Effect of stochastic fluctuations in angular velocity on the stability of two degrees-of-freedom ring-type microelectromechanical systems (MEMS) gyroscopes is investigated. The governing stochastic differential equations (SDEs) are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of largest Lyapunov exponents (LLEs) are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes has been computed to ascertain the stability behavior of the system. External noise that affect the gyroscope dynamic behavior typically results from environment factors and the nature of the system operation can be exerted on the system at any frequency range depending on the source. Hence, a parametric study is performed to assess the noise intensity stability threshold for a number of damping ratio values. The stability investigation predicts the form of threshold fluctuation intensity dependence on damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability.

References

References
1.
Ayazi
,
F.
, and
Najafi
,
K.
,
2001
, “
A HARPSS Polysilicon Vibrating Ring Gyroscope
,”
J. Microelectromech. Syst.
,
10
(
2
), pp.
169
179
.
2.
Acar
,
C.
,
Schofield
,
A. R.
,
Trusov
,
A. A.
,
Costlow
,
L. E.
, and
Shkel
,
A. M.
,
2009
, “
Environmentally Robust MEMS Vibratory Gyroscopes for Automotive Applications
,”
IEEE Sens. J.
,
9
(
12
), pp.
1895
1906
.
3.
Younis
,
M. I.
,
Jordy
,
D.
, and
Pitarresi
,
J. M.
,
2007
, “
Computationally Efficient Approaches to Characterize the Dynamic Response of Microstructures Under Mechanical Shock
,”
J. Microelectromech. Syst.
,
16
(
3
), pp.
628
638
.
4.
Zuo
,
L.
, and
Pei-Sheng
,
Z.
,
2013
, “
Energy Harvesting, Ride Comfort, and Road Handling of Regenerative Vehicle Suspensions
,”
ASME J. Vib. Acoust.
,
135
(
1
), p.
011002
.
5.
Schiehlen
,
W.
,
2006
, “
White Noise Excitation of Road Vehicle Structures
,”
Sadhana
,
31
(
4
), pp.
487
503
.
6.
Oropeza-Ramos
,
L. A.
, and
Turner
,
K. L.
,
2005
, “
Parametric Resonance Amplification in a MEMS Gyroscope
,”
IEEE Sensors
, Irvine, CA, Oct. 30–Nov. 3, p.
4
.
7.
Maluf
,
N.
, and
Williams
,
K.
,
2004
,
Introduction to Microelectromechanical Systems Engineering
,
Artech House
, Boston, MA.
8.
Asokanthan
,
S. F.
,
Ariaratnam
,
S. T.
,
Cho
,
J.
, and
Wang
,
T.
,
2006
, “
MEMS Vibratory Angular Rate Sensors: Stability Considerations for Design
,”
Struct. Control Health Monit.
,
13
(
1
), pp.
76
90
.
9.
Huang
,
S. C.
, and
Soedel
,
W.
,
1987
, “
Effects of Coriolis Acceleration on the Free and Forced In-Plane Vibrations of Rotating Rings on Elastic Foundation
,”
J. Sound Vib.
,
115
(
2
), pp.
253
274
.
10.
Eley
,
R.
,
Fox
,
C. H. J.
, and
McWilliam
,
S.
,
2000
, “
Coriolis Coupling Effects on the Vibration of Rotating Rings
,”
J. Sound Vib.
,
238
(
3
), pp.
459
480
.
11.
Yoon
,
S. W.
,
Lee
,
S.
, and
Najafi
,
K.
,
2011
, “
Vibration Sensitivity Analysis of MEMS Vibratory Ring Gyroscopes
,”
Sens. Actuators A: Phys.
,
171
(
2
), pp.
163
177
.
12.
Kammer
,
D. C.
, and
Schlack
,
A. L.
,
1987
, “
Effects of Nonconstant Spin Rate on the Vibration of a Rotating Beam
,”
ASME J. Appl. Mech.
,
54
(
2
), pp.
305
310
.
13.
Asokanthan
,
S. F.
, and
Cho
,
J.
,
2006
, “
Dynamic Stability of Ring-Based Angular Rate Sensor
,”
J. Sound Vib.
,
295
(
3–5
), pp.
571
583
.
14.
Higham
,
D. J.
,
2001
, “
An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
,”
SIAM Rev.
,
43
(
3
), pp.
525
546
.
15.
Schaffter
,
C. T.
,
2010
, “
Numerical Integration of SDEs: A Short Tutorial
,”
Swiss Federal Institute of Technology in Lausanne
(
EPFL
), Lausanne, Switzerland.
16.
Cho
,
J.
,
2009
, “
Nonlinear Instabilities in Ring-Based Vibratory Angular Rate Sensors
,”
Ph.D. thesis
, The University of Western Ontario, London, ON, Canada.
17.
Kloeden
,
P. E.
, and
Platen
,
E.
,
1999
,
Numerical Solution of Stochastic Differential Equations
,
Springer-Verlag, Berlin
.
18.
Higham
,
D. J.
, and
Kloeden
,
P. E.
,
2002
, “
MAPLE and MATLAB for Stochastic Differential Equations in Finance
,”
Programming Languages and Systems in Computational Economics and Finance
,
Nielson
,
S. B.
, ed.,
Springer
, London, UK.
19.
Kliková
,
B.
, and
Raidl
,
A.
,
2011
, “
Reconstruction of Phase Space of Dynamical Systems Using Method of Time Delay
,”
WDS'11 Proceedings of Contributed Papers—Part III: Physics
, Prague, Matfyzpress, May 31–June 3, pp.
83
87
.
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