Purpose The paper aims to introduce an innovative methodology to analyze the flutter velocity of a two-dimensional wing using numerical step-by-step integration methods. The primary objective is to apply the Theodorsen unsteady aerodynamic function to the two-degrees-of-freedom flutter equation and identify the flutter onset by assessing the decay rates at various reduced frequencies. Design/methodology/approach The proposed methodology transforms the flutter equation into a motion equation for a damped two-degrees-of-freedom system that integrates the Theodorsen function. Numerical step-by-step integration methods, including precise integration, Runge–Kutta, central difference and Newmark methods, are used to compute the time-dependent responses of displacement, velocity and acceleration. Findings The findings reveal that decay rates at different reduced frequencies can serve as a novel criterion for identifying flutter onset, marking a significant first in the field. The results obtained using step-by-step integration methods closely align with those using established eigenvalue calculation techniques, such as the V–g and p–k methods, confirming the accuracy and reliability of the numerical approach. Originality/value This study advances the understanding of flutter dynamics, consistent with established analysis methods while introducing a fresh perspective. The strong agreement among results from various numerical step-by-step integration methods underscores their robustness and reliability. This study offers an efficient and accurate tool for engineers and researchers to predict and analyze flutter in two-dimensional wing structures, essential for designing and ensuring the safety of aerospace vehicles.
Wang et al. (2026) studied this question.