Investigation on thermoelastic damping of micro-plate resonators based on the modified couple stress theory incorporating the memory-dependent derivative heat transfer model

Guobin Zhao; Tianhu He

doi:10.1007/s00419-023-02450-z

journal article May 29, 2023

Investigation on thermoelastic damping of micro-plate resonators based on the modified couple stress theory incorporating the memory-dependent derivative heat transfer model

Guobin Zhao Tianhu He

Archive of Applied Mechanics Vol. 93 No. 9 pp. 3495-3509 · Springer Science and Business Media LLC

View at Publisher Save 10.1007/s00419-023-02450-z

Topics

No keywords indexed for this article. Browse by subject →

References

47

[1]

Li, X., Bhushan, B., Takashima, K., Baek, C.W., Kim, Y.K.: Mechanical characterization of micro/nanoscale structures for MEMS/NEMS applications using nanoindentation techniques. Ultramicroscopy 97(1), 481–494 (2003) 10.1016/s0304-3991(03)00077-9

[2]

Eom, K., Kwon, T.Y., Yoon, D.S., Lee, H.L., Kim, T.S.: Dynamical response of nanomechanical resonators to biomolecular interactions. Phys. Rev. B Condens. Matter 76(11), 113408 (2007) 10.1103/physrevb.76.113408

[3]

Lee, I., Lee, J.: Measurement uncertainties in resonant characteristics of MEMS resonators. J. Mech. Sci. Technol. 27(2), 491 (2013) 10.1007/s12206-012-1269-7

[4]

Pelesko, J.A., Bernstein, D.H.: Modeling Mems and Nems. CRC Press, Boca Raton (2002) 10.1201/9781420035292

[5]

Ciminelli, C., Dell’Olio, F., Armenise, M.N.: High-Q spiral resonator for optical gyroscope applications: numerical and experimental investigation. IEEE Photonics J. 4(5), 1844–1854 (2012) 10.1109/jphot.2012.2218098

[6]

Lin, L.W., Howe, R.T., Pisano, A.P.: Microelectromechanical filters for signal processing. Micro Electron. Mech. Syst. 7(3), 286–294 (1992) 10.1109/84.709645

[7]

Ekinci, K.L., Roukes, M.L.: Nanoelectromechanical systems. Science 76(6), 25–30 (2005)

[8]

Beek, J.V., Puers, R.: A review of MEMS oscillators for frequency reference and timing applications. J. Micromech. Microeng. 22(1), 013001 (2012) 10.1088/0960-1317/22/1/013001

[9]

Duwel, A., Gorman, J., Weinstein, M., Borenstein, J., Ward, P.: Experimental study of thermoelastic damping in MEMS gyros. Sensors Actuators A Phys. 15(1), 70–75 (2003) 10.1016/s0924-4247(02)00318-7

[10]

Zener, C.: Internal friction in solids II: general theory of thermoelastic internal friction. Phys. Today 47(2), 117–118 (1938)

[11]

Thermoelastic damping in micro- and nanomechanical systems

Ron Lifshitz, M. L. Roukes

Physical Review B 2000 10.1103/physrevb.61.5600

[12]

Nayfeh, A.H., Younis, M.I.: Modeling and simulations of thermoelastic damping in microplates. J. Micromech. Microeng. 14(12), 1711–1717 (2004) 10.1088/0960-1317/14/12/016

[13]

Sun, Y.X., Saka, M.: Thermoelastic damping in micro-scale circular plate resonators. J. Sound Vib. 329(3), 328–337 (2010) 10.1016/j.jsv.2009.09.014

[14]

Fang, Y.M., Li, P., Wang, Z.: Thermoelastic damping in the axisymmetric vibration of circular microplate resonators with two-dimensional heat conduction. J. Therm. Stress. 36(8), 830–850 (2013) 10.1080/01495739.2013.788406

[15]

Fang, Y.M., Li, P., Zhou, H.Y.: Thermoelastic damping in rectangular microplate resonators with three-dimensional heat conduction. Int. J. Mech. Sci. 133, 578–589 (2017) 10.1016/j.ijmecsci.2017.09.012

