Macro-fiber Composite Patches Research Articles

Modeling and vibration control of a rotating flexible plate actuated by MFC

The macro fiber composite (MFC) is a novel piezoelectric intelligent material, which is widely used in the field of vibration control due to its flexibility and larger actuation forces than PZT. In this paper, a laminated plate model considering the anisotropy of MFC is developed and applied to the vibration control of a rotating plate. The laminated plate is defined as a layerwise model, which deformation is described by the Absolute Nodal Coordinate Formulation (ANCF). The MFC laminated plate element contains 48 degrees of freedom (DOFs) where the effect of MFC element can be internally incorporated without increasing the DOFs of system. Simultaneously, a neural network PD control is adopted to control the vibration of the rotating plate. Eventually, static, dynamic, and modal analyses are performed to investigate the effects of different parameters. Several vibration simulations are carried out to illustrate the ability of MFC patches on vibration control. The findings in this article would be applied to mechanical prediction and control for rotor blades of helicopters, solar panels, etc.

Experimental investigation of vibration amplitude control in additive manufactured PLA and PLA composite structures with MFC actuator

In this study, Macro Fiber Composite (MFC) as actuator has been used for open-loop active vibration control (AVC) in additive manufactured structures made of polylactic acid (PLA) and PLA composites, such as PLA with short carbon fibers (PLA-SCF composite) and PLA with continuous carbon fibers (PLA-CCF composite), when subjected to forced vibrations. The laser vibrometer has been used to find the natural frequencies and bending mode shapes of each beam structure. The MFC patch (M8507-P2), used here as an actuator, is very sensitive to supplied voltages. Thus, it is very crucial to find out the optimum phase and amplitude of the input voltage. The optimal phase angle and voltage for each structure (PLA, PLA-SCF, PLA-CCF) are estimated by a domain search in an incremental manner. Once tuned with the optimal input voltage values, the proposed technique shows exceptional performance in vibration suppression. The results confirmed that this technique can be used in a wide range of composite materials.

Vibro-acoustic control of a programmable meta-shell with digital piezoelectric shunting

In this paper, a programmable piezoelectric meta-shell is designed to actively control the structural and sound radiation responses. The meta-shell consists of a cylindrical shell, Macro-fiber Composite (MFC) patches and digital shunting circuits. Due to the electro-mechanical coupling effect of the MFC patches, the mechanical properties of the meta-shell structure can be tuned by changing the electric field. The high-order digitally resonant circuits are designed to realize programmable control of the bandgap behaviors of the meta-shell. An analytical structural dynamic model for analyzing the vibration and radiated sound responses of the programmable piezoelectric meta-shell in light fluid is established. The vibro-acoustic characteristics of the meta-shell with the piezoelectric shunting and the effects of electric parameters (including dimensionless gain and electric damping ratio) on the structural and acoustic control performances of the shell are discussed. Experiments on the vibration and acoustic control of a programmable piezoelectric meta-shell are carried out to verify the high-order bandgap characteristic and its programmability. The experimental results demonstrate that the vibration and sound radiation responses of the shell can be effectively suppressed in multiple frequency bands.

Selection of piezoeloectric material and fiber volume fraction to maximize the electrical power produced by macro-fiber composite energy harvesters

A piezoelectric Macro fiber composite (MFC) materials developed in the last decade found widespread applications such as vibration sensing, actuation and structural health monitoring. Unlike conventional ceramic piezoelectric materials (PZT), these composites show many advantages such as flexibility, reliability and high actuation capacity. However, increasing their energy harvesting capabilities still remains a challenge. Modeling and simulation of electrical energy harvesters using MFC patches provide a mean for geometrical optimization and appropriate choice of the MFC composite. This paper proposes a linear analytical model for prediction of the electro-mechanical response of bimorph harvesters using MFC patches. Homogenization technique is used to describe the equivalent piezoelectric properties of the composite structure of the MFC patch. This paper investigates the effect of the volume fraction of the fibers and the material choice of the piezoelectric fibers and epoxy matrix on the generated electrical power. It has been found that an increased fiber volume fraction causes a decrease of the voltage, the power and the velocity amplitudes for a range of load resistance. However, an increase in the fiber volume fraction FVF is achieved by an increase of the current amplitude for a range of load resistance. Maximum amount of power is generated by the bimorph MFC harvester for an FVF of 86% which corresponds to the reference configuration. The piezoelectric fiber material has a significant influence on the output power. In fact, the SONOX-P502 generated the greatest electrical power. However, the material of the matrix has a negligible effect on the generated power.

