Dielectric Elastomer Membrane Research Articles

Robust output regulation of a class of smart actuators described by a minimum phase LPV dynamics

This paper presents a new control strategy for a class of minimum phase linear parameter-varying (LPV) systems representative of smart material actuators. In position control applications of such devices, one is typically interested in achieving output regulation with an arbitrary exponential decay rate. In principle, this problem can be tackled by assigning an exponential decay rate to the full system state, by means of well-established linear matrix inequalities (LMI) methods. For the class of systems under investigation, however, this approach leads to excessively large controller gains in case the desired decay rate is faster than the open-loop zero dynamics. In addition, the existence of unmeasurable state variables related to the material microstructure makes it not possible to directly implement full state feedback laws which are commonly adopted in LPV theory. To overcome these issues, a new design strategy is proposed. The key idea relies on arbitrarily shaping the output exponential decay rate without requiring fast convergence of the full state vector. This goal is achieved by means of a partial state feedback control law which solely depends on the measurable system states. A LMI algorithm is also developed to systematically address the design of the partial state feedback controller. The method is validated by means of simulations on generic examples, as well as via experiments on a mechatronic positioning system based on a dielectric elastomer membrane. In case the desired output convergence speed is faster than the open-loop zero dynamics, it is shown that the new approach leads to better transient behaviors and significantly smaller controller gains than standard LPV design techniques.

Vibration investigation of conical dielectric elastomer thin membrane for energy harvesting system

The dielectric elastomer (DE) has promising application prospects in many fields such as biomedicine, human-machine interface, soft robots, and energy harvesting. In present study, the conical energy harvesting structure is investigated and the DE is viewed as the hyperelastic neo-Hookean model. Considering the rotation and the tension of the DE membrane, the dynamic model of the conical DE thin membrane, i.e. mass-spring system is established based on the Euler-Lagrange method. The experiment is carried out to validate the output voltage of the conical thin membrane. The effects of excitation frequency, geometry size of the conical DE membrane, stiffness of the spring, pre-stretching on the resonance frequency, displacement amplitude and failed region are fully studied. The results demonstrate that the geometric size of the conical DE membrane greatly affects the resonance frequency and the amplitude. The principal resonance frequency of the quasi pointed conical DE structure is greater than the frustum conical DE structure, and the principal frequency of the quasi cylindrical conical DE structure is the lowest. The experiment result fits very well with the theoretical result for the output voltage. These findings can provide beneficial guidance for the design of the energy harvesting structures of high efficiency.

Low-voltage dielectric elastomer actuators by electro-mechanical resonance syntonization

Generally, a serious practical limitation of dielectric elastomer (DE)-based capacitors is the need for high voltage supply (in the order of 1 kV) to activate them. High voltages require a power level that is currently challenging due to the limit in the operating range of existing function generators. These high voltages are also dangerous for humans, thereby overshadowing many applications of dielectric elastomers. The purpose of this work is to develop a new simple actuation technique to introduce low-voltage driven DE-based capacitors, in which the electrical resonant frequency is syntonized to the mechanical natural frequency by tuning the circuit inductance. This results in extensive voltage amplification across the DE capacitor. In turn, this leads the DE membrane to oscillate with a remarkable large motion using a small voltage which is of one-tenth the magnitude of the input voltage required to drive such systems in the absence of electro-mechanical (EM) resonance syntonization. The efficiency of the proposed approach is demonstrated in the context of nonlinear vibration analysis. The results show that the voltage amplitude across the DE capacitor is amplified substantially while the electrical mode is syntonized with the mechanical one, and as a result, the DE motion’s amplitude is at least two hundred times greater than that of the unmatched system. Furthermore, for unbiased AC voltages with large amplitudes, the electro-mechanical modal interaction causes the system to exhibit the formation of frequency combs in the frequency spectrum of the system’s response. The implementation of this method using a simple electrical circuit just requires adequate matching between the electrical and the mechanical natural frequencies that depends on the inductance value. Our proposal effectively eliminates the need for a high source voltage generator which has been the main limitation in designing DE-based capacitors.

