Impact of Numerical Dissipation on Flow-Induced Vibration Simulation: A Comparative Study of Integration Schemes for Nonlinear Self-Excited Oscillations

Flow-induced self-excited vibration may exhibit high-frequency numerical oscillations and chaotic-like responses in long-duration simulations due to strong nonlinearity and multimodal coupling. In this study, a two-node cable finite element model incorporating torsional degrees of freedom, nonlinear aerodynamic forces, and geometric nonlinearity is developed to evaluate the long-term computational performance of the Newmark average acceleration method and the Bathe composite integration scheme. Simulations are conducted for weakly nonlinear, transitional nonlinear, and near 1:1 internal resonance regimes. The results show that, as the degree of nonlinearity increases, the Newmark method produces more pronounced non-principal high-frequency components, a more scattered distribution of Poincaré points, and larger deviations from the expected principal-mode-dominated beating response. These observations indicate that, under the present model and discretization conditions, the chaotic-like response obtained by the Newmark method is strongly affected by non-principal high-frequency contamination. In contrast, the response computed by the Bathe method remains stably governed by the two dominant frequencies associated with the near-resonant beating mechanism. The results indicate that, for the long-duration nonlinear galloping problems considered in this study, appropriate algorithmic dissipation can reduce non-principal high-frequency disturbances and improve the interpretability of the numerical results.