Impact of a Connection Structure of Macro Fiber Composite Patches on Energy Storage in Piezoelectric Energy Harvesting from a Rotating Shaft

Energy collection in a capacitor, which was charged by four connection structures of Macro Fiber Composite (MFC) patches, was the subject of laboratory research. The first structure was the delta circuit created by three MFC patches and connected with a three-phase rectifier; the second structure was the delta circuit created by three MFC patches and connected with a three-phase rectifier; the third structure was the parallel connection of three circuits, each of which consisted of an MFC patch and a full bridge rectifier; and the fourth structure the series connection of three circuits, each of which consisted of an MFC patch and a full bridge rectifier. Laboratory experiments were carried out on a laboratory stand which consisted of a rotating shaft, three MFC patches powering an energy storage system, and a data acquisition system. The star connection generated the highest values of voltage across a capacitor in the long time period. The delta connection produced the highest capacitor-charging power. The shortest time to reach a target voltage on the capacitor equal to a few volts was achieved by use of the delta or parallel connection. The delta connection generated target voltage equal to a few volts across a capacitor in the shortest time at a lower level of stress in the shaft, but the difference between the charging times by the delta circuit and by the parallel connection decreased as the stress in the shaft increased.

Low-speed flutter of artificial stalk-leaf and its application in wind energy harvesting

Developing wind energy harvester (WEH) by mimicking the leaf flutter may provide an innovative way for increasing the power efficiency and decreasing the cut-in speed. The low-speed flutter mechanism of the stalk-leaf system is investigated through introducing a frictionless hinge into the stalk-leaf finite element model. The aeroelastic system is established by the usage of doublet-lattice aerodynamics and the spline interpolation between structural motion and flow downwash. The critical flutter speed and frequency are analyzed via V-g method. The evolution of damping and frequency with wind speed which various from static air to Beaufort level 5 are simulated. The influence of inclined angle of the stalk on the flutter characteristics is studied. The stainless-steel artificial stalk-leaf systems with inclined angles of 0°, 15°, 30°, 45°, 60°, 75°, and 90° are fabricated and tested in wind tunnel. The wind energy harvesting performance is also measured by attaching macro-fiber composite patches on root of the stalk. It is found that the 30° stalk-leaf WEH has the lowest critical flutter speed, while the energy harvesting output (voltage and power) increases slowly with the increase of the wind speed. On the contrary, although the 90° stalk-leaf (vertical stalk) WEH has the steepest velocity-voltage and velocity-power curve, it also has the highest cut-in speed. In the preliminary tests, the 30° stalk-leaf WEH outputs steady power density of 47.46 μW cm−3 with stable oscillating frequency of 6.6 Hz at 11 m s−1 wind, while the 90° stalk-leaf WEH outputs power density of 92.88 μW cm−3 with oscillating frequency of 7.2 Hz at the same wind speed. The stalk-leaf design presents a possible way to balance the performance between the high efficiency and the low cut-in speed for the WEHs.

