EXPERIMENTAL AND NUMERICAL STUDY OF AN AUTONOMOUS
FLAP
Lars O. Bernhammer1, Sachin T. Navalkar1, Jurij Sodja1, Roeland De Breuker1 , Moti Karpel2
1
Delft University of Technology Delft, 2629HS, The Netherlands
l.o.bernhammer@tudelft.nl 2
Technion Israel Institute of Technology Haifa, 32000 Israel
Keywords: Autonomous free-floating flap, aeroelastic instability, limit cycle oscillation.
Abstract: This paper presents the experimental and numerical study of an autonomous load
alleviation concept using trailing edge flaps. The flaps are autonomous units, which for instance can be used for gust load alleviation. The unit is self-powered and self-actuated through trailing edge tabs
which are mounted as aerodynamic control devices on free-floating flaps. The flaps are mass underbalanced such that flutter occurs in the operational envelope unless it is suppressed by the control system. Therefore the system is very responsive to both external excitation and control activity of the trailing edge tab. The electrical energy for control activities is then generated by maintaining the
flap in controlled limit cycle oscillations. The numerical simulation of such an autonomous flap system demonstrates the ability of controlling the amplitude of limit cycle oscillations, while a net gain in power can be used to charge the battery. These results are compared to experimental results
obtained by a wind tunnel study of the said system.
1 INTRODUCTION
The structural design of aircraft wings and wind turbine blades is strongly influenced by their response to gusts or turbulence. A potential concept to alleviate the gust induced loads are actively controlled trailing edge flaps. Flaps combine a sufficiently high control authority on the lift coefficient with a high frequency bandwidth. One such concept are free-floating flaps (FFF). These flaps are free to rotate around a pre-defined hinge axis and are aerodynamically actuated by modifying flow with the help of a small trailing edge tab (Figure Figure 2). The concept has first been introduced by Heinze and Karpel [1]. Their investigation concerns a single FFF to control a very flexible wing. The research has been expanded by Bernhammer et al. [2], who investigated the suppression of free-play introduced flutter on a vertical tail plane with two FFF. Pustilnik and Karpel [3,4] deepened this research by performing studies on the limit cycle behavior of the experiment performed by Bernhammer et al. [2].
In the current research, the load suppression function of the free-floating flap is combined with energy harvesting as presented by Bernhammer, De Breuker and Karpel [5]. In their approach, the FFF is brought into limit cycle oscillations (LCO) either using structural delimiters for the flap deflection or by control activity of the trailing edge flap. It was shown that exploiting the aeroelastic instabilities can dramatically increase the output of the energy
main wing. Similar research on exploiting aeroelastic instabilities has been performed by Bryant and Garcia [6] and Bryant, Fang and Garcia [7] by investigating the power production during flutter of a cantilever beam with a free-floating flap at its end. In their experiments, the mechanical energy was converted into electrical energy using piezoelectric patches embedded into the cantilevered beam. Similarly to Bernhammer, De Breuker and Karpel [5], Park et al. [8,9] use electromagnets to harvest energy. The magnet is attached at the free tip of a T-shaped cantilevered beam. Vortices are shed from the end plate, thereby causing a one degree of freedom flutter.
The integration of both control and harvesting application into a single device has been proposed by Bernhammer et al. [10] and was evaluated experimentally by Bernhammer et al. [11]. Their design combines the functionality of the free-floating flap with the trailing edge tab for control applications with the energy harvester design of Bernhammer, De Breuker and Karpel [5]. The current paper complements the experimental research by providing a numerical study of the autonomous flap concept and a comparison to the experimental results. First, the concept of the autonomous flap is detailed followed by a summary of the wind tunnel model design and the most relevant experimental results. The numerical approach is outlined and the numerical results are presented. Finally a comparison between the numerical model and the experimental results is presented.
2 CONCEPT OF THE AUTONOMOUS FLAP
Autonomous flaps combine the functionality of the free-floating flap with the functionality of an energy harvester. The autonomous flap concept is schematically presented in Figures 1 and 2. The free-floating flap contains all subsystems such as sensors, a control system, actuators, an energy harvesting device and the trailing edge tab, making the system completely autonomous. This permits the installation of the autonomous flap as plug and play device on existing airframes during retrofit operations and makes the concept extremely suitable for easy replacements during maintenance activities.