Modeling, design, and optimization of a dielectric elastomer acoustic liner

The modeling, design, and optimization of an embedded dielectric elastomer (DE) membrane acoustic liner is considered. The acoustic impedance of the liner is modified when the DE is subjected to voltage, resulting in a reduction of the in-plane stress. A lumped element model of an embedded dielectric elastomer acoustic liner is derived and validated in a normal incidence impedance tube and is subsequently used to optimize its performance. The optimization cost functions include (1) maximization of the average absorption coefficient over a targeted frequency range, 400 – 1600 Hz and (2) maximization of the change in the liner fundamental resonance frequency when the membrane is activated. Good agreement between measured and predicted absorption is observed. Tuning of the resonant frequency requires a numerical solution for resonance using the imaginary part of the impedance, since a simple analytical expression for resonance cannot be derived due to the complex coupling between the acoustics of the liner and the electro-mechanics of the DE membrane. Nonetheless, resonant frequency shifts predicted with the lumped element model compare favorably to those measured with the activated liner sample, with a shift of 213 Hz.

Tunable electromechanical properties of double-layer stacked anisotropic dielectric elastomer actuators

The current reported anisotropic dielectric elastomer (DE) actuators have some potential limitations for widespread application, such as the inability to adjust the anisotropic direction, and the related relatively complicated fabrication process. In this work, we propose a method to realize tunable direction and magnitude of electromechanical deformation of DE membranes. Two sheets of unequal-biaxial prestretched VHB 4905 membranes are attached at different rotation angles, forming an anisotropic DE actuator (DEA) with utilization of carbon grease electrodes. Experimental results demonstrate that, the direction and magnitude of the voltage-induced displacement of DEs is adjustable by tuning the unequal-biaxial prestretch ratio and rotation angle. In addition, the dielectric constant and maximum displacement at breakdown of the anisotropic DEA are also related to the rotation angle. The designed anisotropic DEA realizes the diversity of electromechanical actuation in both the planar 2D and the spatial 3D structures, which can be utilized to help design the practical soft actuators.

A time-delayed proportional-derivative controller for a dielectric elastomer circular membrane

• In this paper, an internal resonance of a circular DE membrane is investigated within mechanical and electrical excitations in order to find internal resonances for improving its performance for future applications. • This work proposes a time-delayed proportional-derivative (TDPD) controller for decreasing the oscillations of a DE system with quadratic and cubic nonlinearities. • Averaging method is used to solve the controlled system to obtain the first-order approximation solutions and response equations for the DE system. • The TDPD controller is the best control strategy that can reduce the framework vibrations regardless of the excitation frequency. Due to the substantial deformation generated by voltage excitation, the dielectric elastomer (DE) is a new type of functional polymer that can be employed as a smart actuator. In this paper, an internal resonance of a circular DE membrane is investigated within mechanical and electrical excitations in order to find internal resonances for improving its performance for future applications. All programs that contain DE will perform flawlessly if DE is managed. This work proposes a time-delayed proportional-derivative (TDPD) controller for decreasing the oscillations of a DE system with quadratic and cubic nonlinearities. The system is researched and investigated when using a Proportional–derivative (PD) controller to apply time-delayed control on displacement and velocity. Stability is improved, maximum peak overshoot is reduced, settling time is reduced, and the framework transient response is recovered using this control method. The first-order approximation solutions for the DE system are calculated using the averaging method. Simultaneous resonance is regarded as the worst type of resonance. To obtain the dynamic solution of the device with TDPD controllers, analytical and numerical approaches are used. The Routh-Huriwitz approach is used to review and analyze the consistency of the steady state solution in the near-resonance case. The effects of various factors on the steady-state solution are identified and discussed. The effects of time delay are investigated in order to determine the most stable range of time delays for the best performance. The MATLAB software package is used to generate simulation effects. When the results are compared to the numerical simulations, they show that the approximate solution and the control algorithm used in this paper are well validated. At the end, there is a comparison with previously published work. The focus of this paper is on using a TDPD controller to manage the nonlinear dynamic response and probable internal resonances of a circular DE membrane under mechanical and electrical excitations. The approximate solution of a nonlinear system of differential equations is investigated using the averaging technique in the cases of primary and 1:2 internal resonance, which are the worst-case scenarios that should be avoided. To display and compare controller effects at various system settings, several response curves are used. The TDPD controller is used to research nonlinear dynamics control of the DE system with harmonic force. The stability analysis and the effects of parameter behavior are tested using MATLAB program. To examine the controller effect, several response curves are used. The collected findings demonstrated that the TDPD control efficiency in reducing the system's nonlinear oscillations. The frequency response curves of the system were studied at various uncontrolled and regulated coefficients. Before and after control, response curve diagrams employing frequency response equations are created. Finally, validation curves are shown to measure the degree of similarity between analytical and numerical simulation predictions. At the end, there is a comparison with previously published works.

