Variational Modeling of Ionic Polymer-Based Structures

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 1 V and 3 V \citep{Akle2}. 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. 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 1 Hz to frequencies greater than 1 kHz. Combining the frequency-dependent material paramaters 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. Three structural models are developed to demonstrate this method. First a cantilever beam model is developed and the material properties of a typical polymer are experimentally determined. These properties are then used to simulate both actuation and sensing response of the transducer. The simulations compare very well to the experimental results. This validates the variational method for modeling ionic polymer structures. Next, a plate model is developed in cylindrical coordinates and simulations are performed using a variety of boundary conditions. Finally a plate model is developed in cartesian coordinates. Methods for applying non-homogenious boundary conditions are then developed and applied to the cartesian coordinate model. Simulations are then compared with experimental data. Again the simulations closely match the experiments validating the modeling method for plate models in 2 dimensions.