Figure 1 shows the operational logic of such a device. The flap motion is measured by a single or a set of sensors. In the current paper, accelerometers are used for this purpose. At the same time, the vibration of the flap is converted into electrical energy by the energy harvester. The rotational velocity of the flap is amplified by a gear box in order to overcome the most significant limitation of the approach of Bernhammer, De Breuker and Karpel [5], which was the limited power output due to the low rotational velocities. The generated energy is used both to charge a battery and to power the sensors and the actuation systems. The battery serves as an energy source for non-LCO operation modes. The sensors provide input to the control system, which commands the actuators that set the trailing edge tab position, which in turn controls the moment around the hinge axis, thereby driving the flap motion. Aerodynamics are used as a lever to increase the forces on the wing structure. While the required control force on the trailing edge tab is small, the overall force which can be generated by the free-floating flap is significantly higher.
Figure 1: Flow chart of autonomous flap concept [10]
The locations of the subsystems are shown schematically in Figure 2. The electric generators are aligned with and connected to the rotational axis. The connection to the FFF is geared-up in order to significantly increase the generator's rotational velocity with respect to previous studies [5]. It is desirable to operate the flaps close to the flutter point for two reasons. Not only does the amount of generated electricity increases dramatically when passing the flutter boundary, but so does the control efficiency as the flaps become extremely responsive to a trailing edge tab excitation, which decreases the actuation power requirements. A methodology to maintain the system in a low amplitude limit cycle oscillation will be introduced in the controller design section.
3 AEROELASTIC TEST SET-UP 3.1 Aeroelastic Apparatus
The autonomous, free-floating flap concept was applied to an aeroelastic apparatus consisting of a wing that can undergo pitch and plunge motion. This test set-up has been exhaustively validated for conventional flap systems using CFD data [12]. The aeroelastic apparatus is depicted in Figure 3. The wing model (F) is attached by springs to a frame built of sidewalls (C), which are connected by beams (D). This frame is mounted on a table (B), which can be adjusted to the height of the jet exit of the open test section (A). Struts (E) on both sides of the frame are used to increase its stiffness. Plunge and pitch motion of the wing are decoupled by a global translating system (I) on which rotational springs are mounted. The properties of this set-up are given in Table 1. The springs (H) are attached to load cells, which measure the lift plus inertial forces of the wing. The springs are connected to side plates (I), which are equipped with a pitch sensor and accelerometers that are used as input to the controller. Strain gauges are attached to the root of the wing section and measure the lift produced by the wing.
Figure 3: Experimental set-up in open jet facility: the jet exit (A), the table (B), two sides upright (C), connecting beams (D), struts (E) and the wing (F). Moment sensors (G) are attached to springs (H) on movable side plates
(I) [12]
3.2 Autonomous Flap Design
The detailed design of the autonomous, free-floating flap model was presented by Bernhammer et al. [10]. Table 2 provides an overview of the equipment that has been installed in the autonomous flap. The arrangement of all components in the flap is shown in Figure 4. The accelerometer (A) measures motion in the plunge direction. The potentiometers (B) and the gear boxes (C) hinge to the main wing. The gear box is connected to a generator, in which the rotating magnet is connected to the wing and the stator is integrated in the flap. A pair of servo-motors (D) drives the trailing edge tab (E).
Property Value
Width 1800 mm
Chord 500 mm
Airfoil profile DU96-W-180
Flap chord 100 mm
Plunge spring stiffness 8225 N/m2 Structural damping 77.9 kg/s
Wing assembly mass 22.7 kg
Wing mass 15.2 kg
Side plate mass 7.5 kg
Eigenfrequency of plunge mode 3.0 Hz Table 1: Properties of aeroelastic set-up
Property Value
Material SL-Tool STONElikea
Density 1.37 kg/cm3
Young’s modulus 3.5 GPa
Tensile strength 47 MPa
Skin thickness 2 mm
Servo actuator HiTech HS-7115THb
Gear box Apyxdyna AM022c
Gear ratio 1:80
Generator Kinetron MG 23.0d
Analogue devices ADXL78e
Table 2: Flap design parameters
a. https://www.robotmech.com/uploads/media/robotmech-SL-TOOL-Stonelike\_EN.pdf b. http://hitecrcd.com/products/servos/premium-digital-servos/hs-7115th-hv-ultra-slim-titanium-gear-servo/product c. http://www.apexdyna.nl/en/producten/am-series.html d. http://www.kinetron.eu/micro-generator-technology/ e. www.analog.com/en/mems-sensors/mems-inertial-sensors/adxl78/products/product.html
Figure 4: Free-floating flap with active trailing edge
3.3 Open Jet Facility
The experiment was performed in the Open Jet Facility (OJF) of Delft University of Technology. This wind tunnel is has been designed for large scale models and is particularly suitable for unsteady aeroelastic investigations because of its open test section. The tunnel is a closed circuit design with a jet exit into the test section of 2.85m by 2.85m. Wind speeds up to 35 m/s can be reached, which correspond to Reynolds numbers of 1,230,000 based on a 50cm chord. This Reynolds number is lower than in aircraft or wind turbine applications, but high enough to eliminate viscous flow effects. The Reynolds number at the predicted flutter speed is 320,000 with a reduced frequency of 0.136, which is well within the unsteady region and corresponds to the 3rd flapwise eigenfrequency in typical 5MW turbines.
