicon rings,” J. Sound Vib., vol. 293, no. 1-2, pp. 266–285, 2006. DOI: 10.1016/j.jsv.2005.09.037.
  • S. B. Kim, Y. H. Na and J. H. Kim, “Thermoelastic damping effect on in-extensional vibration of rotating thin ring,” J. Sound Vib., vol. 329, no. 9, pp. 1227–1234, 2010. DOI: 10.1016/j.jsv.2009.12.014.
  • Y. M. Fang and P. Li, “Thermoelastic damping in thin microrings with two-dimensional heat conduction,” Physica E, vol. 69, pp. 198–206, 2015. DOI: 10.1016/j.physe.2015.01.039.
  • P. Li, Y. M. Fang and J. R. Zhang, “Thermoelastic damping in microrings with circular cross-section,” J. Sound Vib., vol. 361, pp. 341–354, 2016. DOI: 10.1016/j.jsv.2015.09.051.
  • S. T. Hossain, S. McWilliam and A. A. Popov, “An investigation on thermoelastic damping of high-q ring resonators,” Int. J. Mech. Sci., vol. 106, pp. 209–219, 2016. DOI: 10.1016/j.ijmecsci.2015.12.023.
  • N. A. Alghamdi and H. M. Youssef, “Dual-phase-lagging thermoelastic damping inextensional vibration of rotating nano-ring,” Microsyst. Technol., vol. 23, no. 10, pp. 4333–4343, 2017. DOI: 10.1007/s00542-017-3294-z.
  • J. H. Kim and J. H. Kim, “Mass imperfections in a toroidal micro-ring model with thermoelastic damping,” Appl. Math. Modell., vol. 63, pp. 405–414, 2018. DOI: 10.1016/j.apm.2018.06.006.
  • H. Y. Zhou, P. Li and Y. M. Fang, “Single-phase-lag thermoelastic damping models for rectangular cross-sectional micro- and nano-ring resonators,” Int. J. Mech. Sci., vol. 163, pp. 105132, 2019. DOI: 10.1016/j.ijmecsci.2019.105132.
  • Y. P. Tai and N. Chen, “Thermoelastic damping in the out-of-plane vibration of a microring resonator with rectangular cross-section,” Int. J. Mech. Sci., vol. 151, pp. 684–691, 2019. DOI: 10.1016/j.ijmecsci.2018.12.026.
  • H. Zhou and P. Li, “Dual-phase-lagging thermoelastic damping and frequency shift of micro/nano-ring resonators with rectangular cross-section,” Thin-Walled Struct., vol. 159, no. 1, pp. 107309, 2021. DOI: 10.1016/j.tws.2020.107309.
  • J. H. Kim and J. H. Kim, “Thermoelastic dissipation including single-phase-lagging of rectangular-cross-sectional micro/nanoring with point masses,” J. Therm. Stresses, vol. 44, no. 6, pp. 755–767, 2021. DOI: 10.1080/01495739.2021.1895695.
  • Y. Tai, P. Li, Y. Zheng and J. Tian, “Entropy generation and thermoelastic damping in the in-plane vibration of microring resonators,” Entropy, vol. 21, no. 7, pp. 631, 2019. DOI: 10.3390/e21070631.
  • J. H. Kim, S. J. Kang and J. H. Kim, “Splitting of quality factors for micro-ring with arbitrary point masses,” J. Sound Vib., vol. 395, pp. 317–327, 2017. DOI: 10.1016/j.jsv.2017.02.030.
  • H. Zhou, P. Li, H. Jiang, H. Xue and B. Bo, “Nonlocal dual-phase-lag thermoelastic dissipation of size-dependent micro/nano-ring resonators,” Int. J. Mech. Sci., vol. 219, pp. 107080, 2022. DOI: 10.1016/j.ijmecsci.2022.107080.
  • H. Zhou, D. Shao and P. Li, “Thermoelastic damping and frequency shift in micro/nano-ring resonators considering the nonlocal single-phase-lag effect in the thermal field,” Appl. Math. Modell., vol. 115, pp. 237–258, 2023. DOI: 10.1016/j.apm.2022.11.002.
  • A. T. Jalil, et al., “Analytical model for thermoelastic damping in in-plane vibrations of circular cross-sectional micro/nanorings with dual-phase-lag heat conduction,” J. Vib. Eng. Technol., 2023. DOI: 10.1007/s42417-023-00876-x.
  • R. Kumar, R. Kumar and H. Kumar, “Effects of phase-lag on thermoelastic damping in micromechanical resonators,” J. Therm. Stresses, vol. 41, no. 9, pp. 1115–1124, 2018. DOI: 10.1080/01495739.2018.1469061.
