Macro-Fiber Composite Bimorph Research Articles

Modeling and analysis of a macro-fiber piezoelectric bimorph energy harvester operating in d33-Mode using Timoshenko theory

Piezoelectric bimorph cantilevered beams are frequently employed in energy harvesting applications. The use of macro-fiber composites, which combine piezoelectric fibers with rectangular cross-sections and interdigitated electrodes, has significantly enhanced their performance by enabling operation in the 33-mode of piezoelectricity, thereby increasing conversion efficiency. In this article, the Timoshenko beam theory is applied to overcome the limitations of the Euler-Bernoulli theory in modeling transverse vibrations of harvesters with low slenderness ratios (length to thickness ratios). The mixture rule formulation is applied to determine the equivalent properties of the macro-fiber composite (MFC) structure. The electromechanical properties of a representative volume element (RVE) bounded by two successive interdigitated electrodes are coupled to the overall electro-elastic dynamic model of the structure using the Timoshenko theory. Frequency response functions for the power and tip vibration displacement of the MFC bimorph beam are determined from the model. Experimental data from the literature are used to validate the improved results predicted by the model developed in this article. A comparative analysis between the electromechanical responses predicted using a model based on Timoshenko and a model based on Euler-Bernoulli theory is conducted showing agreement, for harvesters with large slenderness ratios and discrepancies of up to 30% for low slenderness ratios. It has also been shown that the model based on Euler-Bernoulli theory overestimates both the mechanical and the electrical responses for low slenderness ratios as the shear and rotary inertia effects are not negligible in this case.

High actuation capability and smooth-deformation piezo morphing wing based on multi-layer parallel pre-compressed MFC bimorph

A single macro-fiber composite (MFC) unimorph or bimorph wing can only be applied to micro aerial vehicles (MAV) at speeds lower than 20 m/s owing to its relatively small output work. In this study, a high-actuation MFC pre-compressed bimorph actuator (MFC-PBA) multilayer parallel morphing wing is proposed for application in high-speed miniature unmanned aerial vehicles (mini-UAVs). The morphing wing adopts the proposed ribs with an arc groove and three parallel layers of MFC-PBAs to improve the output work and guarantee smooth morphing wing surface. The large deformation finite element (FE) models of a single MFC-PBA and its multilayer parallel morphing wing are established to evaluate the output deformation and output force. Subsequently, a prototype of the morphing wing is fabricated, and the actuation capabilities of the single MFC-PBAs and morphing wing are tested. The experimental and FE simulation results satisfactorily agree. The results show that at the peak driving voltage, with axial compression forces of 18 and 27 N applied to the side and middle MFC-PBAs, respectively, the deflection angle of the morphing wing reaches ±12°, which is twice that of the morphing wing without compression; and its blocking force is maintained at 1.682 N; thus, its output work has doubled. The multiphysics model of the proposed morphing wing under airflow is established to evaluate the deformation capability. The results show that the present morphing wing achieves a deflection of 5.04° on the side of the incoming flow direction, and a unit lift of 249.1 N/m at an air speed of 40 m/s and angle of attack of 15°. Consequently, the proposed morphing wing exhibits a high deformation capability. We expect the proposed morphing wing will be used for the flight control of mini-UAVs at higher speeds and larger sizes.

Rate-Dependent Hysteresis Modeling and Displacement Tracking Control Based on Least-Squares SVM for Axially Pre-Compressed Macro-Fiber Composite Bimorph.

