In this paper, investigations into the nonlinear asymmetric vibrations of a pressure sensor diaphragm under initial tension are presented. A comprehensive mechanics model based on a plate with in-plane tension is presented and the effect of cubic nonlinearity is studied. Specifically, the nonlinear asymmetric response is investigated when the excitation frequency is close to the natural frequency of an asymmetric mode of the plate. The obtained results show that in the presence of an internal resonance, depending on the initial tension, the response can have not only the form of a standing wave but also the form of a traveling wave. In addition, damping can be used to reduce the nonlinear effect and avoid the nonlinear interactions. The results of this work will benefit the design of diaphragm-type structures used in microscale sensors including pressure sensors.

References

1.
Matsuoka
,
Y.
,
Yamamoto
,
Y.
,
Tanabe
,
M.
,
Shimada
,
S.
,
Yamada
,
K.
,
Yaskuwa
,
A.
, and
Matsuzaka
,
H.
,
1995
, “
Low-Pressure Measurement Limits for Silicon Piezoresistive Circular Diaphragm Sensors
,”
J. Micromech. Microeng.
,
5
(1), pp.
32
35
.10.1088/0960-1317/5/1/006
2.
Pedersen
,
M.
,
Meijerink
,
M. G. H.
,
Olthuis
,
W.
, and
Bergveld
,
P.
,
1997
, “
A Capacitive Differential Pressure Sensor With Polyimide Diaphragm
,”
J. Micromech. Microeng.
,
7
(3), pp.
250
252
.10.1088/0960-1317/7/3/046
3.
Zeng
,
N.
,
Shi
,
C.
,
Wang
,
D.
,
Zhang
,
M.
, and
Liao
,
Y.
,
2003
, “
Diaphragm-Type Fiber-Optic Interferometric Acoustic Sensor
,”
Opt. Eng.
,
42
(
9
), pp.
2558
2562
.10.1117/1.1596433
4.
Cho
,
S. T.
,
Najafi
,
K.
, and
Wise
,
K. D.
,
1992
, “
Internal Stress Compensation and Scaling in Ultrasensitive Silicon Pressure Sensor
,”
IEEE Trans. Electron Devices
,
39
(
4
), pp.
836
840
.10.1109/16.127473
5.
Yu
,
M.
, and
Balachandran
,
B.
,
2005
, “
Sensor Diaphragm Under Initial Tension: Linear Analysis
,”
Exp. Mech.
,
45
(
2
), pp.
123
129
.10.1007/BF02428184
6.
Sheplak
,
M.
, and
Dugundji
,
J.
,
1998
, “
Large Deflections of Clamped Circular Plates Under Initial Tension and Transitions to Membrane Behavior
,”
ASME J. Appl. Mech.
,
65
(
1
), pp.
107
115
.10.1115/1.2789012
7.
Su
,
Y. H.
,
Chen
,
K. S.
,
Roberts
,
D. C.
, and
Spearing
,
S. M.
,
2001
, “
Large Deflection Analysis of a Pre-Stressed Annular Plate With a Rigid Boss Under Axisymmetric Loading
,”
J. Micromech. Microeng.
,
11
(6), pp.
645
653
.10.1088/0960-1317/11/6/305
8.
Yu
,
M.
,
Long
,
X.-H.
, and
Balachandran
,
B.
,
2008
, “
Sensor Diaphragm Under Initial Tension: Nonlinear Responses and Design Implications
,”
J. Sound Vib.
,
312
(1–2), pp.
39
54
.10.1016/j.jsv.2007.07.094
9.
Nayfeh
,
A. H.
, and
Balachandran
,
B.
,
1989
, “
Modal Interactions in Dynamical and Structural Systems
,”
ASME Appl. Mech. Rev.
,
42
(
11
), pp.
175
202
.10.1115/1.3152389
10.
Balachandran
,
B.
, and
Nayfeh
,
A. H.
,
1991
, “
Observations of Modal Interactions in Resonantly Forced Beam-Mass Structures
,”
Nonlinear Dyn.
,
2
(
2
), pp.
77
117
.10.1007/BF00053831
11.
Thomas
,
O.
,
Lazarus
,
A.
, and
Touzé
,
C.
,
2010
, “
A Harmonic-Based Method for Computing the Stability of Periodic Oscillations of Non-Linear Structural Systems
,”
ASME
Paper No. DETC2010-28407.10.1115/DETC2010-28407
12.
Wang
,
L.
,
Ma
,
J.
,
Li
,
L.
, and
Peng
,
J.
,
2013
, “
Three-to-One Resonant Responses of Inextensional Beams on the Elastic Foundation
,”
ASME J. Vib. Acoust.
