STRUCTURAL SHAPE CONTROL USING MACRO FIBER COMPOSITE PIEZOELECTRIC SENSORS

AND ACTUATORSCaio dos Santos Guimarãesa, Flávio Luiz de Silva Bussamraa , Valérie Pommier-Budingerb

A INSTITUTO TECNOLÓGICO DE AERONÁUTICA - ITA , b INSTITUT SUPÉRIEUR DE L’AÉRONAUTIQUE ET DE L’ESPACE (Toulouse, França)

This work presents an approach for sizing and positioning piezoelectric Macro Fiber Composite (MFC) components for attenuating structural vibration. Even though this new material has become popular in the domain of structural vibration control for its easy conformability and repeatable manufacturing process, as well as their durability and efficiency, little is still known regarding the theoretical modeling of these piezoelectric components and their implementation in Finite Element Method software. Being designed empirically, one could say that MFCs have been poorly investigated when it comes to understanding their actuation properties as a function of their design parameters and electrical properties. The work proposes a finite element method to design smart structures with MFCs. An experimental model of a controlled clamped beam was used to validate the numerical results of the proposed method. The actuation and sensing capabilities of these MFC components were then compared to normal hard piezoelectric ceramics with results that had already been obtained in previous studies.

The MFC datasheet supplied by the fabricant does not supply enough information to simulate the d31 patch using our available FEM method. Information such as the d32 coefficient and the shear modulus are not described for all directions, even though it is needed as an input for a finite element method simulation. One possible argument that could be brought up is that these non-supplied coefficients would not have a sensible importance on the final results. A sensitivity analysis shows that the d32 coefficient, not given by the fabricant, can influence significantly depending on the results sought, and should be well estimated.

To model the d31-type MFCs, a mixing rule was used, in which with the information regarding the components of the patch, mean values of the patch’s properties can be calculated to be used as inputs for thefinite element software ANSYS. The results from this homogenization theory, as expected, showed a better correlation with experimental results, if compared to a simple simulation done using data from the supplied datasheet. The method proposed bases itself on the Uniform Field Method (UFM). The object of the mixing-rule is to find the equivalent property matrix for a material of two constituents. For this, the linear piezoelectricity constitutive equations were used.

[1] A. DERAEMAEKER; S.BENELECHI; A. BENJEDDOU; A. PREUMONT; Analytical and Numerical Computation of Homogenized Properties of MFCS: Application to a Composite Boom with MFC Actuators and Sensors; III ECCOMAS THEMATIC CONFERENCE ON SMART STRUCTURES AND MATERIALS, 2007

[2] V. POMMIER-BUDINGER; M.BUDINGER; J.RICHELOT; J.R. MARTINEZ; Design of Structures with Piezoelectric Ceramics for Active Vibration Control, Université de Toulouse, ISAE, 2008.

[3] A.BENT; Active Fiber Composites for Structural Actuation; Department of Aeronautics and Astronautics at Massachusetts Institute of Technology. Massachusetts, USA, 1997.

The MFC model proposed, when in use with the sizing and positioning Modal Base Theory method presented, gave good results of displacement prediction for the first mode of vibration. The actuation/sensing capability of the MFC model was also put into comparison with that of the hard piezoelectric ceramics. Even though the results were close enough so that it was inconclusive whether the MFC was in fact more efficient than the hard PZT ceramics (a tendency showed that this is in fact probable), the MFCs have been seen to have at the least an actuation capability as good as that of the ceramics. Along with this, the fact that it has a less brittle nature and is more easily adaptable to curved structures corroborates the statement that MFCs should replace the hard ceramics in Active Control systems.

The problem of structural vibration is studied in many branches of science. The phenomenon of flutter, for example, occurs at certain speeds and flight angles, when the aerodynamic forces on the airplane’s wing become close to the structure’s natural mode of vibration. A self-feeding vibration movement increases the aerodynamic load on the wing, which in turn helps feeding the vibrating movement. However, even weaker, less destructive vibrations on a wing can cause its accelerated fatigue on the long run. Among other issues, we can mention internal cabin noise which is a very important consequence of these undesired vibrations. As another example, more and more, the telecommunication missions need to send out bigger antennas, and research is constantly being done in order to reduce total weight. Given the requirements of precision in positioning, the structures need to be more and more rigid while keeping in consideration the reduction of weight problem. In general, reducing weight results in reducing stiffness, causing structural instability and therefore, unwanted vibration.