New actuation modes of composite dielectric elastomers

The typical actuation mode of a dielectric elastomer membrane subjected to an electric field across its thickness is in-plane expansion. We show that, by selecting properly the contrast between phases (i.e. shear moduli and permittivity ratios), a hierarchical laminate may display longitudinal contraction when actuated in the same way. In particular, simple and second rank laminates are investigated. The latter performs in general better; however, we provide a guideline on how to optimize the microstructure to limit the values of the contrast parameters at which the new ‘non-conventional’ mode becomes available. As the requirements in terms of permittivity ratio of the two phases are somewhat extreme, we review the availability of materials that have been processed so far to assess the viability of such composite devices.

Integrated Sensing of Camber, Aerodynamic Load, and Vortex Structures over Membrane Wings

Due to the compliant nature of extensible membrane wings, there exists a close relationship between the membrane wing camber and the aerodynamic load. Additionally, the membrane dynamics are often linked to unsteady large-scale flow structures, such as shear layer location or leading-edge vortex shedding. Real-time measurements of the membrane shape, including both mean camber and the frequency content of vibration, provide significant information on the surrounding flowfield. In this work, one method of integrated camber sensing is demonstrated, and the relationships to aerodynamic load and flowfield are shown. Camber is estimated via the capacitance of a dielectric elastomer membrane wing. The relationship between capacitance and camber is defined geometrically. The mean aerodynamic load is shown to be well-captured by applying a simple aeroelastic analysis to the measured camber. Finally, time-resolved membrane kinematics and flowfield measurements are used to illustrate the ties between the dynamic membrane vibration, as measured by capacitance, and the behavior of the shear layer above the wing. Ultimately, this work is a step toward an integrated, closed-loop control method for membrane wings.

Leveraging Dynamics-Induced Snap-Through Instabilities to Access Giant Deformations in Dielectric Elastomer Membranes

Abstract Achieving extreme deformations without electrical breakdown has been a longstanding challenge in the dielectric elastomer community. In this paper, we present a novel approach for accessing giant in-plane stretches in circular dielectric elastomer membranes by leveraging nonlinear dynamics, specifically short-duration voltage pulses. These voltage pulses—applied about nominal bias voltages where the large-stretch equilibrium does not experience dielectric breakdown—create transient stretches that, if sufficiently large, cause the membrane to dynamically snap-through to its large-stretch equilibrium. These giant deformations are reversible; pulsed voltage drops can return the membrane from its large-stretch equilibrium to its small-stretch equilibrium. Parametric analyses are used to determine the combinations of pulse amplitude and duration that result in snap-through. Corresponding through-thickness electric fields are shown to be below stretch-dependent dielectric strengths from the literature, suggesting practical feasibility. Unlike other techniques for accessing extreme stretches in dielectric elastomers, the present approach relies on voltage control alone; it therefore does not require altering the external mechanical forces that cause pre-stretch and can be applied without modifying the elastomer’s mechanical compliance. This research demonstrates that carefully designed voltage pulses may permit existing and emerging soft material technologies to access extreme, large-stretch equilibria without dielectric breakdown.