,
135
(
1
), p.
011015
.10.1115/1.4007019
13.
Sridhar
,
S.
,
Mook
,
D. T.
, and
Nayfeh
,
A. H.
,
1978
, “
Nonlinear Resonances in the Forced Responses of Plates, Part II: Asymmetric Responses of Circular Plates
,”
J. Sound Vib.
,
59
(
2
), pp.
159
170
.10.1016/0022-460X(78)90497-2
14.
Yeo
,
M. H.
, and
Lee
,
W. K.
,
2002
, “
Corrected Solvability Conditions for Non-Linear Asymmetric Vibrations of a Circular Plate
,”
J. Sound Vib.
,
257
(
4
), pp.
653
665
.10.1006/jsvi.2002.5037
15.
Lee
,
W. K.
, and
Yeo
,
M. H.
,
2003
, “
Non-Linear Interactions in Asymmetric Vibrations of a Circular Plate
,”
J. Sound Vib.
,
263
(
5
), pp.
1017
1030
.10.1016/S0022-460X(03)00271-2
16.
Park
,
H. D.
, and
Lee
,
W. K.
,
2008
, “
Basin Boundaries in Asymmetric Vibrations of a Circular Plate
,”
J. Sound Vib.
,
315
(
3
), pp.
556
568
.10.1016/j.jsv.2007.12.030
17.
Arafat
,
H. N.
, and
Nayfeh
,
A. H.
,
2004
, “
Combination Internal Resonances in Heated Annular Plates
,”
Nonlinear Dyn.
,
37
(
4
), pp.
285
306
.10.1023/B:NODY.0000045542.48960.33
18.
Goncalves
,
P. B.
,
Soares
,
R. M.
, and
Pamplona
,
D.
,
2009
, “
Nonlinear Vibrations of a Radially Stretched Circular Hyperelastic Membrane
,”
J. Sound Vib.
,
327
(
1–2
), pp.
231
248
.10.1016/j.jsv.2009.06.023
19.
Touzé
,
C.
,
Thomas
,
O.
, and
Chaigne
,
A.
,
2002
, “
Asymmetric Non-Linear Forced Vibrations of Free-Edge Circular Plates, Part 1: Theory
,”
J. Sound Vib.
,
258
(
4
), pp.
649
676
.10.1006/jsvi.2002.5143
20.
Thomas
,
O.
,
Touzé
,
C.
, and
Chaigne
,
A.
,
2003
, “
Asymmetric Non-Linear Forced Vibrations of Free-Edge Circular Plates, Part 2: Experiments
,”
J. Sound Vib.
,
265
(
5
), pp.
1075
1101
.10.1016/S0022-460X(02)01564-X
21.
Tripathi
,
A.
, and
Bajaj
,
A. K.
,
2014
, “
Design for 1:2 Internal Resonances in In-Plane Vibrations of Plates With Hyperelastic Materials
,”
ASME J. Vib. Acoust.
,
136
(
6
), p.
061005
.10.1115/1.4028268
22.
Long
,
X.-H.
,
Yu
,
M.
, and
Balachandran
,
B.
,
2008
, “
Sensor Diaphragm Under Initial Tension: Nonlinear Interactions During Asymmetric Oscillations
,”
ASME
Paper No. IMECE2008-66821. 10.1115/IMECE2008-6682110.1115/IMECE2008-66821
23.
Thomas
,
O.
, and
Bilbao
,
S.
,
2008
, “
Geometrically Non-Linear Flexural Vibrations of Plates: In-Plane Boundary Conditions and Some Symmetry Properties
,”
J. Sound Vib.
,
315
(
3
), pp.
569
590
.10.1016/j.jsv.2008.04.014
24.
Nayfeh
,
A. H.
, and
Pai
,
P. F.
,
2004
,
Linear and Nonlinear Structural Mechanics
,
Wiley
,
New York
.
25.
Doedel
,
E. J.
,
Champneys
,
A. R.
,
Fairgrieve
,
T. F.
,
Kuznetsov
,
Y. A.
,
Sandstede
,
B.
, and
Wang
,
X.
,
1998
, “
auto97: Continuation and Bifurcation Software for Ordinary Differential Equations (With HomCont)
,” Concordia University, Montreal, Canada.
26.
Nayfeh
,
A. H.
,
2000
,
Nonlinear Interactions Analytical, Computational and Experimental Methods
,
Wiley
,
New York
.
27.
Soedel
,
W.
,
1993
,
Vibrations of Shells and Plates
,
Marcel Dekker
,
New York
.
You do not currently have access to this content.