Thermoelastic dissipation including single-phase-lagging of rectangular-cross-sectional micro/nanoring with point masses

References

• 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.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• 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. S108–S113, 2004. DOI: 10.1088/0960-1317/14/9/019.
   Web of Science ®Google Scholar
• S. J. Wong, C. H. J. Fox and S. McWilliam, “Thermoelastic damping of the in-plane vibration of thin silicon rings,” J Sound Vibr., vol. 293, no. 1-2, pp. 266–285, 2006. DOI: 10.1016/j.jsv.2005.09.037.
   Web of Science ®Google Scholar
• Y. Sun, D. Fang and A. K. Soh, “Thermoelastic damping in micro-beam resonators,” Int J Solids Struct., vol. 43, no. 10, pp. 3213–3229, 2006. DOI: 10.1016/j.ijsolstr.2005.08.011.
   Web of Science ®Google Scholar
• C. Cattaneo, “A form of heat-conduction equations which eliminates the paradox of instantaneous propagation,” Comptes Rendus, vol. 247, pp. 431, 1958.
   Google Scholar
• P. Vernotte, “Les paradoxes de la theorie continue de l'equation de la chaleur,” Compt Rendus, vol. 246, pp. 3154–3155, 1958.
   Google Scholar
• H. W. Lord and Y. Shulman, “A generalized dynamical theory of thermoelasticity,” J Mech Phy Solids, vol. 15, no. 5, pp. 299–309, 1967. DOI: 10.1016/0022-5096(67)90024-5.
   Web of Science ®Google Scholar
• Z. F. Khisaeva and M. Ostoja-Starzewski, “Thermoelastic damping in nanomechanical resonators with finite wave speeds,” J Thermal Stresses, vol. 29, no. 3, pp. 201–216, 2006. DOI: 10.1080/01495730500257490.
   Web of Science ®Google Scholar
• J. N. Sharma, “Thermoelastic damping and frequency shift in micro/nanoscale anisotropic beams,” J Thermal Stresses, vol. 34, no. 7, pp. 650–666, 2011. DOI: 10.1080/01495739.2010.550824.
   Web of Science ®Google Scholar
• Y. Heydarpour and M. M. Aghdam, “Transient analysis of rotating functionally graded truncated conical shells based on the Lord–Shulman model,” Thin-Walled Struct., vol. 104, pp. 168–184, 2016. DOI: 10.1016/j.tws.2016.03.016.
   Web of Science ®Google Scholar
• H. Zhou and P. Li, “Thermoelastic damping in micro-and nanobeam resonators with non-Fourier heat conduction,” IEEE Sensors J, vol. 17, no. 21, pp. 6966–6977, 2017. DOI: 10.1109/JSEN.2017.2754102.
   Web of Science ®Google Scholar
• H. Zhou, P. Li and Y. Fang, “Thermoelastic damping in circular cross-section micro/nanobeam resonators with single-phase-lag time,” Int J Mech Sci., vol. 142-143, pp. 583–594, 2018. DOI: 10.1016/j.ijmecsci.2018.05.024.
   Web of Science ®Google Scholar
• H. Zhou, P. Li and Y. Fang, “Single-phase-lag thermoelastic damping models for rectangular cross-sectional micro-and nano-ring resonators,” Int J Mech Sci., vol. 163, 105132, 2019. DOI: 10.1016/j.ijmecsci.2019.105132.
   Web of Science ®Google Scholar
• J. H. Kim and J. H. Kim, “Phase-lagging of the thermoelastic dissipation for a tubular shell model,” Int J Mech Sci, vol. 163, 105094, 2019. DOI: 10.1016/j.ijmecsci.2019.105094.
   Web of Science ®Google Scholar
• A. K. Kheibari, M. Jafari and M. B. Nazari, “Propagation of heat wave in composite cylinder using Cattaneo-Vernotte theory,” Int J Heat Mass Transfer, vol. 160, pp. 120208, 2020. DOI: 10.1016/j.ijheatmasstransfer.2020.120208.
   Web of Science ®Google Scholar
• C. H. J. Fox, “A simple theory for the analysis and correction of frequency splitting in slightly imperfect rings,” J Sound Vibr., vol. 142, no. 2, pp. 227–243, 1990. DOI: 10.1016/0022-460X(90)90554-D.
   Web of Science ®Google Scholar
• A. K. Rourke, S. McWilliam and C. H. J. Fox, “Multi-mode trimming of imperfect rings,” J Sound Vibr, vol. 248, no. 4, pp. 695–724, 2001. DOI: 10.1006/jsvi.2001.3811.
   Web of Science ®Google Scholar
• P. Bisegna and G. Caruso, “Frequency split and vibration localization in imperfect rings,” J Sound Vibr, vol. 306, no. 3-5, pp. 691–711, 2007. DOI: 10.1016/j.jsv.2007.06.027.
   Web of Science ®Google Scholar
• J. H. Kim, S. J. Kang and J. H. Kim, “Splitting of quality factors for micro-ring with arbitrary point masses,” J Sound Vibr, vol. 395, pp. 317–327, 2017. DOI: 10.1016/j.jsv.2017.02.030.
   Web of Science ®Google Scholar
• J. H. Kim and J. H. Kim, “Mass imperfections on a toroidal micro-ring model including thermoelastic damping,” Appl Math Model., vol. 63, pp. 405–414, 2018. DOI: 10.1016/j.apm.2018.06.006.
   Web of Science ®Google Scholar
• J. H. Kim and J. H. Kim, “Separation of Q-factors for tubular microstructure with point imperfections,” Appl Math Model., vol. 64, pp. 572–583, 2018. DOI: 10.1016/j.apm.2018.07.059.
   Web of Science ®Google Scholar
• W. Soedel and M. S. Qatu, 2005. Vibrations of shells and plates.
   Google Scholar
• M. Chester, “Second sound in solids,” Phys Rev, vol. 131, no. 5, pp. 2013–2015, 1963. DOI: 10.1103/PhysRev.131.2013.
   Web of Science ®Google Scholar