journal article·2023-09

A non-Fourier and couple stress-based model for thermoelastic dissipation in circular microplates according to complex frequency approach

Ahmad Yani, Sherzod Abdullaev, Muataz S. Alhassan, Ramaswamy Sivaraman, Abduladheem Turki Jalil

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Abstract

This research tries to render an unconventional model for thermoelastic dissipation or thermoelastic damping (TED) in circular microplates by accommodating small-scale effect into both structure and heat transfer fields. To accomplish this purpose, the modified couple stress theory (MCST) and Guyer−Krumhansl (GK) heat conduction model are utilized for providing the coupled thermoelastic equations of motion and heat conduction. The equation of heat conduction is then solved to acquire the closed-form of temperature profile in the circular microplate. By placing the extracted temperature profile in the equation of motion, the size-dependent frequency equation influenced by thermoelastic coupling is established. By conducting some mathematical manipulations, the real and imaginary parts of damped frequency are obtained. In the next stage, with the help of the description of TED based upon the complex frequency (CF) approach, an explicit single-term relation consisting of structural and thermal scale parameters is derived for making a size-dependent estimation of TED value in circular microplates. For evaluating the precision and veracity of the proposed model, the results obtained through the presented solution are compared with the ones available from the literature. In addition, by way of several examples, the pivotal role of length scale parameter of MCST and thermal nonlocal parameter of GK model in the magnitude of TED is assessed. Various numerical results are also given to place emphasis on the impact of some parameters such as boundary conditions, geometrical features, material and ambient temperature on TED value. The formulation and results provided in this study can be used as a benchmark for optimal design of microelectromechanical systems (MEMS).
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Research context

OpenAlex topics: Thermoelastic and Magnetoelastic Phenomena · Nonlocal and gradient elasticity in micro/nano structures · Numerical methods in engineering

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (57)

