Investigation of thermoelastic damping in rectangular microplate resonator using modified couple stress theory
Source abstract
Abstract
Thermoelastic damping is a significant energy lost mechanism at room temperature in micro-scale resonators. Prediction of thermoelastic damping (TED) is crucial in the design of high quality MEMS resonators. In this study the governing equations of motion and the thermal couple equation of a microplate with an arbitrary rectangular shape are derived using the modified version of the couple stress theory. Analytical expressions are presented for calculating the quality factor (QF) of TED in a rectangular microplate considering the plane stress and plane strain conditions. As a case study, a rectangular microplate resonator is considered with material property of gold that has a considerably high value of length-scale parameter in comparison with silicon and the effect of the length-scale parameter on the QF of TED is discussed in detail. The relation between QF and temperature increment for microplates with clamped boundary conditions based on plane stress and plane strain models are studied and results obtained by considering classical and modified couple stress theory (MCST) are compared. The effect of thickness of the plate on the rigidity ratio is studied and the critical thickness which is an important design parameter is obtained using the MCST for three boundary conditions. Variations of TED versus the plate thickness for various boundary conditions according to the classical and the modified couple stress theories are investigated.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Thermoelastic and Magnetoelastic Phenomena · Nonlocal and gradient elasticity in micro/nano structures · Composite Structure Analysis and Optimization
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (22)
Show source-provided references
1. Ahangar, S., Rezazadeh, G., Shabani, R., Ahmadi, G., Toloei, A.: On the stability of a microbeam conveying fluid considering modified couple stress theory. Int. J. Mech. Mater. Des. 7, 327–342 (2011)10.1007/s10999-011-9171-5 ↗
2. Altan, B.S., Aifantis, E.C.: On the structure of the mode III crack-tip in gradient elasticity. Scr. Metall. 26, 319–324 (1992)10.1016/0956-716X(92)90194-J ↗
3. Duwel, A., Gorman, J., Weinstein, M., Borenstein, J., Warp, P.: Experimental study of thermoelastic damping in MEMS gyros. Sens. Actuators A 103, 70–75 (2003)10.1016/S0924-4247(02)00318-7 ↗
4. Evoy, S., Oikhovets, A., Sekaric, L., Parpia, J.M., Craighead, H.G., Carr, D.W.: Temperature-dependent internal friction in silicon nano-electromechanical systems. Appl. Phys. Lett. 77, 2397–2399 (2000)10.1063/1.1316071 ↗
5. Feng, J.T., Zhao, Y.P.: Influence of different amount of Au on the wetting behavior of PDMS membrane. Biomed. Microdevices 10(1), 65–72 (2008)10.1007/s10544-007-9110-2 ↗
6. Landau, L.D., Lifshitz, E.M.: Theory of Elasticity. Pergamon Press, Oxford (1959)
7. Leissa, A.W.: Vibration of Plates. NASA, Washington (1969)
8. Lifshitz, R., Roukes, M.L.: Thermoelastic damping in micro-and nano-mechanical systems. Phys. Rev. B 61, 5600–5609 (2000)10.1103/PhysRevB.61.5600 ↗
9. Nayfeh, A., Younis, M.I.: Modeling and simulations of thermoelastic damping in Microplates. J. Micromech. Microeng. 14, 1711–1717 (2004)10.1088/0960-1317/14/12/016 ↗
10. Park, S.K., Gao, X.L.: Variational formulation of a modified couple stress theory and its application to a simple shear problem. Z. Angew. Math. Phys. 59, 904–917 (2008)10.1007/s00033-006-6073-8 ↗
11. Rezazadeh, G., Saeedivahdat, A.S., Pesteii, S.M., Farzi, B.: Study of thermoelastic damping in capacitive micro-beam resonators using hyperbolic heat conduction model. Sens. Transducers J. 108(9), 54–72 (2009)
12. Rezazadeh, G., Saeedivahdat, 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)10.1007/s00707-012-0622-3 ↗
13. Sadd, M.H.: Elasticity Theory Application and Numerics. Elsevier Inc, Amsterdam (2009)
14. Saeedivahdat, A.S., Rezazadeh, G., Ahmadi, G.: Thermoelastic damping in a microbeam resonator tunable with piezoelectric layers. Acta Mech. Solida Sin. 25(1), 73–81 (2012)10.1016/S0894-9166(12)60008-1 ↗
15. Sharma, J.N., Sharma, R.: Damping in micro-scale generalized thermoelastic circular plate resonators. Ultrasonics 51, 352–358 (2011)10.1016/j.ultras.2010.10.009 ↗
16. Sun, Y.X., Tohmyoh, H.: Thermoelastic damping of the axisymmetric vibration of circular plate resonators. J. Sound Vib. 319, 392–405 (2009)10.1016/j.jsv.2008.06.017 ↗
17. Tsiatas, G.C.: A new Kirchhoff plate model based on a modified couple stress Theory. Int. J. Solids Struct. 46, 2757–2764 (2009)10.1016/j.ijsolstr.2009.03.004 ↗
18. Voyiadjis, G.Z., Abu Al-Rub, R.K.: Gradient plasticity theory with a variable length scale parameter. Int. J. Solids Struct. 42, 3998–4029 (2005)10.1016/j.ijsolstr.2004.12.010 ↗
19. Yang, F., Chong, A.C.M., Lam, D.C.C., Tong, P.: Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. 39, 2731–2743 (2002)10.1016/S0020-7683(02)00152-X ↗
20. Yasumura, K.Y., Stowe, T.D., Chow, E.M., et al.: Quality factors in micron- and submicron- thick cantilevers. J. Microelectromech. Syst. 9, 117–125 (2000)10.1109/84.825786 ↗
21. Zener, C.: Internal friction in solids I. Theory of internal friction in reeds. Phys. Rev. 52, 230–235 (1937)10.1103/PhysRev.52.230 ↗
22. Zener, C.: Internal friction in solids II. General theory of thermoelastic internal friction. Phys. Rev. 53, 90–99 (1938)10.1103/PhysRev.53.90 ↗