Dielectric Elastomer Cooperative Microactuator Systems—DECMAS

This paper presents results of the first phase of “Dielectric Elastomer Cooperative Microactuator Systems” (DECMAS), a project within the German Research Foundation Priority Program 2206, “Cooperative Multistable Multistage Microactuator Systems” (KOMMMA). The goal is the development of a soft cooperative microactuator system combining high flexibility with large-stroke/high-frequency actuation and self-sensing capabilities. The softness is due to a completely polymer-based approach using dielectric elastomer membrane structures and a specific silicone bias system designed to achieve large strokes. The approach thus avoids fluidic or pneumatic compo-nents, enabling, e.g., future smart textile applications with cooperative sensing, haptics, and even acoustic features. The paper introduces design concepts and a first soft, single-actuator demonstrator along with experimental characterization, before expanding it to a 3 × 1 system. This system is used to experimentally study coupling effects, supported by finite element and lumped parameter simulations, which represent the basis for future cooperative control methods. Finally, the paper also introduces a new methodology to fabricate metal-based electrodes of sub-micrometer thickness with high membrane-straining capability and extremely low resistance. These electrodes will enable further miniaturization towards future microscale applications.

Dynamic modeling and residual vibration suppression of electrostatically driven soft dielectric elastomer minimum energy structures

Dielectric elastomers (DEs), a special class of soft electro-active polymers that undergo finite deformation under external electrical stimuli, offer a wide range of applications that include but are not limited to soft actuators, soft robots, and energy harvesters. Among the various configurations of dielectric elastomer-based soft mechanisms, DE-based minimum energy structures (DEMES) are elite due to their several advantageous characteristics, such as lightweight, an easy fabrication process, the ability to achieve a desirable complex 3-D shape, the capability of undergoing large out-of-plane actuation despite planar fabrication, fast response, and controllability. However, when a DEMES actuator is driven by an input voltage signal consisting of different Heaviside steps, the intrinsic residual vibrations exhibited by the actuator may restrict the motion precision required in real-world applications. In this work, a nonlinear dynamic model of the DEMES actuator is devised using the Euler–Lagrange equation of motion, and the neo-Hookean material model is utilized to describe the material behavior of the DE membrane. A feedforward control technique is developed to suppress the inherent residual vibrations exhibited by the DEMES actuator. The control technique relies on the balance of the electro-mechanical forces at the minimum point, characterized by zero velocity and minimum bending angle in an oscillation cycle. The capability of the proposed feedforward control technique is demonstrated by controlling the DEMES actuator to different desired positions without residual vibrations. A parametric study is performed to explore the dependence of the proposed control technique on several parameters, such as frame bending stiffness, pre-stretch of the membrane, and membrane damping. The feedforward control technique and the inferences obtained from the current research can be implemented effectively in the design and development of open loop controllers for electrostatically driven soft electro-active devices.

Nonlinear vibration behaviors of dielectric elastomer membranes under multi-frequency excitations

Nonlinear vibration behaviors of dielectric elastomer membranes under multi-frequency excitations

Contact mechanics model of wrinkling instability of dielectric elastomer membranes for anti-biofouling

Contact mechanics model of wrinkling instability of dielectric elastomer membranes for anti-biofouling

Numerical study on nonlinear vibration of FG-GNPRC circular membrane with dielectric properties

Dielectric elastomer membrane has been applied in a wide variety of engineering fields for their excellent dynamic performances. Functionally graded graphene nanoplatelet-reinforced composite (FG-GNPRC) shows great potential for developing high-performance and multifunctional structures. In this work, the damped nonlinear vibration of the FG-GNPRC dielectric membrane is investigated. The effects of damping and dielectric properties are considered in terms of energy while deriving governing equations. Taylor series expansion and differential quadrature together with direct iterative methods are used to discretize and numerically solve the obtained governing equations. The developed model and numerical solution are verified by comparing present results to existing studies. The influences of functionally graded distribution, damping, stretching ratio, dimensions of the membrane, and the attributes of the electrical field and GNP fillers on the nonlinear vibration of the structure are comprehensively investigated. It is found that compared to a uniform distribution, the membrane with functional distribution of GNP demonstrates exhibits more robust performances. The membrane with a smaller thickness-to-radius ratio is more sensitive to the external electrical field. In addition, the direct current voltage is evidenced to have a more significant effect on the nonlinear vibration when the membrane is subject to a relatively small stretching ratio. The present work suggests that the structural behavior of the FG-GNPRC membrane can be actively adjusted by varying the stretching ratio and the properties of the electrical field and the GNP filler. HIGHLIGHTS Effects of damping and dielectric properties are considered for structural behavior in terms of energy. Taylor series expansion and differential quadrature methods are combined to solve governing equations. Two transition regions in frequency ratio are identified due to AC frequency-facilitated polarization and electron tunneling. The effect of the electric field on nonlinear vibration can be regulated by varying the stretching ratio.

