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.
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.
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.
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.
