Inverse Nonlinearity Compensation of Hyperelastic Deformation in Dielectric Elastomer for Acoustic Actuation

Abstract

This paper presents an in-depth examination of the nonlinear deformation induced by dielectric actuation in pre-stressed ideal dielectric elastomers. A nonlinear ordinary differential equation that governs this deformation is formulated based on the hyperelastic model under dielectric stress. By means of numerical integration and neural network approximations, the relationship between voltage and stretch is established. Neural networks are utilized to approximate solutions for voltage-to-stretch and stretch-to-voltage transformations obtained via an explicit Runge-Kutta method. The efficacy of these approximations is illustrated by their use in compensating for nonlinearity through the waveshaping of the input signal. The comparative analysis demonstrates that the approximated solutions are more accurate than baseline methods, resulting in reduced harmonic distortions when dielectric elastomers are used as acoustic actuators. This study highlights the effectiveness of the proposed approach in mitigating nonlinearities and enhancing the performance of dielectric elastomers in acoustic actuation applications.

Figures (11)

• Figure 1: Overview of the system.
• Figure 2: Schematic diagram of dielectric system cross-section. (a) Reference state where no external force is applied. (b) Deformed state with equi-biaxial tension.
• Figure 3: Voltage-stretch curve obtained using RK45. The voltage-to-stretch $f$ curves are plotted in solid lines and the stretch-to-voltage $f^\dagger$ curves are plotted in dotted lines. Colors distinguish variations in $T$, $R$, and $\tau_r$.
• Figure 4: Example illustration of a multi-layer perceptron. Each bundle of arrows represents a linear transformation, and the nodes in each layer represent pointwise nonlinearities.
• Figure 5: Illustration of training processes. Modules where there are no trainable parameters or where parameters are not updated are marked with dashed lines. Red solid lines indicate the gradient back-propagation through the measurement of losses. Please note that $g_\theta$ can also be trained through a standard training process by measuring the loss between $V$ and $\alpha\cdot\hat{x}$.