Electromechanical Model of an Active Polymer Thin Circular Disk

Abstract

Ionic polymers exhibit an electromechanical response similar to a piezoelectric bender. It has been shown that material properties similar to piezoelectric properties can be used to effectively model ionic polymer devices. One proposed ionic polymer device is a circular disk fabricated from the ionic polymer material for shape and vibration control can be accomplished through electrical boundary conditions applied to the ionic polymer rather than by adding external actuators. This paper extends the formulae for natural frequencies and mode shapes of a thin disk to include quasi-piezoelectric properties and electrical boundary conditions. An electromechanical model for ionic polymers using equivalent circuit representation has been previously developed. Three materials properties, which are compatible with accepted piezoelectric actuator and transducer relationships were derived and experimentally verified. The equivalent Young’s modulus, dielectric permittivity, and the strain coefficient were found to be frequency dependant over the range 0.1 Hz to 500 Hz. In this paper the variational energy method is applied to develop a two-dimensional model of a thin electro-active polymer disk. The variational model relies on an extension of the electromechanical material properties derived for ionomeric materials. An example of a disk with simply supported geometric boundary conditions is presented and operational deflection shapes are simulated for electrical excitation between 0.1 and 500 Hz. The model predicts that the frequency dependence of the material properties will produce modal responses with both real and imaginary components, indicating the existence of travelling waves in the disk. Voltage to deflection transfer functions are also developed for several geometric boundary conditions using this model and then compared to experimental results. The model correctly predicts damped resonant frequencies as a result of the viscoelastic properties. It also accurately predicts low frequency phase lag and resonant frequencies of the electromechanical response.