A study on high-frequency voltage-driven structural dynamics might open up new application direction for dielectric elastomer materials


Among the available electrostatic transducers, dielectric elastomer actuators (DEAs) derive their benefits from voltage-driven deformations of polymeric dielectric membranes covered by compliant electrodes, that are able to stretch when subject to a voltage. Some key advantages of DEAs include their ability to provide large deformations, large actuation energy densities and large operating bandwidths. They are also made of resilient and lightweight materials and are promising candidates for numerous applications like soft robots, or lightweight loudspeakers.

DEA systems are known to use a well-defined single actuation mode (often called the pumping mode) at low-frequency voltage input. Interestingly, complex deformation patterns have been reported in broadband voltage or high-frequency excitation by leveraging the structural dynamics of dielectric elastomer membranes. These deformation patterns and high-order mode shapes have opened possibilities for novel designs and functionalities. To date, most studies on complex structural dynamics in DEAs subjected to high-frequency excitation have focused on axial-symmetrical deformations and experimental three-dimensional analysis.

The circular out-of-plane DEA (COP-DEA) is one of the most popular and studied DEA layouts. It comprises an annular membrane connected to a biasing elastic element (e.g., a spring), which provides the membrane with an out-of-plane deformation, allowing it to expand upon excitation. Despite the extensive modeling of the static continuum response and low-frequency dynamic response of the COP-DEAs, their complex structural dynamics at higher frequencies are still poorly understood.

Herein, Dr. Giacomo Moretti, Prof. Gianluca Rizzello, Prof. Marco Fontana and Prof. Stefan Seelecke from Saarland University and Scuola Superiore Sant’Anna reported a thorough characterization of the continuum dynamic response of COP-DEAs subjected to high-frequency voltage excitation. They constructed a fully-coupled continuum model considering the influence of the acoustic pressure loads and electro-hyperelastic dynamics induced by the vibration of the DEA membrane. The vibration response for a set of silicone-based COP-DEA geometries under the influence of different pre-loads and biasing conditions were experimentally characterized using a scanning laser Doppler vibrometer. The work has been published in the journal Mechanical Systems and Signal Processing.

The research team observed that at low excitation frequency, the membrane exhibited pistonic axial motion and the biasing spring introduced resonance peaks in the response because of its structural dynamics. At high excitation frequency, however, complex mode shapes, corresponding to transversal vibrations of the membrane surface, were observed, whereas the pumping motion disappeared because of the large inertia of the biasing spring and the rigid moving frames connected to the DEA. Despite the uniform excitation and the DEA circular geometry, complex circumferential modes were detected on the membrane surface at high frequencies, as a result of inhomogeneities in the membrane thickness and the boundary conditions. The influence of such circumferential modes became increasingly small compared to that of axial-symmetrical modes as the off-plane deformation was increased.

The authors identified the natural frequencies and mode shapes of DEAs under different working conditions and the related velocity spectra over the membrane surface. The presented continuum model predicted the natural frequencies as well as the complex 3D mode shapes of the DEA dynamics, allowing an appropriate selection of design parameters to modify the natural frequency distribution. The natural frequencies were found to strongly depend on the acoustic pressure loads induced by the DEA vibrations. As a result, the continuum model was successfully validated. Moreover, a lumped-parameter reduced version of the model was presented and shown to efficiently describe the DEA forced dynamics, while requiring limited computational burden.

In summary, the authors are the first to experimentally model and characterize the vibration response and complex structural dynamics of COP-DEAs subjected to high-frequency voltage excitation. Their analysis allows the identification of the most appropriate working ranges for DEAs under different conditions. “The modelling and characterization framework presented here will guide the design of multi-function actuators that can achieve different functionalities using different vibrations modes of a same active membrane”, said Dr. Giacomo Moretti, first author of the study, in a statement to Advances in Engineering. “Among other, designing COP-DEAs with highly uncoupled pumping and structural modes will provide devices that can concurrently work as linear actuators and loudspeakers, by leveraging on a combined excitation of low-frequency pumping mode and high-frequency acoustic modes”.

A study on high-frequency voltage-driven structural dynamics might open up new application direction for dielectric elastomer materials - Advances in Engineering

Video: https://www.youtube.com/watch?v=Z9FXuHPdPdE&ab_channel=MSCA-DEtune

About the author

Dr. Giacomo Moretti, Marie-Curie research fellow at the Intelligent Material Systems Laboratory, Saarland University, Germany.

Giacomo Moretti obtained a MSc degree in Energy Engineering from the University of Pisa, Italy (2013) and a PhD in Mechanical Engineering from Scuola Sant’Anna, Pisa, Italy (2017). He has been a visiting scholar at the University of Edinburgh, UK (2016) and at the University of Trento, IT (2017-2020). Since 2020, he holds a position as Marie-Curie research fellow at the Intelligent Material Systems Laboratory, Saarland University (Germany).

Dr. Moretti’s research investigates the application of smart material transducers into mechatronic systems. During his PhD, he explored the application of electro-mechanical generators based on dielectric elastomer (DE) to convert ocean wave energy. Currently, he is the responsible of Marie-Curie European project DEtune, which aims to investigate and develop loudspeakers and acoustic devices made of DEs. In the past, he also worked on robotic artificial muscles based on electroactive and thermoactive polymers.


Moretti, G., Rizzello, G., Fontana, M., & Seelecke, S. (2022). High-frequency voltage-driven vibrations in dielectric elastomer membranesMechanical Systems and Signal Processing, 168, 108677.

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