The new axially pre-compressed macro-fiber composite bimorph (MFC-PBP) can produce large displacement and output power. However, it has the property of strong rate-dependent hysteresis nonlinearity, which challenges the displacement tracking control of morphing structures. In this paper, the least-squares support vector machine (LS-SVM) is applied to model the rate-dependent hysteresis of MFC-PBP. Compared with the predicated results of the series model of the Bouc–Wen model and Hammerstein model (BW-H), the LS-SVM model achieved higher predication accuracy and better generalization ability. Based on the LS-SVM hysteresis compensation model, with the support vector pruning, the displacement tracking feedforward compensator is obtained. In order to improve the displacement tracking accuracy, the LS-SVM feedforward compensator combined with the proportional and integral (PI) controller and the feedforward plus feedback control experiment is carried out on the displacement tracking of MFC-PBP. The test results show that the feedforward plus feedback displacement tracking control loop based on the LS-SVM model also has a higher displacement tracking accuracy than that based on the inverse model of BW-H.

Large deformation mechanical modeling with bilinear stiffness for Macro-Fiber Composite bimorph based on extending mixing rules

Macro-Fiber Composite bimorph is a kind of piezoelectric actuator that allow large bending deformation. However, macro-fiber composites exhibit strong stiffness nonlinearity in their operation range, so it is difficult to accurately estimate their large deformation behavior based on a linear constitutive model. In addition, the macro-fiber composites have active and inactive parts, that significantly differ in their material sizes and properties, so it is not reasonable to consider them as uniform material. Thus, it is necessary develop an accurate modeling and analysis method for the large deformation macro-fiber composite structures. First, the mixing rules are extended to derive the three-dimensional homogenized mechanical and electrical parameters of the macro-fiber composite active part; based on these parameters, the actuation results of linear finite element model is in good agreement with the official data. Then a finite element model of the axially compressed macro-fiber composite bimorph is established, the bilinear tensile stiffness of macro-fiber composite is realized by secondary development in ANSYS. Comparison with the experimental results reveals high accuracy of the established finite element model. Thus, the developed method can be effectively used for the performance evaluation and design of the macro-fiber composite devices with large deformation.

Piezoelectric energy harvesting using macro fiber composite patches

Over the last decade, vibration energy harvesting has received substantial attention of many researchers. Piezoelectric materials are able to capture energy from ambient vibration and convert it into electricity which can be stored in batteries or utilized to power small electronic devices. In order to benefit from the 33-mode of the piezoelectric effect, interdigitated electrodes have been utilized in the design of macro fiber composites which are made of piezoelectric fibers of square cross sections embedded into an epoxy matrix material. This paper presents an analytical model of a macro fiber composite bimorph energy harvester using the 33-mode. The mixing rule is applied to determine the equivalent and homogenized properties of the macro fiber composite structures. The electromechanical properties of a representative volume element composed of piezoelectric fibers and an epoxy matrix between two successive interdigitated electrodes are coupled with the overall electro-elastodynamics of the harvester utilizing the Euler–Bernoulli theory. Macro fiber composite bimorph cantilevers with diverse widths are simulated for power generation when a resistive shunt loading is applied. Stress components in the Kapton layers, which are typically a part of any macro fiber composite patch, and in the bonding layers have been included in the model contrary to previously published studies. Variable tip mass, attached at the free end of the beam, is utilized in this paper to tune the resonance frequency of the harvester. The generated power at the fundamental short circuit and open circuit resonance frequencies of harvesters having three different widths is analyzed. It has been observed that higher electrical outputs are produced by the wider macro fiber composite bimorph using (M8528-P1 patches).

Experimental study of axial-compressed macro-fiber composite bimorph with multi-layer parallel actuators for large deformation actuation

Piezoelectric bimorphs have a promising application in morphing micro air vehicles; however, increasing the actuation displacement is a difficult point. Axial compression can be used to increase the deformation of the piezoelectric bimorph. Compared with piezoelectric ceramics, macro fiber composites offer higher flexibility. In this article, a large displacement actuator of axial-compressed macro fiber composite bimorph is proposed. A multi-layer parallel scheme of macro fiber composite bimorphs is presented to increase the output torque of piezoelectric bimorph within a limited space. The actuation performance of the axial-compressed macro fiber composite bimorph and its multi-layer parallel scheme are verified through quasi-static experiment and displacement tracking control test. The experimental results show that the end-free rotations of both the axial-compressed macro fiber composite bimorph and its multi-layer scheme achieve ±8.1°, which is 60% higher than that of a piezoelectric ceramics bimorph with the same length. The blocking torque of the single-layer macro fiber composite bimorph is 0.028 Nm. The proposed parallel bimorphs method can magnify output torques. In addition, the axial-compressed macro fiber composite bimorph can accurately track any displacement signals in the range of its actuation. It is a continuous and controllable piezoelectric bimorph with large displacement.

