References
329
17. Nguyen, C.T.C.: Micromechanical resonators for oscillators and filters. IEEE Ultrason. Symp.
489–499 (1995)
18. Wang, K., Nguyen, C.T.C.: High-order medium frequency micromechanical electronic filters.
J. Microelectromech. Syst. 8(4), 534–557 (1999)
19. Lepage, S.: Thermoelastic Damping in Vibrating Beam Accelerometer: A New Thermoelastic
Finite Element Approach. Incaneus, Toulouse (2006)
20. Mestrom, R.M.C., Fey, R.H.B., Phan, K.L., Nijmeijer, H.: Simulations and experiments of
hardening and softening resonances in a clamped-clamped beam MEMS resonator. Sens.
Actuator A: Phys. 162(2), 225–234 (2010)
21. Rezazadeh, G., Tahmasebi, A., Zubstov, M.: Application of piezoelectric layers in electrostatic
MEM actuators: controlling of pull-in voltage. Microsyst. Technol. 12(12), 1163–1170 (2006)
22. Sadeghian, H., Rezazadeh, G., Osterberg, P.M.: Application of the generalized differential
quadrature method to the study of pull-in phenomena of MEMS switches. J. Microelectromech. Syst. 16(6), 1334–1340 (2007)
23. Sadeghian, H., Rezazadeh, G.: Comparison of generalized differential quadrature and Galerkin
methods for the analysis of micro-electro-mechanical coupled systems. Commun. Nonlinear
Sci. Num. Simul. 14(6), 2807–2816 (2009)
24. Vahdat, A.S., Rezazadeh, G.: Effect of axial and residual stresses on thermoelastic damping
in capacitive micro-beam resonators. J. Franklin Inst. 348, 622–639 (2011)
25. Kim, S.B., Kim, J.H.: Quality factors for the nano-mechanical tubes with thermoelastic damping and initial stress. J. Sound Vibr. 330, 1393–1402 (2011)
26. Evoy, S., Oikhovets, A., Sekaric, L., Parpia, J.M., Craighead, H.G., Carr, D.W.: Temperaturedependent internal friction in silicon nano-electromechanical systems. Appl. Phys. Lett. 77,
2397–2399 (2000)
27. Zener, C.: Internal friction in solids I. Theory of internal friction in reeds. Phys. Rev. 52(3),
230–235 (1937)
28. Zener, C., Otis, W., Nuckolls, R.: Internal friction in solids III. Experimental demonstration
of thermoelastic internal friction. Phys. Rev. 53(1), 100–101 (1938)
29. Landau, L.D., Lifshitz, E.M.: Theory of Elasticity. Pergamon Press, Oxford (1959)
30. Nayfeh, A.H., Younis, M.I.: Modeling and simulations of thermoelastic damping in
microplates. J. Micromech. Microeng. 14, 1711–1717 (2004)
31. Sun, Y., Saka, M.: Vibrations of microscale circular plates induced by ultra-fast lasers. Int. J.
Mech. Sci. 50(9), 1365–1371 (2008)
32. Sun, Y., Tohmyoh, H.: Thermoelastic damping of the axisymmetric vibration of circular plate
resonators. J. Sound Vibr. 319, 392–405 (2009)
33. Sun, Y., Saka, M.: Thermoelastic damping in micro-scale circular plate resonators. J. Sound
Vibr. 329, 328–337 (2010)
34. Sharma, J.N., Sharma, R.: Damping in micro-scale generalized thermoelastic circular plate
resonators. Ultrason 51, 352–358 (2011)
35. Srinivasa, A.R., Reddy, J.N.: A model for a constrained, finitely deforming, elastic solid with
rotation gradient dependent strain energy, and its specialization to von Kármán plates and
beams. J. Mech. Phys. Sol. 61(3), 873–885 (2013)
36. Berry, B.S.: Precise investigation of the theory of damping by transverse thermal currents. J.
Appl. Phys. 26(10), 1221–1224 (1955)
37. Zhang, W., Turner, K.L.: Thermoelastic damping in the longitudinal vibration: analysis and
simulation. IMECE 145–149 (2004)
38. Vengallator, S.: Analysis of thermoelastic damping in laminated composite micromechanical
beam resonators. J. Micromech. Microeng. 15, 2398–2404 (2005)
39. Prabhakar, S., Vengallatore, S.: Thermoelastic damping in bilayered micromechanical beam
resonators. J. Micromech. Microeng. 17, 532–538 (2007)
40. Yi, Y.B.: Geometric effects on thermoelastic damping in MEMS resonators. J. Sound Vib.
309, 588–599 (2008)
41. Hajnayeb, A., Khadem, S.E., Zamanian, M.: Thermoelastic damping of a double-walled
carbon nanotube under electrostatic force. Micro. Nano Lett. 6(8), 698–703 (2011)
329
17. Nguyen, C.T.C.: Micromechanical resonators for oscillators and filters. IEEE Ultrason. Symp.
489–499 (1995)
18. Wang, K., Nguyen, C.T.C.: High-order medium frequency micromechanical electronic filters.
J. Microelectromech. Syst. 8(4), 534–557 (1999)
19. Lepage, S.: Thermoelastic Damping in Vibrating Beam Accelerometer: A New Thermoelastic
Finite Element Approach. Incaneus, Toulouse (2006)
20. Mestrom, R.M.C., Fey, R.H.B., Phan, K.L., Nijmeijer, H.: Simulations and experiments of
hardening and softening resonances in a clamped-clamped beam MEMS resonator. Sens.