Show source-provided references
1. Akgöz, B., Civalek, Ö.: A microstructure-dependent sinusoidal plate model based on the strain gradient elasticity theory. Acta Mech. 226(7), 2277–2294 (2015)10.1007/s00707-015-1308-4 ↗
2. Allahkarami, F., Nikkhah-bahrami, M., Saryazdi, M.G.: Magneto-thermo-mechanical dynamic buckling analysis of a FG-CNTs-reinforced curved microbeam with different boundary conditions using strain gradient theory. Int. J. Mech. Mater. Des. 14(2), 243–261 (2018)10.1007/s10999-017-9374-5 ↗
3. Borjalilou, V., Asghari, M.: Thermoelastic damping in strain gradient microplates according to a generalized theory of thermoelasticity. J. Therm. Stresses 43(4), 401–420 (2020)10.1080/01495739.2020.1722771 ↗
4. 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. Stresses 42(7), 801–814 (2019)10.1080/01495739.2019.1590168 ↗
5. Borjalilou, V., Asghari, M., Taati, E.: Thermoelastic damping in nonlocal nanobeams considering dual-phase-lagging effect. J. Vib. Control 26(11–12), 1042–1053 (2020)10.1177/1077546319891334 ↗
6. Chang, H., Han, Z., Li, X., Ma, T., Wang, Q.: Experimental investigation on heat transfer performance based on average thermal-resistance ratio for supercritical carbon dioxide in asymmetric airfoil-fin printed circuit heat exchanger. Energy 254, 124164 (2022)10.1016/j.energy.2022.124164 ↗
7. Chong, A.C., Lam, D.C.: Strain gradient plasticity effect in indentation hardness of polymers. J. Mater. Res. 14(10), 4103–4110 (1999)10.1557/JMR.1999.0554 ↗
8. Choudhuri, S.R.: On a thermoelastic three-phase-lag model. J. Therm. Stresses 30(3), 231–238 (2007)10.1080/01495730601130919 ↗
9. Ebrahimi-Mamaghani, A., Mirtalebi, S.H., Ahmadian, M.T.: Magneto-mechanical stability of axially functionally graded supported nanotubes. Mater. Res. Expr. 6(12), 1250 (2020)
10. Eringen, A.C.: Linear theory of nonlocal elasticity and dispersion of plane waves. Int. J. Eng. Sci. 10(5), 425–435 (1972)10.1016/0020-7225(72)90050-X ↗
11. Esen, I., Abdelrahman, A.A., Eltaher, M.A.: On vibration of sigmoid/symmetric functionally graded nonlocal strain gradient nanobeams under moving load. Int. J. Mech. Mater. Des. 17(3), 721–742 (2021)10.1007/s10999-021-09555-9 ↗
12. Esfahani, S., Esmaeilzade Khadem, S., Ebrahimi Mamaghani, A.: Size-dependent nonlinear vibration of an electrostatic nanobeam actuator considering surface effects and inter-molecular interactions. Int. J. Mech. Mater. Des. 15(3), 489–505 (2019)10.1007/s10999-018-9424-7 ↗
13. Fang, Y., Li, P., Wang, Z.: Thermoelastic damping in the axisymmetric vibration of circular microplate resonators with two-dimensional heat conduction. J. Therm. Stresses 36(8), 830–850 (2013)10.1080/01495739.2013.788406 ↗
14. Farokhi, H., Ghayesh, M.H.: Size-dependent behaviour of electrically actuated microcantilever-based MEMS. Int. J. Mech. Mater. Des. 12(3), 301–315 (2016)10.1007/s10999-015-9295-0 ↗
15. Farokhi, H., Ghayesh, M.H.: Nonlinear mechanical behaviour of microshells. Int. J. Eng. Sci. 127, 127–144 (2018)10.1016/j.ijengsci.2018.02.009 ↗
16. Ge, Y., Sarkar, A.: Thermoelastic damping in vibrations of small-scaled rings with rectangular cross section by considering size effect on both structural and thermal domains. Int. J. Struct. Stability Dyn. 25, 85 (2022)
17. Ge, X., Li, P., Fang, Y., Yang, L.: Thermoelastic damping in rectangular microplate/nanoplate resonators based on modified nonlocal strain gradient theory and nonlocal heat conductive law. J. Therm. Stresses 44(6), 690–714 (2021)10.1080/01495739.2021.1906807 ↗
18. Golmakani, M.E., Malikan, M., Pour, S.G., Eremeyev, V.A.: Bending analysis of functionally graded nanoplates based on a higher-order shear deformation theory using dynamic relaxation method. Continuum Mech. Thermodyn. 8, 1–20 (2021)