4 AEROELASTIC ANALYSIS
The design process of the wind tunnel model can be found in [10,11]. Hence, only a summary of the critical design results is presented here in order to understand the aeroelastic response of the model in the wind tunnel experiment and the presented time domain simulations. One of the main design parameters was the flutter speed as it is critical to operate the model at the flutter boundary. The design variable was the plunge stiffness, which could be matched by selecting appropriate springs for the plunge-pitch apparatus. The aeroelastic analysis was performed in MSC/Nastran using a PK-method [13]. Figure 5 shows the most relevant modes. Elastic modes of the wing do not contribute to the aeroelastic response of the system as their frequency is more than an order of magnitude higher than the rigid-body modes. The system becomes unstable due to an interaction of the flap deflection modes and the plunge dominated mode at a frequency of 3Hz and a velocity of 11m/s. The full frequency and damping plots are provided by Bernhammer et al. [11].
Figure 5: Structural modes
The aeroelastic time domain simulation was implemented in Simulink and re-uses the framework developed by Bernhammer, De Breuker and Karpel [5]. The structural mode shapes are obtained by MSC/Nastran. The first 15 modes have been used as input to an aeroelastic analysis in ZAERO [14]. ZAERO was used to extract the aeroelastic state-space time-domain model based on rational function approximation of the unsteady aerodynamic force coefficient matrices [14]. A modal damping coefficient of 0.057 has been applied to the structural model as identified by Sterenborg [12] for the test set-up. The aerodynamic model was divided into 5 zones, one for the main wing and two for the flaps, one for each trailing edge tab. Figure 6 shows how the state-space model was integrated into the Simulink simulations. A feedback loop is included for each flap, introducing electromechanical forces and forces of the structural delimiters for the flap deflection.
g
x= A x+ B u+u
y= C x+ D u
(1) where ae ae ac c ac c ac cA
B
0
A=
0
A
0
0
0
A
0
0
B= B
0
0
B
C
0
C=
0
C
ac c ae ac c
D
0
D=
0
D
x
x= x
x
A, B, C and D are the state, the input, the output and the feed-through matrices, respectively. x is the state vector containing the modal displacements and velocities, the aerodynamic lag and the control states and u is the input vector of the trailing edge tab deflection, the non-linear feedback moments and gust time history. Actuator dynamics and a controller have also been included. Equation 1 describes the open-loop model. The subscripts ‘ae’ denote the aeroelastic model, ‘ac’ the actuator and ‘c’ the controller. The system was closed by including a feedback loop from the output vector y to the input vector u. The electromagnetic resistance moment of the flap is modeled based on the electrical power of the generator. It is a function of the rotational velocity.
0
open bat bat open batd
nl
U
U
U
U
dt
U
U
(2)where n is the number of coil turns, l the length of a coil loop and ϕ the magnetic field strength. The magnetic field strength was determined experimentally by matching the generated voltage during the wind tunnel experiment. The coefficient k approximating the term
nl
k
2, has a value of 9.1mNms/rad and a gear ratio of 80 is applied. The resistance in the loopR
coil
R
var is chosen to be 75Ω, which corresponds to the impedance matching condition. The structural stiffness coefficient K is 3800Nm/rad and the structural free-play zone is 17 degree in both directions, again corresponding to the experimental results.The generated electrical power P, which is harvested, damps the system. The electromechanical power of the damping is given in Equation 3. A mechanical power of the same magnitude is generated by opposing moments.
2 2 2 var var k coil coild
nl
nl
dt
P
R
R
j L
R
R
(3)θ is the flap deflection angle. Note that Equation 3 is approximated using a constant magnetic flux ϕk multiplied by the rotational velocity. Also, the impedance jωL is omitted as it is two
orders of magnitudes smaller than the resistance of the coil Rcoil and the variable resistance
Rvar. The mechanical moments, which cause in structural damping, have been implemented in
generalized coordinates into the state-space system together with a structural free-play zone as shown in Figure 6. The output of the state-space system are the plunge acceleration of the wing and the rotation angles of both free-floating flaps. The rotational velocities are obtained as output of the aeroelastic state-space system and serve as input to Equation 3.
