DOF3FreeP version 0.1

This is a set of Matlab codes to perform preform bifurcation analysis on a typical aeroelastic section with freeplay in the pitch or control degree of freedom. Some of the codes in this distribution are heavily modified versions of codes released with [1].

There bifurcation analysis is applied to three experimental test cases from the literature:
1. Conner et al 1997 [2]
2. Tang and Dowell 2010 [3]
3. Verstraelen et al 2017 [4]

Installation:
1. Unzip the DOF3FreeP_v0.1.zip file and place anywhere in the search path of your Matlab distribution.

3. Run the codes:
- For Conner et al 1997:
  a. Harmonic Balance with Theodorsen theory aerodynamics: run ./Conner et al 1997/HB_Theodorsen/dof3_HBcont_Theodorsen_freeplay.m
  b. Harmonic Balance with Wagner theory aerodynamics: run ./Conner et al 1997/HB_Wagner/dof3_HBcont_Wagner_freeplay.m
  c. Shooting-based numerical continuation with Wagner theory aerodynamics: run ./Conner et al 1997/Shooting/dof3_shoot_cont.m
  d. Secondary branch shooting-based continuation: run ./Conner et al 1997/Shooting/dof3_shoot_switch.m
- For Tang and Dowell 2010:
  a. Harmonic Balance with Theodorsen theory aerodynamics: run ./Tang Dowell 2010/HB_Theodorsen/dof3_HBcont_Theodorsen_freeplay.m
  b. Harmonic Balance with Wagner theory aerodynamics: run ./Tang Dowell 2010/HB_Wagner/dof3_HBcont_Wagner_freeplay.m
  c. Shooting-based numerical continuation with Wagner theory aerodynamics: run ./TangDowell2010/Shooting/dof3_shoot_cont.m
  d. Secondary branch shooting-based continuation: run ./Tang Dowell 2010/Shooting/dof3_shoot_switch.m
  e. Shooting-based continuation in the preload direction: run ./Tang Dowell 2010/Shooting/dof3_shoot_preload.m
- For Verstraelen et al 2017:
  a. Harmonic Balance with Theodorsen theory aerodynamics: run ./Verstraelen et al 2017/HB_Theodorsen/dof3_HBcont_Theodorsen_freeplay.m
  b. Harmonic Balance with Wagner theory aerodynamics: run ./Verstraelen et al 2017/HB_Wagner/dof3_HBcont_Wagner_freeplay.m
  c. Shooting-based numerical continuation with Wagner theory aerodynamics: run ./Verstraelen et al 2017/Shooting/dof3_shoot_cont.m

References:
1. Dimitriadis, G., Introduction to Nonlinear Aeroelasticity, Wiley, 2017.
2. Conner, M., Tang, D., Dowell, E., and Virgin, L., Nonlinear behaviour of a typical airfoil section with control surface freeplay: a numerical and experimental study, Journal of Fluids and Structures, Vol. 11, No. 1, 1997, pp. 89–109.
3. Tang, D. and Dowell, E. H., Aeroelastic Airfoil with Free Play at Angle of Attack with Gust Excitation, AIAA Journal, Vol. 48, No. 2, 2010, pp. 427–442.
4. Verstraelen, E., Dimitriadis, G., Rossetto, G. D. B., and Dowell, E. H., Two-domain and three-domain limit cycles in a typical aeroelastic system with freeplay in pitch, Journal of Fluids and Structures, Vol. 69, 2017, pp. 89–107.

Copyright (C) 2026 Grigorios Dimitriadis 
 
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see <https://www.gnu.org/licenses/>.


