Flávio D. Marques

Effective properties evaluation for smart composite materials

The purpose of this article is to present a method which consists in the development of unit cell numerical models for smart composite materials with piezoelectric fibers made of PZT embedded in a non-piezoelectric matrix (epoxy resin). This method evaluates a globally homogeneous medium equivalent to the original composite, using a representative volume element (RVE). The suitable boundary conditions allow the simulation of all modes of the overall deformation arising from any arbitrary combination of mechanical and electrical loading. In the first instance, the unit cell is applied to predict the effective material coefficients of the transversely isotropic piezoelectric composite with circular cross section fibers. The numerical results are compared to other methods reported in the literature and also to results previously published, in order to evaluate the method proposal. In the second step, the method is applied to calculate the equivalent properties for smart composite materials with square cross section fibers. Results of comparison between different combinations of circular and square fiber geometries, observing the influence of the boundary conditions and arrangements are presented. Keywords: smart composite materials, piezoelectric fiber composite, active fiber composite, finite element analyses, effective properties

Application of time-delay neural and recurrent neural networks for the identification of a hingeless helicopter blade flapping and torsion motions

System identification consists of the development of techniques for model estimation from experimental data, demanding no previous knowledge of the process. Aeroelastic models are directly influence of the benefits of identification techniques, basically because of the difficulties related to the modelling of the coupled aero- and structural dynamics. In this work a comparative study of the bilinear dynamic identification of a helicopter blade aeroelastic response is carried out using artificial neural networks is presented. Two neural networks architectures are considered in this study. Both are variations of static networks prepared to accomodate the system dynamics. A time delay neural networks (TDNN) for response prediction and a typical recurrent neural networks (RNN) are used for the identification. The neural networks have been trained by Levemberg-Marquardt algorithm. To compare the performance of the neural networks models, generalization tests are produced where the aeroelastic responses of the blade in flapping and torsion motions at its tip due to noisy pitching angle are presented. An analysis in frequency of the signals from simulated and the emulated models are presented. In order to perform a qualitative analysis, return maps with the simulation results generated by the neural networks are presented.

Aeroelastic parameter identification in wind tunnel testing via the extended eigensystem realization algorithm

Aeroelastic instability may occur in aircraft during flight, therefore their prediction represents an important issue within aerospace engineering. Experimental aeroelasticity is still an important field in providing the tools to validate and understand instability phenomena analysis. As many industrial practices require fast evaluations of critical conditions, e.g. flight flutter testing, there exists a natural demand for on-line aeroelastic identification. A number of different methods have been proposed to characterize systems, but recently those showing most success for on-line identification have been based on subspace approaches. The eigensystem realization algorithm (ERA) represents one of the first subspace methods for identification, with the advantage of dealing with multi-input, multi-output data. However, its need for repeated application of the singular value decomposition and a dependence on impulse response functions implies limitations to on-line identification. Generalization studies of the ERA method have led to recursive forms of that algorithm. A recursive form closely related to ERA has been developed in terms of a modified batch estimation approach, and it is denoted as the extended eigensystem realization algorithm (EERA). This work presents results on the application of extended EERA method viewing on-line aeroelastic parameters identification of an experimental apparatus in the wind tunnel. Designed to reproduce the conditions for typical section aeroelastic behavior, an apparatus has been used to show the EERA capabilities in identifying on-line aeroelastic frequency and damping parameters. Results have shown that the approach is robust and adequate for aeroelastic characterization during experimental activities.

Airfoil control surface discontinuous nonlinearity experimental assessment and numerical model validation

A variety of dynamic behaviors that may be encountered in aeroelastic systems with discontinuous nonlinearities has motivated investigations that may support future applications in flight controls design, flutter prediction, instability characterization and energy harvesting. In this paper, the case of an airfoil with control surface freeplay is assessed experimentally and modeled numerically using an alternative continuous approximation for the discontinuous nonlinearity based on hyperbolic tangent function representation. The unsteady aerodynamic loads are computed using the modified unsteady Theodorsen approximation for arbitrary motions. The validity of the proposed freeplay representation is performed through comparison with experimental data. Adjustments to the pitching restoring moments have been carried out to account for a smooth polynomial concentrated nonlinearity. Data analysis is performed to characterize and investigate the experimental signals. Sub-critical bifurcation behavior is observed from both experimental data and the numerical model prediction. The results confirm the validity of hyperbolic tangent function combinations for freeplay nonlinearity representation for the experimental setup conditions.