Compared to the simulations of Bernhammer, De Breuker and Karpel [5] a control loop has been included to the aeroelastic simulations as well. The controller architecture is analogous to the experiment [11] and the controller parameters are provided in Table 3
1
2 3K s
K s K s K s
(4)where K1(s) = k is a simple gain, K2(s) is a phase lead compensator and K3(s) is an inverted
notch. The filter K2 adds an adequate amount of phase within the bandwidth to achieve the
right amount of damping,
1 2 2 1 1 s K s s (5)and K3 enhances feedback at a single frequency, which is the same as the resonance frequency
ωr = 3.0 Hz:
s r
2 2s r 1While in the experiment the plunge frequency remained constant for all wind speeds, numerically a drop in the frequency of the plunge mode has been observed from 3.0 Hz for 0.0 m/s to 2.3Hz at 11.0 m/s, which is the flutter speed. The notch filter in the controller design has been scheduled to match the frequency at the given wind speed.
Parameter Symbol Value
Controller gain k 0.0016
Phase lead start frequency ω1 0.001 Hz
Phase lead end frequency ω2 0.5 Hz
Resonant frequency ωr
Scheduled with wind speed
Notch damping ζ 0.5
Table 3: Control parameters
5 EXPERIMENTAL RESULTS 5.1 Limit Cycle Oscillation
During the experiment, two different types of limit cycles were investigated, namely structurally limited cycles and limit cycles that were reached through control of the trailing edge tab. The structural limit was achieved by limiting the maximum deflection of the flaps during the experiment from -20 to 20 degrees. This is slightly higher than in the numerical simulations. A quasi rigid stop was used in the experiment, while in the numerical simulations the structural limit was modelled using a smoother transition to the delimiters, the overall maximum deflection was equal. Figure 7 shows the structurally limited oscillations. Due to high damping for low amplitude oscillations, the trailing edge tabs were used to initiate the vibration. Only when the vibration amplitude increased the modal damping coefficient of 0.057, which had been identified, was reached.
When an oscillation at 3Hz was initialized by the trailing edge tab, the flap immediately started to vibrate in the plunge dominated mode. These oscillations increased as a result of the unstable aeroelastic system until the flap deflection was limited by the structural delimiters. A time delay between flap motion and growth in wing plunge was observed as a result of the wing inertia. While the tab is not active, a sustained limit cycle oscillation was observed in the experiment. Once the controller is active, the amplitude of the flap deflections reduce immediately to below 10 degrees from which point on the amplitude decays further until the system is completely damped out. The oscillation of the wing decays much slower, such that the wing is at rest only 4 seconds after the controller has been switched on, while the flaps already stopped vibrating after 2 seconds.
Figure 7: Structurally limit cycle oscillation
The second possibility to achieve limit cycle oscillations is to actively use the controller to limit the cycle amplitude. The controller design, which was used both in numerical simulations and for the first experiment, is updated by an on/off condition, such that the controller is only active when the amplitude of the flap oscillation exceeded a specified threshold. In the case of the experiment this threshold was 30 degree peak-to-peak amplitude. The initialization of the limit cycle oscillation is identical to the controlled experiment. The differences occur only when the control system is activated after 11 seconds as shown in Figure 8. Instead of stabilizing the flap almost immediately, the vibration is slowly reduced to a lower amplitude limit cycle. To maintain the amplitude, the controller switches between passive and active phases, with the majority of the total LCO time being in a passive mode. The controller is active only 11% of the time. When the tab is controlled, it almost instantly reduces the amplitude of the flap oscillation. Due to the inertia of the main wing, the system keeps vibrating, which through aerodynamic forces causes the flap to oscillate once the controller is switched off. A stable pattern develops with the flap amplitude decreasing rapidly, when the controller is active, and increasing over 3-4 cycles while the controller is passive.
5.2 Power Balance
During structural limit cycle oscillation, the generators were producing a mean power of 0.3133W or a root mean square power of 0.564W. This harvested energy should exceed the
experiment and the majority of the consumption could be attributed to the aerodynamically unloaded oscillation of the actuators. The difference in power consumption between cases including and excluding aerodynamic forces peaks at 3Hz as shown in Figure 9. At higher frequencies, the power source was unable to provide the demanded voltage of 7.6V to the actuators, such that the difference between unloaded and loaded oscillation approaches 0W. Assuming a time fraction of 11% of controller activity, this translates into an average power consumption of 0.0427W, which is 13.6% of the generated power.