Experimental Analysis of the Arrays of Macro Fiber Composite Patches for Rotational Piezoelectric Energy Harvesting from a Shaft

Four arrays of three MFC patches, glued onto a rotating shaft, were compared in laboratory research. The first array was based on a delta circuit and equipped with one three-phase rectifier; the second array was based on a star circuit and equipped with one three-phase rectifier; the third array was based on parallel connection and equipped with three full-bridge rectifiers; and the fourth array was based on a series connection and equipped with three full-bridge rectifiers. The array based on a delta circuit generated the highest value of maximal electric power in comparison to the rest of arrays. It was experimentally observed that the arrays based on delta or star circuits of MFC patches and equipped with one three-phase rectifier generated a higher value of maximal power than arrays based on the connections of three full-bridge rectifiers, connected in parallel or in series. The array based on parallel connection generated the highest maximal value of current in comparison to rest of arrays for low values of load resistance (from 10 kΩ to 40 kΩ depending on the experiment). For higher values of load resistance arrays based on delta circuits and star circuits generated higher values of current than the array based on parallel connection.

Impact of Series and Parallel Connection of Macro Fiber Composite Patches in Piezoelectric Harvester on Energy Storage

A beam containing a piezoelectric layer or layers is used for piezoelectric harvesting from various processes. The structure of the beam is made by gluing the piezoelectric material on one side (unimorph) or both sides (bimorph) of a carrying substrate. Two piezoelectric layers, glued on both sides of the substrate, may be electrically parallel or series connected. This paper presents an experimental analysis of the impact of parallel and series connections of two Macro Fiber Composite (MFC) MFC patches in a bimorph on the charging of a capacitor. In experiments, the effective charging process of the capacitor was obtained both for parallel and series connection of two MFC patches. The bimorph with a parallel connection generated a larger capacitor charging power than the bimorph with a series connection in the range of voltage across the capacitor from 1 to 18 V. However, the bimorph with a series connection was more effective than a parallel connection for voltage across the charged capacitor from 18 to 20 V. The maximum capacitor charging power generated by the bimorph, in which two MFC patches were parallel connected, was 1.8 times larger than that generated by the bimorph with a series connection and was 3.3 times larger than that generated by a unimorph with one MFC patch. The impact of level of voltage across the capacitor on its discharging process has a significant meaning for the ratio of maximum power between bimorphs and between the bimorph and unimorph.

Theoretical and experimental investigations on modified LQ terminal control scheme of piezo-actuated compliant structures in finite time

This study focuses on the open-loop dynamic shape control to realize a rapid and smooth morphing process for a flexible plate which is actuated by a macro fiber composite patch. A finite element model of the system is established and verified for theoretical investigations. Steady-state and dynamic analyses are carried out to satisfy the desired rest-to-test morphing requirement. Spurious oscillations and large overshoots are observed while applying some common voltage signals. The results imply that the voltage profile of the actuator plays a key role in the dynamic morphing behavior of the system. Therefore, a quantitative criterion is proposed to determine the critical voltage slope for evaluating the boundary between quasi-static and dynamic processes. An optimal finite-time feedforward control approach named “modified linear quadratic (LQ) terminal controller” is proposed to optimize the voltage profiles by simultaneously considering the suppression of transient and residual vibration. The superiority of the proposed open-loop control scheme is appreciated when it is compared with the standard LQ terminal controller. An experimental setup is designed for verification. The effectiveness of the theoretical model is validated through modal analysis, static deformation, and dynamic responses. It is indicated by the experiment results that rapid and smooth dynamic shape morphing processes with negligible vibration within a short period of time can be achieved using the optimized voltage profile.

Spectral Analysis of Macro-Fiber Composites Measured Vibration of Double-Panel Structure Coupled with Solenoids.

Noise may have a negative impact on humans health and well being. Noise is a direct result of the vibration of structures. Many industrial workers and people using household appliances may be exposed to these harmful factors. To minimize their negative consequences, different approaches to noise and vibration reduction may be applied, e.g., active, semi-active or passive methods. In this research, a semi-active approach to vibration reduction of a cubic rigid casing enclosing a noise- and vibration-generating device is presented. One of the casing walls consists of double thin steel panels, coupled with the use of electromagnetic dampers—solenoids installed in the space between the panels. Other casing walls are built of single plywood panels. Vibrations of the outer (radiating) panel of the wall are measured by Macro-Fiber Composite patches. Spectral analysis of structure vibration is carried out to identify the benefits of the proposed coupling solution in terms of vibration reduction of the wall. The frequency range, where vibration reduction is observed, depends on the number of activated solenoids and the duty cycle of a Pulse Width Modulation (PWM) signal. Advantages and drawbacks of the proposed method are discussed and future improvements of the examined setup are suggested.