[16]

Zuo, W.L., Li, P., Zhang, J.R.: Analytical modeling of thermoelastic damping in bilayered microplate resonators. Int. J. Mech. Sci. 106, 128–137 (2016) 10.1016/j.ijmecsci.2015.12.009

[17]

Eringen, A.C.: Nonlocal Continuum Field Theories. Springer, New York (2002)

[18]

Aifantis, E.C.: Gradient deformation models at nano, micro, and macro scales. J. Eng. Mater. Technol. 121(2), 189–202 (1999) 10.1115/1.2812366

[19]

Couple stress based strain gradient theory for elasticity

F. Yang, A.C.M. Chong, D.C.C. Lam et al.

International Journal of Solids and Structures 2002 10.1016/s0020-7683(02)00152-x

[20]

Tsiatas, G.C.: A new Kirchhoff plate model based on a modified couple stress theory. Int. J. Solids Struct. 46(13), 2757–2764 (2009) 10.1016/j.ijsolstr.2009.03.004

[21]

Zhong, Z.Y., Zhang, W.M., Meng, G., Wang, M.Y.: Thermoelastic damping in the size-dependent microplate resonators based on modified couple stress theory. J. Microelectromech. Syst. 24(2), 431–445 (2015) 10.1109/jmems.2014.2332757

[22]

Segovia, F.J., Piazza, G.: Analytical and numerical methods to model anchor losses in 65-MHz AlN contour mode resonators. J. Microelectromech. Syst. 25, 459–468 (2016) 10.1109/jmems.2016.2539224

[23]

Maxwell, J.C.: On the dynamical theory of gases. Phil. Mag. 157, 49–88 (1972)

[24]

Cattaneo, C.: A form of heat conduction equation which eliminates the paradox of instantaneous propagation. C. R. Phys. 247, 431–433 (1958)

[25]

Vernotte, P.M., Hebd, C.R.: Paradoxes in the continuous theory of the heat conduction. C. R. Phys. 246, 3154–3155 (1958)

[26]

Tzou, D.Y.: A unified field approach for heat conduction from macro-to-micro-scales. J. Heat Transf. 117(1), 8–16 (1995) 10.1115/1.2822329

[27]

Choudhuri, S.K.: On a thermoelastic three-phase-lag model. J. Therm. Stress. 30(3), 231–238 (2007) 10.1080/01495730601130919

[28]

A generalized dynamical theory of thermoelasticity

H.W. Lord, Y. Shulman

Journal of the Mechanics and Physics of Solids 2007 10.1016/0022-5096(67)90024-5

[29]

Green, A.E., Lindsay, K.A.: Thermoelasticity. J. Elast. 2(1), 1–7 (1972) 10.1007/bf00045689

[30]

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) 10.1016/j.ijengsci.2014.04.014

[31]

Zhou, H.Y., Li, P.: Thermoelastic damping in micro-and nanobeam resonators with non-Fourier heat conduction. IEEE Sens. J. 17(21), 6966–6977 (2017) 10.1109/jsen.2017.2754102

[32]

Guo, X., Yi, Y.B., Pourkamali, S.: A finite element analysis of thermoelastic damping in vented MEMS beam resonators. Int. J. Mech. Sci. 74, 73–82 (2013) 10.1016/j.ijmecsci.2013.04.013

[33]

Three-dimensional thermoelastic damping models for rectangular micro/nanoplate resonators with nonlocal-single-phase-lagging effect of heat conduction

Hongyue Zhou, Dongfang Shao, Xiangrong Song et al.