Various systems of Passive Control (damping systems attached to the structure that require no external influence or intervention) have been implemented to solve this sort of problem. The advance in study of Active Control of vibration, however, has been allowing controlling structure vibration with more precision and efficiency. The main idea in active control is to cancel out certain vibration by creating a source of similar vibration in the opposing direction, at each instant. At first sight, the expected performance of this type of damping system is unlimited (whereas the efficiency of passive control system depends strongly on the damping material used), since, at least in theory, the initial vibration can always be cancelled out. However, the performance efficiency value has some limitations, since an energy supply is needed to control these types of vibrations. Structures equipped with Active Control systems are called Smart Structures. They consist basically of a system of actuators and sensors, and a system of control. The sensor senses the vibration, and sends a signal to the control system. In turn, the control system interprets the signal and sends another signal for the desired deformation of the actuator, which will generate the opposing vibration.

BACKGROUND

PURPOSE

MATERIALS AND METHODS

RESULTS AND CONCLUSIONS

BIBLIOGRAPHY

The main applications of piezoelectric materials are as actuators and sensors for active control. The PZT (Lead Zirconate Titanate), for example, is a type of piezoelectric ceramic that has a very good actuation capability. However, hard ceramics suffer with a few down sides while used in active control. Their difficulty in adapting themselves to complex curved structures as well as their fragile composition limits their use in various geometries. One of the solutions developed is what is known as piezocomposite transducers. Piezocomposite transducers are made of an active layer between two electrode layers. The active layer is composed of a mixture of Epoxy Resin and Piezoelectric fibers of materials equivalent to the fore-mentioned piezoelectric ceramics. The problem in creating this type of piezocomposite patch is in how to display the active layer with the piezoelectric fiber and the epoxy resin matrix to be used in between layers. Even a very small thin layer of epoxy resin, due to its great difference of dielectric constant in relation to that of the piezoelectric fiber, causes a huge reduction in the electric field to pass by the active layer.

Between 1997 and 2002, MIT researchers attempted to solve this impasse by trying to increase the permittivity of the epoxy resin material, without success. Another proposed solution was to bring the electrodes in direct contact with the fibers, but the manufacturing difficulty made it a process not repeatable. An interesting solution appeared with the actuator called Macro Fiber Composites (or simply, MFCs) developed by NASA around the year 2000. The idea is that the piezoelectric fiber displayed as rectangular piezo-ceramic rods aligned with rectangular layers of the epoxy resin. The advantage lies in the cost of manufacturing (relatively cheap) and its repeatability. The disposition of the fibers allows them to be in direct contact with the electrodes, solving the problem of dielectric mismatch.

To be sure that the model is reasonable enough for further applications, a simple clamped beam structure was tested with 1 piezoelectric actuator and the experimental results were compared to those of the numerical modeling . In the experimental configuration, a laser vibrometer is used to measure the vibration velocity at a certain point of the structure. Achieving satisfying results, the same model of the patch would be able to be used for sizing active control structures. Sizing an active control system consists of determining the volume and position of piezoelectric patch that will give N.v = - F, where F is the external perturbation that should be cancelled. Knowing precisely how many patches to use can mean saving money (by not using more piezoelectric patches than needed), and can also mean protecting the structure (by not using less piezoelectric patches than needed). The existence of a maximum value of the electric field that can be applied to the piezoelectric patch, and a maximum stress that it can support, gives the idea of the maximum value of vibratory amplitude that it can generate.

To sum up, the method here proposed shows how to use a finite element model to design and predict an active control structure. Having a good FEM model, the parameters necessary are calculated, making it possible to predict displacements, as well as size and position the piezoelectric sensors and actuators.