Nonlinear vibration of dielectric elastomer membranes with axial inertia effects

Dielectric elastomers are a compelling class of electro-active materials that show great promise for large-deformation actuation, sensing, and energy generation applications. In many of these applications, the applied voltages are transient, leading to meaningful dynamic stretches with rich and atypical nonlinear behavior. Existing works either jettison dynamic thickness changes at the outset or do not examine their overall effects on dynamic behavior. In this paper, a Newtonian framework accounting for dynamic thickness changes during planar motion is used to model the nonlinear dynamics of circular dielectric elastomer membranes. A distinguishing feature of the resulting equation of motion is the presence of additional nonlinear terms that we call axial inertia. A small-vibration model is derived, and its agreement with the full nonlinear model is quantified in terms of the vibration amplitude, applied voltage, and membrane thickness. The natural frequency is found to be sensitive to membrane thickness when vibrations occur about small-stretch equilibria, but not large-stretch equilibria. The impact of axial inertia on the membrane’s frequency response is examined for sinusoidal voltage fluctuations. At sufficiently low voltages where the membrane has only one equilibrium, the frequency response transitions from softening behavior at low amplitudes to hardening behavior at moderate-to-high amplitudes. Axial inertia results in atypical frequency response, with regions where three steady-state dynamic stretches are possible and additional jumps occur during frequency sweeps through resonance. Secondary subharmonic resonances are possible for thick membranes at low voltages, which have frequency ranges where four steady-state dynamic stretches are possible, the first known demonstration of this phenomenon. Electric fields needed to access this and other novel nonlinear dynamic response are shown to be below stretch-dependent dielectric strengths from the literature. Our results show that the effects of axial inertia on nonlinear dynamics can be significant even for thin membranes undergoing large dynamic stretches.

Biomimetic human eyes in adaptive lenses with conductive gels

To investigate the imaging effect, adaptive robust lenses are prepared by sealing transparent liquid or gel. Lenses are fabricated using the negative-pressure method, which is a benefit for a stable biconvex shape. Under the action of an electric field, the soft lens deforms following the dielectric elastomer actuator (DEA). DE (dielectric elastomer) membranes expand in the plane perpendicular to the electric field lines. The toroidal driving area leads to a decrease in lens diameter and an increase in convex curvature. Therefore, the focal length of the lens becomes shorter. The experimental measurement utilizes the double focal length method. As a result, the largest focal length change that could be achieved was 44.7% (190 mm→105 mm) of the soft lens using a DEA with carbon grease electrodes. Furthermore, the ECG (electrocardiogram) conductive gel could replace traditional carbon grease for DEA electrodes in optics. This type of transparent electrode is creatively applied to a biomedical lens. Under the same conditions, the electrostriction rate in a DEA with ECG gel was achieved at 33%, which was greater than that of 28% in a DEA coupled with carbon grease electrode. Adaptive lenses have characteristics such as easy fabrication, low cost, and strong operability, and they possess great potential application value in biomedical feild.

Effect of continuously variable material parameters on dynamic stability of viscoelastic dielectric elastomers

As is known, the internal material parameters of dielectric elastomers (DEs) may largely affect the corresponding electromechanical performances. In this article, the dynamic stability analysis of viscoelastic DEs with different material parameters is investigated by using the continuous method. Several affecting material parameters, including the geometrical size, viscous damping, limiting stretch, and shear modulus, are considered, respectively. Continuous variation of geometrical size is found to induce the dynamic instability of DE, while the viscous damping and limiting stretch have limited connection with the occurrence of dynamic instability. Furthermore, increase in the ratio of the shear modulus also causes the dramatic jump of dynamic deformation of DE membranes.

