Financial support of CNPq, CAPES and FAPESP.

 

Nonlinear aeroelastic responses can be observed when the nonlinear behavior comes from the structural dynamics,  or from the unsteady aerodynamic loading, or in both cases together. This research topic has focused on structural nonlinearities in typical aeroelastic sections. Most of the results are related to exam the freeplay nonlinearity in the airfoil control surface hinge and combined hardening in pitching motion with control surface freeplay acting together. Experimental and numerical investigation has been performed, where for numerical aerodynamic modeling a linear, potential flow approach was used and validated.

Results are concentrated in the following research:

  • Characterization and detection of nonlinearities related to freeplay of airfoil control surface … more
  • Bifurcation phenomena due to hardening and free-play nonlinearities combined in a typical aeroelastic section … more

 

Characterization and detection of nonlinearities related to freeplay of airfoil control surface
EXPERIMENT_1

Experimental apparatus for aeroelastic tests on structural nonlinearities effects in typical section.

Characterization of nonlinearities in aircraft is critical to the solution of aeroelastic problems where an optimal relation between performance and safety is desirable.

Nonlinear time series analysis and identification techniques were used to an airfoil  with control surface freeplay experimental signals and numerical prediction. A mathematical model of typical section with control surface freeplay nonlinearity was implemented and used to generate a reliable database to test the ability of nonlinear time series analysis methods.

cima

Control surface freeplay adjustment device.

The techniques are applied to the experimental signals, such as state space reconstruction, Poincaré sections and determination of system’s invariants, as the largest Lyapunov exponents, etc..

 

MAIN RESULTS

(1) Use of combination of hyperbolic functions to represent the freeplay nonlinearity – experimental validation:

tanh_01

Bifurcation diagram using different representations for freeplay in control surface hinge (Vasconcellos et al., 2012).

Because discontinuous behavior should, in principle, be represented by a discontinuous function, important issues on equations of motion time integration arise. Alternative approach has been proposed where a combination of hyperbolic tangent functions is used to fit the freeplay nonlinearity. This method leads to no manipulations to the time integration of aeroelastic equations of motion, which allows the use of conventional numerical methods.

 

(2) Characterization of nonlinear aeroelastic behavior:

CS_freeplay_tests1

Control surface freeplay wind tunnel test.

Nonlinear  behavior was characterized using techniques from time series analysis and in frequency domain (power spectrum). Experimental signals can be manipulated in order to yield reconstructed state spaces, for example. LCOs can be observed. Numerical model using representations for concentrated nonlinearities was validated.

The results show that the freeplay may generate similar behavior to those presented by non-linear systems with cubic hardening nonlinearity under periodic conditions. However, the subcritical behavior caused by freeplay, and the occurrence of complex nonlinear behavior are features that distinguish these nonlinearities.

espacodeestadoscomp

Reconstructed state space.
FFTbetacomp

Power spectrum comparison.

 

(3) Grazing bifurcation associated to freeplay nonlinearity in aeroelastic systems:

grazing_1

Grazing bifurcation in pitch/plunge airfoil.

Grazing bifurcations are caused by a limit cycle that becomes tangent to the discontinuity boundary of the phase portrait. These types of bifurcations can occur only to piecewise smooth systems, for example in impact oscillators, shock sensors, gears, cutting tools, tapping mode atomic force microscopy, and aeroelastic systems with freeplay.

For the freeplay case, it was observed that grazing effect let the bifurcation diagram to present transition points, where LCOs change abruptly its structure. This phenomenon reveals an important issue on freeplay nonlinearity problem concerning abrupt changes of behavior.

 

Related publications:

