Euler–Bernoulli Beam Model for Flapping Wings

This repository provides a MATLAB implementation of a finite-element Euler–Bernoulli beam model with prescribed root rotation, time integration via Runge–Kutta (RK4), and a solar power proxy based on the dot product between the Sun vector and time-varying local surface normals inferred from nodal rotations. The workflow supports parametric sweeps in flapping frequency and amplitude, as well as different PV element “block” placements along the span.

Key capabilities

• Euler–Bernoulli beam FE model:
  • global stiffness/mass assembly
  • boundary condition reduction (clamped root, prescribed rotation)
• Time integration of the reduced-order system
• Smooth ramp-in of prescribed motion (smootherstep)
• Solar power proxy:
  • precomputed Sun vector in the body frame
• Parametric sweeps:
  • frequency (Hz) and amplitude (deg)
  • PV block placement along nodes
• Spectral post-processing:
  • Welch PSD and spectrogram of total power signal

Power generation

PSD

Spectrogram

Requirements

• MATLAB R20XXa or later
• Signal Processing Toolbox recommended (for pwelch / spectrogram)

Assumptions and limitations (summary)

• Structural model: linear Euler–Bernoulli bending with small strains.
• Kinematics: nodal rotations are used to approximate local panel orientation.
• “Power” is a proxy proportional to irradiance projection; it does not include full PV I–V dynamics or MPPT behavior.

Corresponding authors

• Vítor D. Marchiori
• Rodrigo B. Santos
• Douglas D. Bueno

How to cite

The content is available for non-commercial research under the following terms: (i) GMSINT Group and UNESP Ilha Solteira should be acknowledged as the source of the data; (ii) this repository should be cited as follows:

Marchiori, V. D.; Santos, R. B.; Bueno, D. D. (2025). Flapping-wings UAV: CAD Prototype. GitHub, https://github.com/vitordmarchiori/Flapping-Wing-Beam-Simulation.

BibTeX

If you are using a LaTeX Editor, you can cite this repository using these BibTeX citations:

@misc{marchiori2025,
  author       = {Marchiori, Vítor D. and Santos, Rodrigo B. and Bueno, Douglas D.},
  title        = {Euler--Bernoulli Beam Model for Flapping Wings},
  year         = {2025},
  howpublished = {\url{https://github.com/vitordmarchiori/Flapping-Wing-Beam-Simulation}},
  note         = {[Simulation codes]. GitHub}
}

Funding

São Paulo Research Foundation, FAPESP, Grant number 2023/15904-4.

License

Creative Commons Attribution-NonCommercial-ShareAlike (CC-BY-NC-SA): A creative commons license that bans commercial use and requires you to release any modified works under this license.