Actuator A: Phys. 162(2), 225–234 (2010)
21. Rezazadeh, G., Tahmasebi, A., Zubstov, M.: Application of piezoelectric layers in electrostatic
MEM actuators: controlling of pull-in voltage. Microsyst. Technol. 12(12), 1163–1170 (2006)
22. Sadeghian, H., Rezazadeh, G., Osterberg, P.M.: Application of the generalized differential
quadrature method to the study of pull-in phenomena of MEMS switches. J. Microelectromech. Syst. 16(6), 1334–1340 (2007)
23. Sadeghian, H., Rezazadeh, G.: Comparison of generalized differential quadrature and Galerkin
methods for the analysis of micro-electro-mechanical coupled systems. Commun. Nonlinear
Sci. Num. Simul. 14(6), 2807–2816 (2009)
24. Vahdat, A.S., Rezazadeh, G.: Effect of axial and residual stresses on thermoelastic damping
in capacitive micro-beam resonators. J. Franklin Inst. 348, 622–639 (2011)
25. Kim, S.B., Kim, J.H.: Quality factors for the nano-mechanical tubes with thermoelastic damping and initial stress. J. Sound Vibr. 330, 1393–1402 (2011)
26. Evoy, S., Oikhovets, A., Sekaric, L., Parpia, J.M., Craighead, H.G., Carr, D.W.: Temperaturedependent internal friction in silicon nano-electromechanical systems. Appl. Phys. Lett. 77,
2397–2399 (2000)
27. Zener, C.: Internal friction in solids I. Theory of internal friction in reeds. Phys. Rev. 52(3),
230–235 (1937)
28. Zener, C., Otis, W., Nuckolls, R.: Internal friction in solids III. Experimental demonstration
of thermoelastic internal friction. Phys. Rev. 53(1), 100–101 (1938)
29. Landau, L.D., Lifshitz, E.M.: Theory of Elasticity. Pergamon Press, Oxford (1959)
30. Nayfeh, A.H., Younis, M.I.: Modeling and simulations of thermoelastic damping in
microplates. J. Micromech. Microeng. 14, 1711–1717 (2004)
31. Sun, Y., Saka, M.: Vibrations of microscale circular plates induced by ultra-fast lasers. Int. J.
Mech. Sci. 50(9), 1365–1371 (2008)
32. Sun, Y., Tohmyoh, H.: Thermoelastic damping of the axisymmetric vibration of circular plate
resonators. J. Sound Vibr. 319, 392–405 (2009)
33. Sun, Y., Saka, M.: Thermoelastic damping in micro-scale circular plate resonators. J. Sound
Vibr. 329, 328–337 (2010)
34. Sharma, J.N., Sharma, R.: Damping in micro-scale generalized thermoelastic circular plate
resonators. Ultrason 51, 352–358 (2011)
35. Srinivasa, A.R., Reddy, J.N.: A model for a constrained, finitely deforming, elastic solid with
rotation gradient dependent strain energy, and its specialization to von Kármán plates and
beams. J. Mech. Phys. Sol. 61(3), 873–885 (2013)
36. Berry, B.S.: Precise investigation of the theory of damping by transverse thermal currents. J.
Appl. Phys. 26(10), 1221–1224 (1955)
37. Zhang, W., Turner, K.L.: Thermoelastic damping in the longitudinal vibration: analysis and
simulation. IMECE 145–149 (2004)
38. Vengallator, S.: Analysis of thermoelastic damping in laminated composite micromechanical
beam resonators. J. Micromech. Microeng. 15, 2398–2404 (2005)
39. Prabhakar, S., Vengallatore, S.: Thermoelastic damping in bilayered micromechanical beam
resonators. J. Micromech. Microeng. 17, 532–538 (2007)
40. Yi, Y.B.: Geometric effects on thermoelastic damping in MEMS resonators. J. Sound Vib.
309, 588–599 (2008)
41. Hajnayeb, A., Khadem, S.E., Zamanian, M.: Thermoelastic damping of a double-walled
carbon nanotube under electrostatic force. Micro. Nano Lett. 6(8), 698–703 (2011)