19. Green, A.E., Naghdi, P.: Thermoelasticity without energy dissipation. J. Elast. 31(3), 189–208 (1993)10.1007/BF00044969 ↗
20. Gürses, M., Akgöz, B., Civalek, Ö.: Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation. Appl. Math. Comput. 219(6), 3226–3240 (2012)
21. Guyer, R.A., Krumhansl, J.A.: Solution of the linearized phonon Boltzmann equation. Phys. Rev. 148(2), 766 (1966)10.1103/PhysRev.148.766 ↗
22. Hosseini, S.M.H., Arvin, H.: Thermo-rotational buckling and post-buckling analyses of rotating functionally graded microbeams. Int. J. Mech. Mater. Des. 17(1), 55–72 (2021)10.1007/s10999-020-09509-7 ↗
23. Huang, K., Su, B., Li, T., Ke, H., Lin, M., Wang, Q.: Numerical simulation of the mixing behaviour of hot and cold fluids in the rectangular T-junction with/without an impeller. Appl. Therm. Eng. 204, 117942 (2022)10.1016/j.applthermaleng.2021.117942 ↗
24. 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)10.1016/j.ijheatmasstransfer.2019.118997 ↗
25. Kumar, H., & Mukhopadhyay, S. (2022). Size-dependent thermoelastic damping analysis in nanobeam resonators based on Eringen’s nonlocal elasticity and modified couple stress theories. Journal of Vibration and Control, 10775463211064689.10.1177/10775463211064689 ↗
26. Lam, D.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P.: Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51(8), 1477–1508 (2003)10.1016/S0022-5096(03)00053-X ↗
27. Lifshitz, R., Roukes, M.L.: Thermoelastic damping in micro-and nanomechanical systems. Phys. Rev. B 61(8), 5600 (2000)10.1103/PhysRevB.61.5600 ↗
28. Lim, C.W., Zhang, G., Reddy, J.: A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J. Mech. Phys. Solids 78, 298–313 (2015)10.1016/j.jmps.2015.02.001 ↗
29. Liu, Y., Zhou, S., Wu, K., Qi, L.: Size-dependent electromechanical responses of a bilayer piezoelectric microbeam. Int. J. Mech. Mater. Des. 16(3), 443–460 (2020)10.1007/s10999-019-09478-6 ↗
30. Liu, D., Geng, T., Wang, H., Esmaeili, S.: Analytical solution for thermoelastic oscillations of nonlocal strain gradient nanobeams with dual-phase-lag heat conduction. Mech. Based Des. Struct. Mach. 54, 1–31 (2021)
31. Liu, H., Sahmani, S., Safaei, B.: Nonlinear buckling mode transition analysis in nonlocal couple stress-based stability of FG piezoelectric nanoshells under thermo-electromechanical load. Mech. Adv. Mater. Struct. 6, 1–21 (2022)
32. Li, M., Cai, Y., Fan, R., Wang, H., Borjalilou, V.: Generalized thermoelasticity model for thermoelastic damping in asymmetric vibrations of nonlocal tubular shells. Thin-Walled Struct 174, 109142 (2022b)10.1016/j.tws.2022.109142 ↗
33. Li, P., Fang, Y., Hu, R.: Thermoelastic damping in rectangular and circular microplate resonators. J. Sound Vib. 331(3), 721–733 (2012)10.1016/j.jsv.2011.10.005 ↗
34. Li, S., Chen, S., Xiong, P.: Thermoelastic damping in functionally graded material circular micro plates. J. Therm. Stresses 41(10–12), 1396–1413 (2018)10.1080/01495739.2018.1505446 ↗
35. Li, M., Cai, Y., Bao, L., Fan, R., Zhang, H., Wang, H., Borjalilou, V.: Analytical and parametric analysis of thermoelastic damping in circular cylindrical nanoshells by capturing small-scale effect on both structure and heat conduction. Arch. Civ. Mech. Eng. 22(1), 1–16 (2022a)10.1007/s43452-021-00319-y ↗
36. Lord, H.W., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15(5), 299–309 (1967)10.1016/0022-5096(67)90024-5 ↗
37. Lu, Z.Q., Liu, W.H., Ding, H., Chen, L.Q.: Energy Transfer of an Axially Loaded Beam With a Parallel-Coupled Nonlinear Vibration Isolator. J. Vib. Acoust. 144(5), 051009 (2022)10.1115/1.4054324 ↗
38. Ma, Q., Clarke, D.R.: Size dependent hardness of silver single crystals. J. Mater. Res. 10(4), 853–863 (1995)10.1557/JMR.1995.0853 ↗
