Microbeam resonators are widely used due to their scientific and engineering applications. The accurate prediction of thermoelastic damping (TED) is necessary to evaluate the performance of resonators at micro- and nanoscales with less energy dissipation. This article aims to present an analytical method for analyzing TED and dynamic behavior of microbeam resonators based on the Moore–Gibson–Thompson (MGT) generalized thermoelasticity theory. The finite Fourier sine transform and Laplace transform methods are used to solve the coupled thermoelastic equations. The analytical solutions are obtained for deflection and thermal moment of beams. The vibration responses of deflection and thermal moment are established in microbeams with simply supported and isothermal boundary conditions. The responses of deflection and thermal moment in beams are analyzed by comparing the results obtained under the MGT model with the corresponding results under the Lord–Shulman (LS) and Green–Naghdi (GN-III) models. The obtained results show that the amplitudes of deflection and thermal moment are attenuated, and the vibration frequency is increased due to the effect of thermoelastic coupling. It has been observed that the amplitudes of deflection under these three models are approximately the same, while the amplitude of thermal moment under the MGT model is higher than under the GN-III model and agrees with the LS model. It has been further noticed that TED depends on the size of the beams when the thermoelastic coupling effect is considered.
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Zhang, C., Xu, G., Jiang, Q.: Analysis of the air-damping effect on a micromachined beam resonator. Math. Mech. Solids 8(3), 315–25 (2003)
Zener, C.: Internal friction in solids II. General theory of thermoelastic internal friction. Phys. Rev. 53, 90–99 (1938)
Zener, C.: Internal friction in solids. I. Theory of internal friction in reeds. Phys. Rev. 52(3), 230–235 (1937)
Berry, B.S.: Precise investigation of the theory of damping by transverse thermal currents. J. Appl. Phys. 26, 1221–1224 (1955)
Roszhardt, R.V.: The effect of thermoelastic internal friction on the Q of micromachined silicon resonators. In: IEEE Solid State Sensor and Actuator Workshop, Hilton Head Island, SC, USA, 13–16 (1990)
Lifshitz, R., Roukes, M.L.: Thermoelastic damping in micro- and nanomechanical systems. Phys. Rev. B 61, 5600–5609 (2000)
Khisaeva, Z.F., Ostoja-Starzewski, M.: Thermoelastic damping in nanomechanical resonators with finite wave speeds. J. Therm. Stress. 29, 201–216 (2006)
Green, A.E., Lindsay, K.A.: Thermoelasticity. J. Elast. 2(1), 1–7 (1972)
Green, A.E., Naghdi, P.M.: A re-examination of the base postulates of thermomechanics. Proc. R. Soc. Lond. A 432(1885), 171–194 (1991)
Green, A.E., Naghdi, P.M.: Thermoelasticity without energy dissipation. J. Elast. 31(3), 189–209 (1993)
Abbas, I.: A GN model for thermoelastic interaction in a microscale beam subjected to a moving heat source. Acta Mech. 226, 2527–2536 (2015)
Guo, F.L., Rogerson, G.A.: Thermoelastic coupling effect on a micro-machined beam machined beam resonator. Mech. Res. Commun. 30, 513–518 (2003)
Ezzat, M.A., Othman, M.I., EI-Karamany, A.S.: Electromagneto-thermoelastic plane waves with thermal relaxation in a medium of perfect conductivity. J. Therm. Stress. 24, 411–432 (2001)
Sun, Y., Fang, D., Soh, A.K.: Thermoelastic damping in micro-beam resonators. Int. J. Solids Struct. 43, 3213–3229 (2006)
Lord, H.W., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15, 299–309 (1967)
