# Engineering Mechanics

Proceedings Vol. 32 (2026)

ENGINEERING MECHANICS 2026

Copyright © 2026 Institute of Thermomechanics of the Czech Academy of Sciences, Prague

 

Fischer C., Náprstek J.
pages 45 - 48, full text

This paper analyzes post-critical stationary solutions of a two-degree-of-freedom (2DOF) aeroelas- tic system modeled by a generalized van der Pol formulation. The sign of the linear damping term is shown to govern the qualitative character of instability, distinguishing cases with stable trivial equilibrium from self- excited oscillatory regimes corresponding to flutter- and galloping-type behavior. Stationary responses are derived using harmonic balance, yielding generalized modal amplitudes and multiplicative coupled solutions. The stability of trivial and nontrivial branches is examined analytically. Higher-order nonlinear damping terms of fourth and sixth degree are shown to ensure bounded post-critical motion and suppress excessive vibration growth. The linear stability boundary is related to Routh–Hurwitz conditions of the underlying 2DOF aeroelas- tic system, identifying flutter limits as the onset of Hopf bifurcation. The proposed framework provides a unified analytical interpretation of post-critical aeroelastic oscillations and their nonlinear saturation mechanisms.

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