Resonant nonlinearities of piezoelectric macro-fiber composite cantilevers with interdigitated electrodes in energy harvesting

We explore the modeling and analysis of nonlinear nonconservative dynamics of macro-fiber composite (MFC) piezoelectric structures, guided by rigorous experiments, for resonant vibration-based energy harvesting, as well as other applications leveraging the direct piezoelectric effect, such as resonant sensing. The MFCs employ piezoelectric fibers of rectangular cross section embedded in Kapton with interdigitated electrodes to exploit the 33-mode of piezoelectricity. Existing modeling and analysis efforts for resonant nonlinearities have so far considered conventional piezoceramics that use the 31-mode of piezoelectricity. In the present work, we develop a framework to represent and predict nonlinear electroelastic dynamics of MFC bimorph cantilevers under resonant base excitation for primary resonance behavior. The interdigitated electrodes are shunted to a set of resistive electrical loads to quantify the electrical power output. Experiments are conducted on a set of MFC bimorphs over a broad range of mechanical excitation levels to identify the types of nonlinearities present and to compare the harmonic balance model predictions and experiments. The experimentally observed interaction of quadratic piezoelectric material softening and cubic geometric hardening effects is captured and demonstrated by the model. It is shown that the linearized version of the model yields highly inaccurate results for typical base acceleration levels and frequencies involved in vibration energy harvesting, while the nonlinear framework presented here can accurately predict the amplitude-dependent resonant frequency response.

Nonlinear elastodynamics of piezoelectric macro-fiber composites with interdigitated electrodes for resonant actuation

Macro-fiber composite (MFC) piezoelectric materials are used in a variety of applications employing the converse piezoelectric effect, ranging from morphing and bioinspired actuation to vibration control in flexible structures. Most of the existing literature to date considered linear material behavior for geometrically linear oscillations. However, in many applications, such as bioinspired locomotion using MFCs, material and geometric nonlinearities are pronounced and linear models fail to represent and predict the governing dynamics. The predominant types of nonlinearities manifested in resonant actuation of MFC cantilevers are piezoelectric softening, geometric hardening, and inertial softening. In the present work, we explore nonlinear actuation of MFC cantilevers and develop an experimentally validated mathematical framework for modeling and analysis. In the experimental setting, an in vacuo actuation scenario is considered for a broad range of voltage levels (from low to moderate values) while eliminating nonlinear fluid damping. Experiments are conducted for an MFC bimorph cantilever, and model simulations based on the method of harmonic balance are compared with experimental frequency response curves under resonant actuation. The resulting experimentally validated framework can be used for simulating the dynamics of MFCs under resonant actuation, as well as parameter identification and structural optimization for linear to moderately nonlinear regime.

Coupling of experimentally validated electroelastic dynamics and mixing rules formulation for macro-fiber composite piezoelectric structures