Kakhki, E.K., Hosseini, S.M., Tahani, M.: An analytical solution for thermoelastic damping in a micro-beam based on generalized theory of thermoelasticity and modified couple stress theory. App. Math. Model. 40(4), 3164–3174 (2016)
Kumar, R., Kumar, R.: Effects of phase lags on thermoelastic damping in micro-beam resonators. Int. J. Struct. Stab. Dyn. 19(09), 1971005 (2019)
Roychoudhuri, S.K.: On a thermoelastic three-phase-lag model. J. Therm. Stress. 30(3), 231–238 (2007)
Kumar, H., Mukhopadhyay, S.: Thermoelastic damping analysis for size-dependent microplate resonators utilizing the modified couple stress theory and the three-phase-lag heat conduction model. Int. J. Heat Mass Transf. 148, 118997 (2020)
Zhou, H., Li, P., Fang, Y.: Thermoelastic damping in circular cross-section micro/nanobeam resonators with single-phase-lag time. Int. J. Mech. Sci. 142, 583–94 (2018)
Sharma, J.N.: Thermoelastic damping and frequency shift in micro/nanoscale anisotropic beams. J. Therm. Stress. 34(7), 650–66 (2011)
Zhang, H., Kim, T., Choi, G., Cho, H.H.: Thermoelastic damping in micro-and nanomechanical beam resonators considering size effects. Int. J. Heat Mass Transf. 103, 783–90 (2016)
Kumar, R., Kumar, R.: A study of thermoelastic damping in micromechanical resonators under unified generalized thermoelasticity formulation. Noise Vib. World-wide 5 . 0957456519853814 (2019)
Rezazadeh, G., Vahdat, A.S., Tayefeh-rezaei, S., Cetinkaya, C.: Thermoelastic damping in a micro-beam resonator using modified couple stress theory. Acta Mech. 223, 1137–1152 (2012)
Kumar, H., Mukhopadhyay, S.: Analysis of the quality factor of micro-beam resonators based on heat conduction model with a single delay term. J. Therm. Stress. 18, 1–4 (2019)
Borjalilou, V., Asghari, M., Bagheri, E.: Small-scale thermoelastic damping in micro-beams utilizing the modified couple stress theory and the dual-phase-lag heat conduction model. J. Therm. Stress. 1, 1–4 (2019)
Bostani, M., Mohammadi, A.K.: Thermoelastic damping in microbeam resonators based on modified strain gradient elasticity and generalized thermoelasticity theories. Acta Mech. 229(1), 173–192 (2018)
Guo, F.L., Wang, G.Q., Rogerson, G.A.: Analysis of thermoelastic damping in micro-and nanomechanical resonators based on dual-phase-lagging generalized thermoelasticity theory. Int. J. Eng. Sci. 60, 59–65 (2012)
Kumar, R., Kumar, R., Kumar, H.: Effects of phase-lag on thermoelastic damping in micromechanical resonators. J. Therm. Stress. 41, 1115–1124 (2018)
Guo, F.L., Jiao, W.J., Wang, G.Q., Chen, Z.Q.: Distinctive features of thermoelastic dissipation in microbeam resonators at nanoscales. J. Therm. Stress. 39(4), 360–369 (2016)
Kumar, H., Mukhopadhyay, S.: Thermoelastic damping in micro and nano-mechanical resonators utilizing entropy generation approach and heat conduction model with a single delay term. Int. J. Mech. Sci. 165, 105211 (2020)
Quintanilla, R.: Moore–Gibson–Thompson thermoelasticity. Math. Mech. Solids 24(12), 4020–4031 (2019)
Duwel, A., Gorman, J., Weinstein, M., Borenstein, J., Ward, P.: Experimental study of thermoelastic damping in MEMS gyros. Sens. Actuators A 103, 70–75 (2003)
One of the authors (Harendra Kumar) acknowledges the full financial support from the Council of Scientific and Industrial Research (CSIR), India, to carry this work with file no.: 09/1217(0014)/2017-EMR-I.
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Kumar, H., Mukhopadhyay, S. Thermoelastic damping analysis in microbeam resonators based on Moore–Gibson–Thompson generalized thermoelasticity theory. Acta Mech 231, 3003–3015 (2020). https://doi.org/10.1007/s00707-020-02688-6
- Thermoelastic damping
- Microbeam resonators
- Generalized thermoelasticity theories
- Integral transform