International Journal of Heat and Mass Transfer 2022 10.1016/j.ijheatmasstransfer.2022.123271

[34]

Wang, Y.W., Chen, J., Zheng, R.Y., Li, X.F.: Thermoelastic damping in circular microplate resonators based on fractional dual-phase-lag model and couple stress theory. Int. J. Heat Mass Transf. 201, 123570 (2023) 10.1016/j.ijheatmasstransfer.2022.123570

[35]

Small-scale thermoelastic damping in micro-beams utilizing the modified couple stress theory and the dual-phase-lag heat conduction model

Vahid Borjalilou, Mohsen Asghari, Emadoddin Bagheri

Journal of Thermal Stresses 2019 10.1080/01495739.2019.1590168

[36]

Analysis of size effects on thermoelastic damping in the Kirchhoff’s plate resonator under Moore–Gibson–Thompson thermoelasticity

Bhagwan Singh, Harendra Kumar, Santwana Mukhopadhyay

Thin-Walled Structures 2022 10.1016/j.tws.2022.109793

[37]

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. Appl. Math. Model. 40(4), 3164–3174 (2016) 10.1016/j.apm.2015.10.019

[38]

Thermoelastic damping analysis in micro-beam resonators considering nonlocal strain gradient based on dual-phase-lag model

Bingdong Gu, Tianhu He, Yongbin Ma

International Journal of Heat and Mass Transfer 2021 10.1016/j.ijheatmasstransfer.2021.121771

[39]

Stephen, T.: Theory of Plates and Shells. McGraw-Hill, New York (1959)

[40]

Dym, C.L., Shames, I.H.: Solid mechanics: a variational approach. Heidelberg Dordrecht, London (1980)

[41]

Li, P., Fang, Y.M., Hu, R.F.: Thermoelastic damping in rectangular and circular microplate resonators. J. Sound Vib. 331(3), 721–733 (2012) 10.1016/j.jsv.2011.10.005

[42]

Zhong, Z.Y., Zhang, W.M., Meng, G.: Thermoelastic damping in the size-dependent microplate resonators based on modified couple stress theory. J. Microelectromech. Syst. 24(2), 431–445 (2015) 10.1109/jmems.2014.2332757

[43]

Chakraverty, S., Pradhan, K.K.: Free vibration of functionally graded thin rectangular plates resting on Winkler elastic foundation with general boundary conditions using Rayleigh–Ritz method. Int. J. Appl. Mech. 6(4), 1450043 (2014) 10.1142/s1758825114500434

[44]

Shi, S.H., He, T.H., Jin, F.: Thermoelastic damping analysis of size-dependent nano-resonators considering dual-phase-lag heat conduction model and surface effect. Int. J. Heat Mass Transf. 170(6), 120977 (2021) 10.1016/j.ijheatmasstransfer.2021.120977

[45]

Small-scale analysis of plates with thermoelastic damping based on the modified couple stress theory and the dual-phase-lag heat conduction model

Vahid Borjalilou, Mohsen Asghari

Acta Mechanica 2018 10.1007/s00707-018-2197-0

[46]

Babaei, A., Noorani, M.S., Ghanbari, A.: Temperature-dependent free vibration analysis of functionally graded micro-beams based on the modified couple stress theory. Microsyst Technol 23, 4599–4610 (2017) 10.1007/s00542-017-3285-0

[47]

Babaei, A., Rahmani, A.: On dynamic-vibration analysis of temperature-dependent Timoshenko microbeam possessing mutable nonclassical length scale parameter. Mech. Adv. Mater. Struct. 27(16), 1451–1458 (2020) 10.1080/15376494.2018.1516252

Metrics

10

Citations

47

References

Details

Published: May 29, 2023
Vol/Issue: 93(9)
Pages: 3495-3509
License: View

Authors

Funding

the National Natural Science Foundation of China Award: 11972176

Cite This Article

Guobin Zhao, Tianhu He (2023). Investigation on thermoelastic damping of micro-plate resonators based on the modified couple stress theory incorporating the memory-dependent derivative heat transfer model. Archive of Applied Mechanics, 93(9), 3495-3509. https://doi.org/10.1007/s00419-023-02450-z

Investigation on thermoelastic damping of micro-plate resonators based on the modified couple stress theory incorporating the memory-dependent derivative heat transfer model

You May Also Like