Piezoelectric structures have been used in a variety of applications ranging from vibration control and sensing to morphing and energy harvesting. In order to employ the effective 33-mode of piezoelectricity, interdigitated electrodes have been used in the design of macro-fiber composites which employ piezoelectric fibers with rectangular cross section. In this article, we present an investigation of the two-way electroelastic coupling (in the sense of direct and converse piezoelectric effects) in bimorph cantilevers that employ interdigitated electrodes for 33-mode operation. A distributed-parameter electroelastic modeling framework is developed for the elastodynamic scenarios of piezoelectric power generation and dynamic actuation. Mixing rules (i.e. rule of mixtures) formulation is employed to evaluate the equivalent and homogenized properties of macro-fiber composite structures. The electroelastic and dielectric properties of a representative volume element (piezoelectric fiber and epoxy matrix) between two neighboring interdigitated electrodes are then coupled with the global electro-elastodynamics based on the Euler–Bernoulli kinematics accounting for two-way electromechanical coupling. Various macro-fiber composite bimorph cantilevers with different widths are tested for resonant dynamic actuation and power generation with resistive shunt damping. Excellent agreement is reported between the measured electroelastic frequency response and predictions of the analytical framework that bridges the continuum electro-elastodynamics and mixing rules formulation.

Electrohydroelastic Euler–Bernoulli–Morison model for underwater resonant actuation of macro-fiber composite piezoelectric cantilevers

Bio-inspired hydrodynamic thrust generation using smart materials has received growing attention over the past few years to enable improved maneuverability and agility, small form factor, reduced power consumption, and ease of fabrication in next-generation aquatic swimmers. In order to develop a high-fidelity model to predict the electrohydroelastic dynamics of macro-fiber composite (MFC) piezoelectric structures, in this work, mixing rules-based (i.e. rule of mixtures) electroelastic mechanics formulation is coupled with the global electroelastic dynamics based on the Euler–Bernoulli kinematics and nonlinear fluid loading based on Morison’s semi-empirical model. The focus is placed on the dynamic actuation problem for the first two bending vibration modes under geometrically and materially linear, hydrodynamically nonlinear behavior. The electroelastic and dielectric properties of a representative volume element (piezoelectric fiber and epoxy matrix) between two subsequent interdigitated electrodes are correlated to homogenized parameters of MFC bimorphs and validated for a set of MFCs that have the same overhang length but different widths. Following this process of electroelastic model development and validation, underwater actuation experiments are conducted for different length-to-width aspect ratios (L/b) in quiescent water, and the empirical drag and inertia coefficients are extracted from Morison’s equation to establish the electrohydroelastic model. The repeatability of these empirical coefficients is demonstrated for experiments conducted using aluminum cantilevers of different aspect ratios with a focus on the first two bending modes. The convergence of the nonlinear electrohydroelastic Euler–Bernoulli–Morison model to its hydrodynamically linear counterpart for increased L/b values is also reported. The proposed model, its harmonic balance analysis, and experimental results can be used not only for underwater piezoelectric actuation, but also for sensing and energy harvesting problems.

Hydrodynamic thrust generation and power consumption investigations for piezoelectric fins with different aspect ratios

Bio-inspired hydrodynamic thrust generation using piezoelectric transduction has recently been explored using Macro-Fiber Composite (MFC) actuators. The MFC technology strikes a balance between the actuation force and structural deformation levels for effective swimming performance, and additionally offers geometric scalability, silent operation, and ease of fabrication. Recently we have shown that mean thrust levels comparable to biological fish of similar size can be achieved using MFC fins. The present work investigates the effect of length-to-width (L/b) aspect ratio on the hydrodynamic thrust generation performance of MFC cantilever fins by accounting for the power consumption level. It is known that the hydrodynamic inertia and drag coefficients are controlled by the aspect ratio especially for L/b< 5. The three MFC bimorph fins explored in this work have the aspect ratios of 2.1, 3.9, and 5.4. A nonlinear electrohydroelastic model is employed to extract the inertia and drag coefficients from the vibration response to harmonic actuation for the first bending mode. Experiments are then conducted for various actuation voltage levels to quantify the mean thrust resultant and power consumption levels for different aspect ratios. Variation of the thrust coefficient of the MFC bimorph fins with changing aspect ratio is also semi-empirically modeled and presented.

