Page 8 - Mechanical design of microresonators _ modeling and applications

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Design at Resonance of Mechanical Microsystems

Design at Resonance of Mechanical Microsystems 7
4
3.5 ξ = 0.1
3
2.5 ξ = 0.25
X/Xst 2
1.5
ξ = 0.5
1
0.5 ξ = 1

0 1 2 3 4 5
β

Figure 1.7 Plot of the amplitude ratio versus the frequency ratio.

180
φ [d eg rees] 120 ξ = 1 ξ = 0.25 ξ = 0.5 120

60
60
ξ = 0.1
0
0 1 2 3 4 5
β
Figure 1.8 Plot of the phase angle versus the frequency ratio.

An important qualifier of mechanical microresonators is the quality
factor Q, which, for a harmonic oscillator, is defined as
2ʌU s
Q = (1.20)
U d

where U s is the energy stored and U d is the energy dissipated during
one cycle of oscillation. High quality factors indicate low losses through
damping, and definitely microresonators having quality factors as large
as possible are sought.
For a single-DOF damped system, such as the one pictured in
Fig. 1.6, the energy stored per cycle is simply

kX 2
U = 2 (1.21)
s
The energy dissipated per cycle is defined as

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