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).

Dynamic Modelling and Experimental Characterization of a Self-Powered Structural Health-Monitoring System with MFC Piezoelectric Patches.

The paper deals with theoretical and experimental studies for the development of a self-powered structural health monitoring (SHM) system using macro-fiber composite (MFC) patches. The basic idea is to integrate the actuation, sensing, and energy harvesting capabilities of the MFC patches in a SHM system operating in different regimes. As an example, during flight, under the effects of normal structural vibrations, the patches can work as energy harvesters by maintaining or restoring the battery charge of the stand-by SHM electronic board; on the other hand, if relevant/abnormal loadings are applied, or if local faults produce a noticeable stiffness variation of the monitored component, the patches can act as sensors for the power-up SHM board. During maintenance, the patches can then work as actuators, to stress the structure with pre-defined load profiles, as well as sensors, to monitor the structural response. In this paper, the investigation, based on the electromechanical impedance technique, is carried out on a system prototype made of a cantilevered composite laminate with six MFC patches. A high-fidelity nonlinear model of the system, including the piezoelectric hysteresis of the patches and three vibration modes of the laminate beam, is presented and validated with experiments. The results support the potential feasibility of the system, pointing out that the energy storage can be used for recharging a 3V-65mAh Li-ion battery, suitable for low-power electronic boards. The model is finally used to characterize a condition-monitoring algorithm in terms of false alarms rejection and vulnerability to dormant faults, by simulating built-in tests to be performed during maintenance.

Wireless stress sensor based on piezoelectric energy harvesting for a rotating shaft

A shaft is a mechanical component which transmits mechanical power and torque. A failure of the shaft may result in serious damage to machine in operation. Contact or noncontact monitoring techniques of rotating shaft have been developed in order to prevent this damage. The application of contact monitoring techniques requires the use of additional devices. First of all, a slip ring assembly, which enables a sensor supply and a sending of measurement data from a rotating shaft to some receivers. The use of the slip ring assembly, which requires an access to the front of the rotating shaft and an additional channel located in an inside of this shaft, are the most important weaknesses of contact techniques. In contrast to these approaches, the article presents a contact technique of stress monitoring in the rotating shaft, in which the slip ring assembly is not required. Presented contact technique consists of a wireless sensor based on piezoelectric energy harvester and a radio transmission system. The piezoelectric energy harvester consists of Macro Fiber Composite (MFC) patch and a system of energy storage and energy transfer control. MFC patch is directly glued to the rotating shaft surface and product an amount of electric energy which is enough to supply only a radio transmitter. Such built wireless sensor based on piezoelectric energy harvester was tested in laboratory stand which contained a rotating shaft with a system of force generation, a belt transmission with a system of generation of rotational motion, and a measurement system. The time between radio signals was measured for selected values of the rate of rotation of the shaft and for selected values of stress in the shaft in laboratory experiments. The experiments showed that dependence between the value of stress in the shaft and the number of radio signals per second can be approximated by a straight line. A method of measurement of stress in the rotating shaft was elaborated on the basis of the experiments. The method is based on the number of radio signals per second, which is linearly correlated with an average value of stress in the shaft, for the known value of the rate of rotation of the monitored shaft. The elaborated piezoelectric wireless sensor of stress were tested as a main part of sensor of cracks in the shaft surface in the last experiments. The time, after which the crack was detected, depended on a sampling period of such piezoelectric wireless sensor. The sampling period in turn depended on the three parameters: an average value of stress in a place where MFC patch is glued, the rate of rotation of shaft, a capacity of capacitor in a system of energy storage in a piezoelectric energy harvester.