Bio-inspired aquatic robotics by untethered piezohydroelastic actuation

This paper investigates fish-like aquatic robotics using flexible bimorphs made of macro-fiber composite (MFC) piezoelectric laminates for carangiform locomotion. In addition to noiseless and efficient actuation over a range of frequencies, geometric scalability, and simple design, bimorph propulsors made of MFCs offer a balance between the actuation force and velocity response for performance enhancement in bio-inspired swimming. The experimental component of the presented work focuses on the characterization of an elastically constrained MFC bimorph propulsor for thrust generation in quiescent water as well as the development of a robotic fish prototype combining a microcontroller and a printed-circuit-board amplifier to generate high actuation voltage for untethered locomotion. From the theoretical standpoint, a distributed-parameter electroelastic model including the hydrodynamic effects and actuator dynamics is coupled with the elongated-body theory for predicting the mean thrust in quiescent water. In-air and underwater experiments are performed to verify the incorporation of hydrodynamic effects in the linear actuation regime. For electroelastically nonlinear actuation levels, experimentally obtained underwater vibration response is coupled with the elongated-body theory to predict the thrust output. The measured mean thrust levels in quiescent water (on the order of ∼10 mN) compare favorably with thrust levels of biological fish. An untethered robotic fish prototype that employs a single bimorph fin (caudal fin) for straight swimming and turning motions is developed and tested in free locomotion. A swimming speed of 0.3 body-length/second (7.5 cm s−1 swimming speed for 24.3 cm body length) is achieved at 5 Hz for a non-optimized main body-propulsor bimorph combination under a moderate actuation voltage level.

Lightweight High Voltage Electronic Circuits for Piezoelectric Composite Actuators

The purpose here is to enable peak-to-peak actuation of piezocomposite devices to perform shape control of structures, specifically bimorph variable-camber control surfaces on small aircraft. One of the major drawbacks in implementing control with piezocomposite actuation is its asymmetry in the positive and negative voltage directions. To remedy this situation, a novel, solid-state electrical circuit employing diodes and resistors is proposed. The circuit allows a single bipolar amplifier to control a bimorph composed of two piezoceramic composite actuators known as Macro-Fiber Composite (MFC). The MFCs have an asymmetric actuation range of -500 to 1500 V; hence an MFC bimorph with conventional serial or parallel electrical connection limits the actuation to the -500 to 500 V range. The proposed circuit allows the division of the input voltage so that: (1) The MFC that is in extension receives 1500 V, and (2) The MFC that is in compression receives -500 V. The circuit also allows the actuation in the opposite direction without any physical changes (i.e., not using any electromechanical switches) The input-output relationship of the circuit is characterized experimentally. An MFC bimorph is used to further demonstrate the capability of the circuit.

Nonlinear Control of a Membrane Mirror Strip Actuated Axially and in Bending

The sliding mode technique is used to control the deformation of a membrane mirror strip augmented with two macrofiber composite bimorphs located near the ends of the strip. The first bimorph is actuated in bending and the second is actuated axially. The structure is modeled as an Euler-Bernoulli beam under tensile load and the macrofiber composite patches are modeled as monolithic piezoceramic wafers. To cast the system into a finite-dimensional state-space form, the finite element method is used, and the model presented accounts for the dynamics of the augmented bimorphs. The membrane strip is placed under uniform tension. Because one of the bimorphs acts axially, the resulting tension in the membrane strip is discontinuous at the location of this bimorph and, consequently, the obtained model is nonlinear. First, we validate the model experimentally by considering the system in its quasi-linear state, then we consider the control problem. We formulate the regulation problem by using the sliding mode technique. Additionally, to allow coupling this system with an adaptive optics scheme, the shape-control problem is considered as well. The control law uses both actuators: the bending and axial bimorphs. However, a system singularity dictates using a switching command to avoid this singularity. Various examples are presented for the regulation and shape-control problems. The simulation results demonstrate the efficacy of the proposed control law.