Figure 8: Controlled limit cycle oscillation
6 RESULTS OF TIME DOMAIN SIMULATION 6.1 Limit Cycle Oscillation
In a first step the controller design of the experiment has been tuned to the numerical simulation to account for the frequency shift as described before. Figure 10 displays the time history of the limit cycle oscillation and the subsequent controller activity. The results aim to reproduce the experimental counterpart presented in Figure 7. In contrast to the experiment, the vibration in the numerical results has not been initialized by tab activity, but by a small initial deflection of the plunge mode. The result is identical. The perturbation post flutter speed leads to a diverging motion until the flap reaches its structural limit. When the controller is activated after 5 seconds, the system stabilizes and the vibrations damp out. The time scale in the numerical simulation associated to the damping is longer than in the experiment, a fact that can be attributed to the lower tab deflections with a maximum of 10
degrees, while in the experiments, the values reached can be up to 20 degree. This results in a lower damping of the flap motion and consequently a longer decay time.
Figure 9: Power consumption of actuation system as function of actuation frequency and wind speed for 20 degree tab amplitudes
Figure 10: Structural limit cycle and active control
The second comparison study concerns the controlled limit cycle through tab activity. The numerical results are shown in Figure 11. The corresponding experimental results are presented in Figure 8. The numerical procedure is identical to the methodology for obtaining Figure 10, except that a controller on/off condition is included based on the recent time history of the flap oscillation amplitude. Figures 10 and 11 are identical until the first time the
amplitude of 10 degrees, similar to the experimental results (Figure 8). However, two differences in the results can be observed. The first difference is that the control activity during the experiment causes an immediate drop in flap oscillation amplitude from 15 to 5 degree in the simulation, while in the numerical simulation this drop is much lower. The reason is again, that the tab deflections set by the controller are around 5 degree, while in the experiment they reach 20 degrees. The result is a more continuous control activity. In the experiment the time fraction the controller was active was 11%, while in the numerical simulations this time fraction is above 60%. The energy requirements on the flap are however lower, as the power consumption of the flaps is proportional to the rotational velocity of the tab and the aerodynamic forces on the flap, which are proportional to the amplitude when assuming that the lift is a linear function of the angle of attack. Decreasing the tab amplitude by a factor 4 yields a decrease in actuation requirements by a factor 16.
The second difference is that the a repetitive pattern observed in the experimental results is not reproduced by the numerical simulation. In the experiments, the strong drop in flap amplitude caused by control activity, recovers over several cycles before the amplitude surpasses the specified limit. Due to the small drop in flap oscillation amplitude in the numerical simulations, the oscillation might or might not grow to the specified amplitude within a single cycle.
Figure 11: Structural limit cycle and active control
6.2 Numerical simulation of power production
In a final step the power production of the autonomous flap system has been analyzed. Figures 12 and 13 show the time history of flap rotation and voltage production. The voltage provided in Figure 13 is the sum of the voltages of all 4 actuators as if they were connected in series. While the first 3 wind speeds correspond to aeroelastically stable systems, for 12m/s the autonomous flap system is operating past the flutter point. The first three cases produce a small voltage at the beginning, due to the vibrations introduced by the initial conditions. For 10m/s the flap deflection amplitude reaches 7.5 degree at which point the controller becomes active for a very short period, which causes the results with and without controller to be different. For wind speeds of 3 and 8m/s, controlled and uncontrolled results are identical. For
12m/s the open-loop results are confined by the structural limit, while in the closed-loop case, the controller sets the limit cycle amplitude.
Figure 12: Rotation angles open (-) and closed loop (- -)
The flap vibrations are converted into electrical energy. The fraction of the extracted energy is small, such that the electromechanical damping effect remains negligible. Due to the lower amplitude of the controlled limit cycle, the voltage output of the system is reduced in the closed-loop case.
In a final step, the average power production using different limit cycle amplitudes was computed for a range of wind speeds. During the experiment, a mean power per flap of 313mW was produced. Figure 14 shows the total power of both flaps combined due to the initial conditions with a small amplitude in plunge mode. The time results include the incremental phase of the oscillation, such that the actual power production during LCO, certainly for 11m/s, which is only slightly unstable, will be slightly higher. By far the highest power production is achieved for the structural LCO. For a wind speed of 12m/s a value of 510mW is reached, which corresponds well with the experiment, certainly when considering that the LCO production in the numerical simulation should be slightly higher than the reported value. The controlled limit cycles with an amplitude of 10 degrees produce 111mW, while for 5 degrees, the average power is 29mW.