  • R. Kumar and R. Kumar, “Effects of phase lags on thermoelastic damping in micro-beam resonators,” Int. J. Str. Stab. Dyn., vol. 19, no. 09, pp. 1971005, 2019. DOI: 10.1142/S0219455419710056.
  • R. Tiwari and R. Kumar, “Non-local effect on quality factor of micro-mechanical resonator under the purview of three-phase-lag thermoelasticity with memory-dependent derivative,” Appl. Phys. A, vol. 128, no. 3, pp. 190, 2022. DOI: 10.1007/s00339-022-05322-5.
  • R. Kumar, R. Tiwari and R. Kumar, “Significance of memory-dependent derivative approach for the analysis of thermoelastic damping in micromechanical resonators,” Mech. Time-Depend. Mater., vol. 26, no. 1, pp. 101–118, 2022. DOI: 10.1007/s11043-020-09477-7.
  • H. R. Ahmadi, Z. Rahimi and W. Sumelka, “Thermoelastic damping in orthotropic and isotropic NEMS resonators accounting for double nonlocal thermoelastic effects,” J. Therm. Stresses, vol. 44, no. 3, pp. 1–16, 2021. DOI: 10.1080/01495739.2020.1853639.
  • L. Yang, P. Li, Q. Gao and T. Gao, “Thermoelastic damping in rectangular micro/nanoplate resonators by considering three-dimensional heat conduction and modified couple stress theory,” J. Therm. Stresses, vol. 45, no. 11, pp. 843–864, 2022. DOI: 10.1080/01495739.2022.2103058.
  • X. Ge, P. Li, Y. Fang and L. Yang, “Thermoelastic damping in rectangular microplate/nanoplate resonators based on modified nonlocal strain gradient theory and nonlocal heat conductive law,” J. Therm. Stresses, vol. 44, no. 6, pp. 690–714, 2021. DOI: 10.1080/01495739.2021.1906807.
  • B. Gu, S. Shi, Y. Ma and T. He, “Thermoelastic damping analysis in nanobeam resonators considering thermal relaxation and surface effect based on the nonlocal strain gradient theory,” J. Therm. Stresses, vol. 45, no. 12, pp. 974–992, 2022. DOI: 10.1080/01495739.2022.2130845.
  • B. A. Hamidi, S. A. Hosseini, R. Hassannejad and F. Khosravi, “An exact solution on gold microbeam with thermoelastic damping via generalized Green-Naghdi and modified couple stress theories,” J. Therm. Stresses, vol. 43, no. 2, pp. 157–174, 2022. DOI: 10.1080/01495739.2019.1666694.
  • W. Soedel, Vibration of Shells and Plates, Third Edition, Revised and Expanded. Marcel Dekker Inc., 2004.
  • A. C. Eringen, “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves,” J. Appl. Phys., vol. 54, no. 9, pp. 4703–4710, 1983. DOI: 10.1063/1.332803.
  • S. Gopalakrishnan and S. Narendar, Wave Propagation in Nanostrucutres. Springer, 2013.
  • A. Duwel, J. Gorman, M. Weinstein, J. Borenstein and P. Ward, “Experimental study of thermoelastic damping in MEMS gyros,” Sens. Actuators. A: Phys, vol. 103, no. 1-2, pp. 70–75, 2003. DOI: 10.1016/S0924-4247(02)00318-7.
  • M. Chester, “Second sound in solids,” Phys. Rev., vol. 131, no. 5, pp. 2013–2015, 1963. DOI: 10.1103/PhysRev.131.2013.
  • P. H. Francis, “Thermo-mechanical effects in elastic wave propagation: a survey,” J. Sound Vib., vol. 21, no. 2, pp. 181–192, 1972. DOI: 10.1016/0022-460X(72)90905-4.
  • J. Zhang, X. Huang, Y. Yue, J. Wang and X. Wang, “Dynamic response of graphene to thermal impulse,” Phys. Rev. B, vol. 84, no. 23, pp. 235416, 2011. DOI: 10.1103/PhysRevB.84.235416.
  • R. Quintanilla and R. Racke, “A note on stability in three-phase-lag heat conduction,” Int. J. Heat Mass Transf., vol. 51, no. 1-2, pp. 24–29, 2008. DOI: 10.1016/j.ijheatmasstransfer.2007.04.045.
  • Y. B. Li, “Finite element analysis of thermoelastic damping in contour-mode vibrations of micro- and nanoscale ring, disk, and elliptical plate resonators,” J. Vib. Acoust., vol. 132, pp. 041015, 2010.
  • N. Satish, S. Gunabal, K. Brahma Raju and S. Narendar, “Thermoelastic damping in nonlocal rod using three-phase lag heat conduction model,” J. Therm. Stresses, vol. 44, no. 8, pp. 955–969, 2021. DOI: 10.1080/01495739.2021.1915219.

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