Thermoelastic damping (TED) has been recognized as a significant mechanism of energy loss in vacuum-operated microresonators. Three-layered microbeams are common elements in many microresonators. However, only the model for TED in the three-layered microbeams with symmetric structure has been developed in the past. The first and the third layers in these beams have the same thickness and material properties. Thus, the temperature field is symmetric in these beams. In this paper, an analytical expression for TED in the asymmetric three-layered microbeams is developed in the form of an infinite series. The temperature fields in the asymmetric three-layered microbeams are asymmetric. The total damping is obtained by computing the energy dissipated in each layer. It is seen that the values for TED computed by the present model agree well with those computed by the finite-element model. The limitations of the present model are assessed. A simple model is also presented by retaining only the first term. The accuracy of the simple model is also discussed. The present model can be used to optimize the design of three-layered microbeams.

Reference

Reference
1.
Mohanty
,
P.
,
Harrington
,
D. A.
,
Ekinci
,
K. L.
,
Yang
,
Y. T.
,
Murphy
,
M. J.
, and
Roukes
,
M. L.
,
2002
, “
Intrinsic Dissipation in High-Frequency Micromechanical Resonators
,”
Phys. Rev. B
,
66
(
8
), p.
085416
.
2.
Tilmans
,
H. A. C.
,
Elwenspoek
,
M.
, and
Fluitman
,
J. H. J.
,
1992
, “
Micro Resonant Force Gauges
,”
Sens. Actuators, A
,
30
(
1–2
), pp.
35
53
.
3.
Yazdi
,
N.
,
Ayazi
,
F.
, and
Najafi
,
K.
,
1998
, “
Micromachined Inertial Sensors
,”
Proc. IEEE
,
86
(
8
), pp.
1640
1659
.
4.
Belardinelli
,
P.
,
Brocchini
,
M.
,
Demeio
,
L.
, and
Lenci
,
S.
,
2013
, “
Dynamical Characteristics of an Electrically Actuated Microbeam Under the Effects of Squeeze-Film and Thermoelastic Damping
,”
Int. J. Eng. Sci.
,
69
, pp.
16
32
.
5.
Zener
,
C.
,
1937
, “
Internal Friction in Solids—I: Theory of Internal Friction in Reeds
,”
Phys. Rev.
,
52
(
3
), pp.
230
235
.
6.
Zener
,
C.
,
1938
, “
Internal Friction in Solids—II: General Theory of Thermoelastic Internal Friction
,”
Phys. Rev.
,
53
(
1
), pp.
90
99
.
7.
Lifshitz
,
R.
, and
Roukes
,
M. L.
,
2000
, “
Thermoelastic Damping in Micro- and Nanomechanical Systems
,”
Phys. Rev. B
,
61
(
8
), pp.
5600
5609
.
8.
Wong
,
S. J.
,
Fox
,
C. H. J.
, and
McWilliam
,
S.
,
2006
, “
Thermoelastic Damping of the In-Plane Vibration of Thin Silicon Rings
,”
J. Sound Vib.
,
293
(
1
), pp.
266
285
.
9.
Li
,
P.
,
Fang
,
Y. M.
, and
Hu
,
R. F.
,
2012
, “
Thermoelastic Damping in Rectangular and Circular Microplate Resonators
,”
J. Sound Vib.
,
331
(
3
), pp.
721
733
.
10.
Nayfeh
,
A. H.
, and
Younis
,
M. I.
,
2004
, “
Modeling and Simulations of Thermoelastic Damping in Microplates
,”
J. Micromech. Microeng.
,
14
(
12
), pp.
1711
1717
.
11.
Sun
,
Y. X.
,
Fang
,
D. N.
, and
Soh
,
A. K.
,
2006
, “
Thermoelastic Damping in Micro-Beam Resonators
,”
Int. J. Solids Struct.
,
43
(
10
), pp.
3213
3229
.
12.
Pei
,
Y. C.
,
2012
, “
Thermoelastic Damping in Rotating Flexible Micro-Disk
,”
Int. J. Mech. Sci.
,
61
(
1
), pp.
52
64
.
13.
Bishop
,
J. E.
, and
Kinra
,
V. K.
,
1997
, “
Elastothermodynamic Damping in Laminated Composites
,”
Int. J. Solids Struct.
,
34
(
9
), pp.
1075
1092
.
14.
Vengallatore
,
S.
,
2005
, “
Analysis of Thermoelastic Damping in Laminated Composite Micromechanical Beam Resonators
,”
J. Micromech. Microeng.
,
15
(
12
), pp.
2398
2404
.
15.
Prabhakar
,
S.
, and
Vengallatore
,
S.
,
2007
, “
Thermoelastic Damping in Bilayered Micromechanical Beam Resonators
,”
J. Micromech. Microeng.
,
17
(
3
), pp.
532
538
.
16.
Nourmohammadi
,
Z.
,
Prabhakar
,
S.
, and
Vengallatore
,
S.
,
2013
, “
Thermoelastic Damping in Layered Microresonators: Critical Frequencies, Peak Values, and Rule of Mixture
,”
J. Microelectromech. Syst.
,
22
(
3
), pp.
747
754
.
17.
Parkus
,
H.
,
1976
,
Thermoelasticity
,
Springer-Verlag
,
New York
.
18.
Timoshenko
,
S.
,
1940
,
Theory of Plates and Shells
,
McGraw-Hill Book Company
,
New York
.
19.
Nowick
,
A. S.
, and
Berry
,
B. S.
,
1972
,
Anelastic Relaxation in Crystalline Solids
,
Academic
,
New York
.
20.
Ozisik
,
M. N.
,
1980
,
Heat Conduction
,
Wiley
,
New York
.
You do not currently have access to this content.