Figure 14: Power production of generators due to an initial impulse
CONCLUSIONS
The concept of the autonomous, free-floating flap has been studied experimentally and numerically. The concept was retrofitted into an aeroelastic apparatus for wind tunnel research. Two autonomous flaps containing accelerometers, generators, and servo actuators driving a trailing edge tab have been installed on a 1.8 m span wing. The flutter speed of the system was numerically determined to be 11m/s. Experimentally the flutter speed could not be exactly determined due to non-linearities in the damping of the spring system for low amplitude oscillations.
A controller has been designed that forces the system into stable limit cycle oscillations with a lower amplitude than structurally limited oscillations. It was shown that the system was able to generate sufficient energy to power sensors and actuators such that the system can act autonomously during the limit cycle operation. The results have been numerically confirmed. The control activity in the numerical model was lower than in the experiment, such that the damping of the flap caused by the trailing edge tab was reduced compared to the experimental study. The result is a more continuous control activity with lower power requirements.
ACKNOWLEDGMENTS
This research has been funded by the Far and Large Offshore Wind (FLOW) project of the Dutch Ministry of Economic Affairs.
REFERENCES
[1] Heinze, S. and Karpel, M., Analysis and wind tunnel testing of a piezo-electic tab for aeroelastic control applications, Journal of Aircraft, Vol. 43, No. 6, 2006, pp. 1799-1804.
[2] Bernhammer, L.O., De Breuker, R., Karpel, M., and van der Veen, G., Aeroelastic Control Using Distributed Floating Flaps Actuated by Piezoelectric Tabs, Journal of Aircraft, Vol. 50, No. 3, 2013, pp. 732-740.
[3] Pustilnik, M. and Karpel, M., Dynamic Loads Alleviation Using Active Free-Floating Flaps," Proceedings of 53rd Israel Annual Conference on Aerospace Sciences, Haifa, Israel, 2013.
[4] Pustilnik, M. and Karpel, M., Loads, Vibration and Maneuver Control Using Active Floating Flaps, Proceedings of International Forum on Aeroelasticity and Structural Dynamics, Royal Aeronautical Society, Bristol, UK, 2013.
[5] Bernhammer, L., Karpel, M., and De Breuker, R., Energy Harvesting for Actuators and Sensors using Free-Floating Flaps, Journal of Intelligent Material Systems and Structures, submitted.
[6] Bryant, M. and Garcia, E., Modeling and Testing of a Novel Aeroelastic Flutter Energy Harvester, Journal of Vibration and Acoustics, Vol. 133, 2011, pp. 1:10.
[7] Bryant, M., Fang, A., and Garcia, E., Self-powered smart blade: Helicopter blade energy harvesting, Proceedings of the SPIE, Vol. 7643, 2010, pp. 1:10.
[8] Park, J., Kim, K., Kwon, S., and Law, K. H., An aero-elastic utter based electromagnetic energy harvester with wind speed augmenting funnel, Proceedings of Int. Conference on Advances in Wind and Structures, KAIST, Seoul, Korea, 2012.
[9] Park, J., Morgenthal, G., Kim, K., Kwon, S., and Law, K. H., Power Evaluation for Flutter-Based Electromagnetic Energy Harvester using CFD Simulations, Proceedings of First International Conference on Performance-based and Life-cycle Structural Engineering, Hong Kong, China, 2012.
[10] Bernhammer, L., Sodja, J., Karpel, M., and De Breuker, R., Design of an autonomous ap for laod alleviation, Proceedings of 25nd International Conference on Adaptive Structures and Technologies, The Hague, Netherlandes, 2014.
[11] Bernhammer, L., Navalkar, S., Sodja, J., Karpel, M., and De Breuker, R., Experimental investigation of an autonomous flap for load alleviation, Proceedings of AIAA SciTech, Kissimmee, USA, 2015.
[12] Sterenborg, J., Experimental and numerical investigation of an aeroelastic wing, TU Delft, 2014, PhD Thesis.
[13] Rodden, W. and Johnson, E., MSC Nastran Aeroelastic Analysis User's Guide, MSC. software corporation USA, 1994.
[14] Zona Technology, ZAERO Theoretical Manual, Scottsdale, USA, 2011.
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