Dynamics and energy harvesting performance of a nonlinear arc-cylinder type dielectric elastomer oscillator under unidirectional harmonic excitations

To harvest vibration energy, a nonlinear arc-cylinder type dielectric elastomer oscillator (ADEO), which has greater advantages than the VI DEG in vibration environments, is proposed. We first study the dynamic behaviors and the energy harvesting (EH) performance of the ADEO subjected to unidirectional harmonic excitations. The energy harvester, which consists of a hollow arc cylinder, two pairs of straight cylindrical frames, two dielectric elastomer membranes (DEMs) and an inner free moving ball, can convert vibration energy into electricity. The dynamic and electrical analysis models of the ADEO system are developed under the unidirectional harmonic excitation. Two impact models are verified by experimental results and are compared with each other, and the instantaneous impact model with computational efficiency and accuracy is selected. The rich dynamic behaviors of the ADEO system under diverse parameters, including the excitation amplitude and frequency, the tilt angle, the impact angle and the radius of the curvilinear motion of the ball, are fully investigated through two kinds of bifurcation diagrams and 3-D frequency spectrums. The effects of these parameters on the system EH performance are also studied. The research results show that the system EH performance can be enhanced by appropriately adjusting these parameters. This work can not only help guide the design and optimization of the ADEO system under the unidirectional vibration, but also lay the foundation for the design and optimization of the system in the bidirectional vibration environment.

A pendulum-based absorber-harvester with an embedded hybrid vibro-impact electromagnetic-dielectric generator

In this paper, a novel hybrid vibro-impact electromagnetic-dielectric generator (VI EDG) is proposed, which is further embedded into a pendulum structure to form a pendulum-based absorber-harvester (PAH) system. The PAH system can convert the vibration energy into electrical one with the help of the VI EDG, and has the potential to reduce the swing amplitude of the pendulum. The physical model of the PAH system is first introduced, and its governing equations involving the dynamical and electrical parts are derived based on the Euler-Lagrange’s equation of a non-conservative system. Next, the governing equations of the PAH system are validated experimentally by measuring the swing motion of the pendulum under a given harmonic excitation. On this basis, the system energy harvesting performance under different excitation parameters (amplitude and frequency) and dimensional parameters (the rod’s length and the distance between two dielectric elastomer membranes) is fully investigated and explained through numerical simulations. Finally, the vibration absorption performance of the VI EDG is discussed by comparing the peak-to-peak values of the swing motions between the proposed PAH system and the conventional pendulum without embedded VI EDG. Research results show that the proposed VI EDG can not only effectively harvest ambient vibration energy from the pendulum system, but also has the potential to absorb the vibration of the system.

Improvement of Adaptive Motion Performance in a Flexible Actuator, Based on Electrically Induced Deformation

An actuator built with flexible material has the advantage of smaller size and can withstand certain collisions better than actuators with rigid material. This paper proposes a crawling actuator model driven by dielectric elastomer (DE), which uses the electrically induced deformation of the DE membrane to drive the motion of the actuator. When the dielectric elastomer in the actuator is at higher voltage, the DE material produces higher deformation, and the deformation is transmitted to the ground through the friction foot thus driving the motion of the actuator. An interpolation fitting estimation algorithm (IFEA) was constructed based on the relevant material properties and principles. The pre-stretch length of the DE membrane was determined and verified through experiment; the verified results showed that the actuator has better driving performance when the membrane pre-stretching ratio is equal to 3. The crawling actuator can achieve a speed of about 50 mm/s at 4 kv and can reach 11 mm/s when loaded with four times its weight. The new crawling actuator achieved an excellent turning ability of 8.2°/s at 60% duty cycle and 32 Hz frequency. Compared with other types of crawling actuators, the actuator presented in this work has better load capacity and crawling performance.