Improved analytical homogenization of the piezoelectric macro-fiber composite: active layer embedded among passive layers

Predicting the effective electromechanical properties for piezoelectric fiber composite patches is crucial for analysis of smart structures equipped with such patches. In particular, analytical homogenization models are attractive but are limited by the complexity of the microstructure and the multiphysics involved. The macro-fiber composite (MFC) has emerged as the most popular piezoelectric fiber composite. But typical reports of its effective properties provide layerwise homogenization with low-order mechanical plate theories. This approach discards most of the out-of-plane properties and may introduce significant error from the assumptions about the plate kinematics. Moreover, the effective permittivities of the transducer are not available analytically. In an attempt to overcome these limitations, a new analytical scheme for homogenizing all layers in the MFC patch is proposed. Based on the newly discovered mechanics of structure genome, we avoid all kinematical assumptions and obtain an exact analytical solution for a periodic, multi-layered, linear-piezoelectric material. In doing so, we prove that in any such multi-layered composite, the in-plane strains and the transverse stresses are equal in each layer and the in-plane electric fields and transverse electric displacement are constant between the electrodes. Using this knowledge, a hybrid rule of mixtures is developed to homogenize all the MFC layers to obtain the complete set of properties of the full MFC. In doing the new analytical framework can homogenize any layered piezoelectric medium. Finally, since we were able to avoid the plate-kinematics assumptions, we present studies on their effect on the properties they obtain. We find that the in-plane elastic properties are not affected but the transverse shear moduli are overpredicted from 100% to 300%. What is more, studies are presented on how using the ubiquitous plane-stress-like assumptions to homogenize the fiber layers causes an 8% underprediction of the lateral elastic modulus of the MFC.

Topology optimization of piezoelectric macro-fiber composite patches on laminated plates for vibration suppression

This work presents a new methodology for the topology optimization of piezoelectric actuators in laminated composite structures with the objective of controlling external perturbation induced by structural vibrations. The linear-quadratic regulator (LQR) optimal control technique is used and the topology optimization is formulated seeking to find the optimum localization of the macro-fiber composite (MFC) active piezoelectric patch by means of the maximization of the controllability index. For the structural model, we propose a simplified MFC/structure interaction model. It is assumed that the MFC is one of the orthotropic material layers with an initial strain arising from the application of an electric potential. This strain acts on the remainder of the structure and its effect is considered analytically. Numerical results show that the proposed MFC structure interaction model presents good agreement with experiments and numerical simulations of models that take into account the electromechanical effect. Results of the actuator location optimization show that the implemented technique improves the structural vibration damping. Results and comparisons are presented for the vibration control strategy using the LQR controller.

Exploiting the subharmonic parametric resonances of a buckled beam for vibratory energy harvesting

The potential of harvesting vibratory energy via a bistable beam subjected to subharmonic parametric excitations is investigated. The vibrating structure is a buckled beam with two stable equilibria separated by a potential barrier. The beam is subjected to a superposition of a static axial load beyond its buckling load and a harmonic axial excitation whose frequency is around twice the frequency of the buckled beam’s first vibration mode. A macro-fiber composite patch is attached to one side of the beam to convert the strain energy resulting from the beam’s oscillation into electricity. The study considers two regimes of excitations: an amplitude sweep and a frequency sweep. In the first regime, the amplitude of excitation is quasi-statically varied while the excitation frequency is tuned at twice the natural frequency of the first vibration mode. In the second regime, the excitation frequency is swept forward and backward around the subharmonic resonant frequency while the amplitude of excitation is kept constant. A theoretical model which governs the electromechanical coupling of the transverse vibrations of the beam and the output voltage is used to monitor the response as the excitation parameters are changed. An experimental setup is also built and a series of tests is performed to validate the theoretical findings. It is shown that, depending on the amplitude and frequency of excitation, the harvester can perform small-amplitude periodic intra-well motion, intra- and inter-well chaotic motions, as well as periodic inter-well motions. Experimental results also show that, as compared to the classical linear resonance, utilizing the sub-harmonic resonance of a bistable energy harvesters can result in a broadband frequency response.