Numerical model for the simulation of fixed wings aeroelastic response

A numerical model for the simulation of fixed wings aeroelastic response is presented. The methodology used in the work is to treat the aerodynamics and the structural dynamics separately and then couple them in the equations of motion. The dynamic characterization of the wing structure is done by the finite element method and the equations of motion are written in modal coordinates. The unsteady aerodynamic loads are predicted using the vortex lattice method. The exchange of information between the aerodynamic and structural meshes is done by the surface splines interpolation scheme, and the equations of motion are solved iteratively in the time domain, employing a predictor-corrector method. Numerical simulations are performed for a prototype aircraft wing. The aeroelastic response is represented by time histories of the modal coordinates for different airspeeds, and the flutter occurrence is verified when the time histories diverge (i.e. the amplitudes keep growing). Fast Fourier Transforms of these time histories show the coupling of frequencies typical of the flutter phenomenon.

An Experimental Study of Added Mass on a Plunging Airfoil Oscillating with High Frequencies at High Angles of Attack

Experiments are conducted to measure the unsteady plunging forces on an airfoil at zero forward velocity. The aim is to investigate the variation of the added mass with the oscillation frequency of the wing section for various angles of attack. Data of the measured forces is presented and compared with predicted forces from potential flow approximations. The results show a significant departure from those estimates especially at the high frequencies. The results show that the added mass varies linearly with the frequency of the oscillations. Furthermore, the added mass is largest for the cases of 10 and 20 degrees angles of attack. These results raise the question of how to account for the unsteady flow generated by the airfoil motion.

Chaotic Patterns in Aeroelastic Signals

This work presents the analysis of nonlinear aeroelastic time series from wing vibrations due to airflow separation during wind tunnel experiments. Surrogate data method is used to justify the application of nonlinear time series analysis to the aeroelastic system, after rejecting the chance for nonstationarity. The singular value decomposition (SVD) approach is used to reconstruct the state space, reducing noise from the aeroelastic time series. Direct analysis of reconstructed trajectories in the state space and the determination of Poincare sections have been employed to investigate complex dynamics and chaotic patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincare mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents.

On the Investigation of State Space Reconstruction of Nonlinear Aeroelastic Response Time Series

Stall-induced aeroelastic motion may present severe non-linear behavior. Mathematical models for predicting such phenomena are still not available for practical applications and they are not enough reliable to capture physical effects. Experimental data can provide suitable information to help the understanding of typical non-linear aeroelastic phenomena. Dynamic systems techniques based on time series analysis can be adequately applied to non-linear aeroelasticity. When experimental data are available, the methods of state space reconstruction have been widely considered. This paper presents the state space reconstruction approach for the characterization of the stall-induced aeroelastic non-linear behavior. A wind tunnel scaled wing model has been tested. The wing model is subjected to different airspeeds and dynamic incidence angle variations. The method of delays is used to identify an embedded attractor in the state space from experimentally acquired aeroelastic response time series. To obtain an estimate of the time delay used in the state space reconstruction from time series, the autocorrelation function analyis is used. For the calculation of the embedding dimension the correlation integral approach is considered. The reconstructed attractors can reveal typical non-linear structures associated, for instance, to chaos or limit cycles.

Effective properties evaluation for smart composite materials with imperfect fiber–matrix adhesion

A numerical approach is proposed to evaluate the effective properties of piezoelectric fibers embedded in a nonpiezoelectric matrix, considering imperfect contact between fiber and matrix. Firstly, a Representative Volume Element is analyzed via Finite Element Method for different loadings with suitable boundary conditions applied in a unique way. Transversely, isotropic piezoelectric materials with circular and square cross-section fibers are analyzed for square arrangements with different fiber volume fractions as well as with perfect and imperfect contact conditions. The results for circular and square cross-section fibers with perfect contact are compared to the literature data in order to verify the consistency of proposed numerical approach. After that, the results with imperfect contact are discussed, observing the influence of the fiber volume fraction and the level of the imperfection in the fiber–matrix adhesion. Results show that the imperfect contact not only influences the elastic constants, but also the piezoelectric effective values.

Design of an experimental flutter mount system

Aeroelastic instabilities may occur in aircraft surfaces, leading then to failure. Flutter is an aeroelastic instability that results in a self-sustained oscillatory behaviour of the structure. A two-degree-of-freedom flutter can occur with coupling of bending and torsion modes. A flexible mount system has been developed for flutter tests in wind tunnels. This apparatus must provide a well-defined 2DOF system on which rigid wings encounter flutter. Simulations and Experimental Tests are performed during the design period. The dimensions of the system are determined by Finite Element analysis and verified with an Aeroelastic Model. The system is modified until first bending and torsion modes become the first and second modes and other modes become higher than these. After this, a Modal Analysis is performed. An identification algorithm, ERA, is used to determine modes shape and frequencies from experimental data. Detailed results are presented for first bending and torsion modes, which are involved in flutter. The flutter mechanism is demonstrated by Frequency Response Functions obtained in several wind tunnel velocities until flutter achievement and by a V-g-f plot obtained from an identification process performed with an extended ERA. Mode coupling, damping behaviour and the self-sustained oscillatory behaviour are verified characterising flutter.