FEM-Based Modeling of Generalized Amplitudes in Stochastic van der Pol Systems

This paper investigates various approaches for approximating the stationary aeroelastic response characteristics under near-resonance conditions, with a focus on the lock-in regime.A reduced form of the Fokker-Planck equation-derived via stochastic averaging-is used to represent the long-term behavior.Comparative analysis is performed between traditional finite element solutions and refined semi-analytical techniques based on a Galerkin-type expansion of an analytical solution available for exact resonance conditions.Although full verification via Monte Carlo simulations is constrained due to the elusive nature of the generalized partial amplitudes inherent in the reduced FPE framework, indicative comparisons reveal an unexpectedly analogy across methods.These results highlight both the practical value and the limitations of different modeling strategies in the probabilistic assessment of nonlinear systems.