39. Melaibari, A., Daikh, A.A., Basha, M., Abdalla, A.W., Othman, R., Almitani, K.H., Eltaher, M.A.: Free vibration of FG-CNTRCs nano-plates/shells with temperature-dependent properties. Mathematics 10(4), 583 (2022)10.3390/math10040583 ↗
40. Quintanilla, R.: Moore–Gibson–Thompson thermoelasticity. Math. Mech. Solids 24(12), 4020–4031 (2019)10.1177/1081286519862007 ↗
41. Razavilar, R., Alashti, R.A., Fathi, A.: Investigation of thermoelastic damping in rectangular microplate resonator using modified couple stress theory. Int. J. Mech. Mater. Des. 12(1), 39–51 (2016)10.1007/s10999-014-9286-6 ↗
42. Sarparast, H., Alibeigloo, A., Borjalilou, V., Koochakianfard, O.: Forced and free vibrational analysis of viscoelastic nanotubes conveying fluid subjected to moving load in hygro-thermo-magnetic environments with surface effects. Arch. Civ. Mech. Eng. 22(4), 1–28 (2022)10.1007/s43452-022-00489-3 ↗
43. Shi, S., He, T., 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, 120977 (2021)10.1016/j.ijheatmasstransfer.2021.120977 ↗
44. Stölken, J.S., Evans, A.G.: A microbend test method for measuring the plasticity length scale. Acta Mater. 46(14), 5109–5115 (1998)10.1016/S1359-6454(98)00153-0 ↗
45. Tong, L.H., Wen, B., Xiang, Y., Lei, Z.X., Lim, C.W.: Elastic buckling of nanoplates based on general third-order shear deformable plate theory including both size effects and surface effects. Int. J. Mech. Mater. Des. 17(3), 521–543 (2021)10.1007/s10999-021-09545-x ↗
46. Toupin, R.A.: Theories of elasticity with couple-stress. Arch. Ration. Mech. Anal. 17(2), 85–112 (1964)10.1007/BF00253050 ↗
47. Tzou, D.Y.: Macro-to microscale heat transfer: the lagging behavior. John Wiley & Sons (2014)10.1002/9781118818275 ↗
48. Weng, W., Lu, Y., Borjalilou, V.: Size-dependent thermoelastic vibrations of Timoshenko nanobeams by taking into account dual-phase-lagging effect. Eur. Phys. J. Plus 136(7), 1–26 (2021)10.1140/epjp/s13360-021-01785-2 ↗
49. Xiao, C., Zhang, G., Hu, P., Yu, Y., Mo, Y., Borjalilou, V.: Size-dependent generalized thermoelasticity model for thermoelastic damping in circular nanoplates. Waves Random Complex Media 45, 1–21 (2021)10.1080/17455030.2021.1968538 ↗
50. Xie, L., Zhu, Y., Yin, M., Wang, Z., Ou, D., Zheng, H., Yin, G.: Self-feature-based point cloud registration method with a novel convolutional Siamese point net for optical measurement of blade profile. Mech. Syst. Signal Process. 178, 109243 (2022)10.1016/j.ymssp.2022.109243 ↗
51. Yang, F.A.C.M., Chong, A.C.M., Lam, D.C.C., Tong, P.: Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. 39(10), 2731–2743 (2002)10.1016/S0020-7683(02)00152-X ↗
52. Yin, M., Zhu, Y., Yin, G., Fu, G., & Xie, L. (2022). Deep Feature interaction network for point cloud registration, with applications to optical measurement of blade profiles.IEEE Trans. Industr. Inf.10.1109/TII.2022.3220889 ↗
53. Yu, J.N., She, C., Xu, Y.P., Esmaeili, S.: On size-dependent generalized thermoelasticity of nanobeams. Waves Random Complex Media 4, 1–30 (2022)10.1080/17455030.2021.2019351 ↗
54. Zener, C.: Internal friction in solids I Theory of internal friction in reeds. Phys. Rev. 52(3), 230 (1937)10.1103/PhysRev.52.230 ↗
55. Zhang, J., Zhang, C., Xue, Q.: Insight into energy dissipation behavior of a SDOF structure controlled by the pounding tuned mass damper system. Earthq. Eng. Struct. Dyn. 51(4), 958–973 (2022)10.1002/eqe.3599 ↗
56. Zhou, H., Li, P.: Dual-phase-lagging thermoelastic damping and frequency shift of micro/nano-ring resonators with rectangular cross-section. Thin-Walled Struct. 159, 107309 (2021)10.1016/j.tws.2020.107309 ↗
57. Zhou, H., Li, P., Fang, Y.: Single-phase-lag thermoelastic damping models for rectangular cross-sectional micro-and nano-ring resonators. Int. J. Mech. Sci. 163, 105132 (2019)10.1016/j.ijmecsci.2019.105132 ↗