Model predictive control of piezo-actuated structures using reduced order models

A model predictive control method for a flexible structure consisting of two beams, equipped with macro fiber composite (MFC) patches as piezoelectric actuators is presented. Adjacent beams are connected at the tip by an elastic string. The equations of motion are derived by the evaluation of the extended Hamilton’s principle. Spatially dependent parameters are considered, due to different material characteristics of the carrier beams and the MFC patches. The spatially dependent variable is approximated using Galerkin’s method, leading to the state space representation of the beam structure by means of ordinary differential equations (ODEs). In order to avoid approximation errors, a high order approximation of the distributed-parameter system is required. With a model order reduction a small system describing approximately the same dynamics is obtained. A model predictive controller is designed, analyzed and evaluated in a simulation and at the experimental set-up. For the real-time capability of the model predictive controller a move blocking method by downsampling the prediction horizon is presented.

Control of flow separation around an airfoil at low Reynolds numbers using periodic surface morphing

The paper investigates experimentally the low Reynolds number flow (Rec=50,000) around a model that approximates a NACA 4415 airfoil and the control of separation using periodic surface motion. Actuation is implemented by bonding two Macro Fiber Composite patches to the underside of the suction surface. Time-resolved measurements reveal that the peak-to-peak displacement of the surface motion is a function of both the amplitude and frequency of the input voltage signal but the addition of aerodynamic forces does not cause significant changes in the surface behavior. The vibration mode is uniform in the spanwise direction for frequencies below 80 Hz; above this frequency, a secondary vibration mode is observed. The flow around the unactuated airfoil exhibits a large recirculation region as a result of laminar separation without reattachment and consequently produces relatively high drag and low lift forces. Various actuation frequencies were examined. When actuated at Vf+=2.0, the spectra in the vicinity of the trailing edge and near-wake were found to be dominated by the actuation frequency. Sharp peaks appear in the spectra suggesting the production of Large Coherent Structures at this frequency. The increased momentum entrainment associated with these enabled a significant suppression of the separated region. The result was a simultaneous increase in CL and decrease in CD and therefore a large increase in the L∕D ratio. In addition, a delay in the onset of stall results in a significant increase in the maximum achievable lift.

Homogenization for macro-fiber composites using Reissner–Mindlin plate theory

This article deals with the equivalent elastic and piezoelectric constants of macro-fiber composite patches. Two types of macro-fiber composite patches, macro-fiber composite-d31 and macro-fiber composite-d33, are considered. The former one is dominated by the d31 effect, while the latter one mainly uses the d33 effect. First, based on the representative volume element technique, homogenized elastic and piezoelectric constants of those fiber-based substrate layers in macro-fiber composite patches are obtained through linear mixing rules. Second, using the obtained homogenized constants for fiber-based substrate layers, the overall elastic and piezoelectric constants of macro-fiber composite patches are obtained by modeling of multi-layer laminated macro-fiber composites based on the Reissner–Mindlin hypothesis. Finally, the homogenized overall material constants of macro-fiber composite patches are used to evaluate the structural behavior of macro-fiber composite bonded smart structures. The results calculated by homogenized constants are compared with those obtained by multi-substrate-layer modeling approach, as well as with those reported in the literature.

Computation of macro-fiber composite integrated thin-walled smart structures

Due to high flexibility, reliability, and strong actuation forces, piezo fiber based composite smart material, macro-fiber composite (MFC), is increasingly applied in various fields for vibration suppression, shape control, and health monitoring. The complexity arrangement of MFC materials makes them difficult in numerical simulations. This paper develops a linear electro-mechanically coupled finite element (FE) model for composite laminated thin-walled smart structures bonded with MFC patches considering arbitrary piezo fiber orientation. Two types of MFCs are considered, namely, MFC-d31 in which the d31 effect dominates the actuation forces, and MFC-d33 which mainly uses the d33 effect. The proposed FE model is validated by static analysis of an MFC bonded smart plate.