  • Vasconcellos, R. M. G.; Abdelkefi, A.; Marques, F. D.; Hajj, M. R.. Modeling and analysis of control surface free-play nonlinearity in an aeroelastic wing. In: International Forum of Aeroelasticity and Structural Dynamics – IFASD 2011, Paris, França, 2011.
  • Vasconcellos, R. M. G.; Abdelkefi, A.; Marques, F. D.; Hajj, M. R.. Modeling and experimental identification of an aeroelastic wing with pitch free-play nonlinearity. In: 7th European Nonlinear Dynamics Conference (ENOC 2011), Rome, Italy, 2011.
  • Abdelkefi, A.; Vasconcellos, R. M. G.; Hajj, M. R.; Marques, F. D.. Bifurcation analysis of an aeroelastic system with concentrated nonlinearities. Nonlinear Dynamics, v. 1, p. 1, 2011.
  • Vasconcellos, R. M. G., Doctorate Thesis, Characterization and detection of freeplay nonlinearity in aeroelastic systems. EESC/USP, 2012.
  • Vasconcellos, R. M. G.; Abdelkefi, A.; Marques, F. D.; Hajj, M. R.. Representation and analysis of control surface freeplay nonlinearity. Journal of Fluids and Structures, v. 31, p. 79-91, 2012.
  • Vasconcellos, R. M. G.; Abdelkefi, A.; Marques, F. D.; Hajj, M. R.. Control Surface Freeplay Nonlinearity: Modeling and Experimental Validation. In: 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Honolulu, HW, USA, 2012
  • Abdelkefi, A., Vasconcellos, R. M. G., Marques, F. D. and Hajj, M. R.. Modeling and identification of freeplay nonlinearity. Journal of Sound and Vibration, v. 331, 1898–1907, 2012.
  • Vasconcellos, R. M. G.; Abdelkefi, A.; Hajj, M. R.; Marques, F. D.. Discontinuity Induced Bifurcation in Aeroelastic systems with Freeplay Nonlinearity. In: 22nd International Congress of Mechanical Engineering – COBEM 2013, Ribeirão Preto, SP, Brazil, 2013.
  • Vasconcellos, R. M. G.; Pereira, D. A.; Marques, F. D.. Time series and spectral analysis of nonlinear aeroelastic oscillations. In: 22nd International Congress of Mechanical Engineering – COBEM 2013, Ribeirão Preto, SP, Brazil, 2013.
  •  Vasconcellos, R. M. G.; Abdelkefi, A.; Marques, F. D.; Hajj, M. R.. Modeling and Experimental Investigation of an Aeroelastic System with Concentrated Nonlinearity and Control Surface. In: 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Boston, 2013.
  • Vasconcellos, R. M. G., Abdelkefi, A.; Hajj, M. R.; Marques, F. D.. Grazing Bifurcation in Aeroelastic Systems with Freeplay Nonlinearity. Communications in Nonlinear Science & Numerical Simulation, v. 19, p. 1611-1625, 2013.
  • Vasconcellos, R. M. G.; Abdelkefi, A.; Hajj, M. R.; Pereira, D. A.; Marques, F. D.. Airfoil control surface discontinuous nonlinearity experimental assessment and numerical model validation. Journal of Vibration and Control, 2014.
  • Pereira, D. A.; Vasconcellos, R. M. G.; Marques, F. D.. Continuous function modeling to represent an airfoil control surface freeplay. In: Congresso Nacional de Engenharia Mecânica – CONEM 2014, Uberlândia, MG, 2014.
  •  Vasconcellos, R. M. G.; Abdelkefi, A.; Hajj, M. R.; Marques, F. D.. Characterization of grazing bifurcations in airfoils with control surface freeplay nonlinearity. In: Ninth International Conference on Structural Dynamics – EURODYN 2014, Porto, Portugal, 2014.

 

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Bifurcation phenomena due to hardening and free-play nonlinearities combined in a typical aeroelastic section
drawing_exp_v1

Variable hardening experimental apparatus.

This research work aims to analyze and identify the dynamic response of typical section with hardening nonlinearity in the pitching stiffness and freeplay nonlinearity in the control surface stiffness. The investigation has been performed experimentally and numerically.

An experimental device was conceived to control on hardening intensity, which permits to study how hardening in pitching influences Hopf bifurcations. Videos: LCOs…

This ongoing work is related to Master’s degree research of Eng. Daniel A. Pereira.

 

MAIN RESULTS

(1) Hardening nonlinearity in pitching influence on typical section aeroelastic dynamics:

The hardening nonlinearity does not change the subcritical or supercritical behavior of the system. Its intensity is directly related to the amplitude of LCOs. Numerical model has proved to be robust on predicting the nonlinear aeroelastic behavior for different hardening effects.

alfa_hardening_hopf-eps-converted-to

Hardening influence on LCO amplitudes.

(2) Combination of hardening nonlinearity in pitching and control surface freeplay:

The freeplay nonlinearity leads to subcritical bifurcation and increase the range of dangerous LCOs.

plunge_freeplay_hopf-eps-converted-to

Combination of hardening (pitch) and freeplay (control surface).

(3) Control on supercritical and subcritical bifurcations by parameter change:

The linear-related parameters of the airfoil determines the supercritical or subcritical bifurcation when the system presents only hardening nonlinearity. Therefore, the investigation of those parameters leads to a relevant tool to avoid the subcritical behavior.

 

 

 

Related publications:

 

 

 

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