## Abstract

Ionomeric polymers are a promising class of intelligent material which exhibit electromechanical coupling similar to that of piezoelectric bimorphs. Ionomeric polymers are much more compliant than piezoelectric ceramics or polymers and have been shown to produce actuation strain on the order of 2% at operating voltages between $1V$ and $3V$ (Akle et al., 2004, Proceedings IMECE). Their high compliance is advantageous in low force sensing configurations because ionic polymers have a very little impact on the dynamics of the measured system. Here we present a variational approach to the dynamic modeling of structures which incorporate ionic polymer materials. To demonstrate the method a cantilever beam model is developed using this variational approach. The modeling approach requires a priori knowledge of three empirically determined material properties: elastic modulus, dielectric permittivity, and effective strain coefficient. Previous work by Newbury and Leo has demonstrated that these three parameters are strongly frequency dependent in the range between less than $1Hz$ to frequencies greater than $1kHz$. Combining the frequency-dependent material parameters with the variational method produces a second-order matrix representation of the structure. The frequency dependence of the material parameters is incorporated using a complex-property approach similar to the techniques for modeling viscoelastic materials. A transducer is manufactured and the method of material characterization is applied to determine the mtaerial properties. Additional experiments are performed on this transducer and both the material and structural model are validated. Finally, the model is shown to predict sensing response very well in comparison to experimental results, which supports the use of an energy-based variational approach for modeling ionomeric polymer transducers.

1.
Akle
,
B. J.
,
Bennett
,
M. D.
, and
Leo
,
D. J.
, 2004, “
High-Strain Ionomeric-Ionic Liquid Composites via Electrode Tailoring
,”
Proceedings of IMECE 2004
, p.
61246
.
2.
Kanno
,
R.
,
Tadokoro
,
S.
,
Takamori
,
T.
, and
Hattori
,
M.
, 1996, “
Linear Approximate Dynamic Model of icpf Actuator
,”
Proceedings of IEEE International Conference on Robotics and Automation
, pp.
219
225
.
3.
Newbury
,
K. M.
, and
Leo
,
D. J.
, 2002, “
Electromechanical Modeling and Characterization of Ionic Polymer Benders
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
13
, pp.
51
60
.
4.
Newbury
,
K. M.
, and
Leo
,
D. J.
, 2003, “
Linear Electromechanical Model of Ionic Polymer Transducers Part i: Model Development
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
14
(
6
), pp.
333
342
.
5.
Franklin
,
J. W.
, 2003, “
Electromechanical Model of Encapsulated Ionic Polymer Transducers
,” Master’s thesis, Virginia Polytechnic Institute and State University, VA.
6.
Tadokoro
,
S.
,
Takamori
,
T.
, and
Oguro
,
K.
, 2001, “
Chapter 13 Modeling ipmc for Design of Actuation Mechanisms
,”
Electroactive Polymer (EAP) Actuators of Artificial Muscles
,
Y.
Bar-Cohen
, ed.,
SPIE
, Bellingham, WA, pp.
331
366
.
7.
Newbury
,
K. M.
, and
Leo
,
D. J.
, 2003, “
Linear Electromechanical Model of Ionic Polymer Transducers Part ii: Experimental Validation
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
14
(
6
), pp.
343
357
.
8.
Hagood
,
N.
,
Chung
,
W.
, and
von Flotow
,
A.
, 1990, “
Modeling of Piezoelectric Actuator Dynamics for Active Structural Control
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
1
(
3
), pp.
327
354
.
9.
Inman
,
D.
, 2001,
Engineering Vibrations
, 2nd ed.
Prentice–Hall
, Upper Saddle River, NJ.
10.
Blevins
,
R. D.
, 1995,
Formulas for Natural Frequency and Mode Shape
,
Krieger
, Malabar, FL.
11.
McTavish
,
D.
, and
Hughes
,
P. J.
, 1993, “
Modeling of Linear Viscoelastic Space Structures
,”
J. Vibr. Acoust.
0739-3717,
115
, pp.
102
110
.
12.
Gere
,
J. M.
, and
Timoshenko
,
S. P.
, 1997,
Mechanics of Materials
, 4th ed.,
PWS Publishing Company
, Boston, MA.
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