Friction-induced vibration in aircraft disc brakes is particularly complex, and different analysis methods often produce inconsistent results. In the paper, the performance of complex mode analysis (CMA) and explicit transient dynamic analysis (TDA) based on the finite element (FE) method is compared to investigate such vibration. First, a simplified FE model of an aircraft disc brake is developed. Then, under a constant friction coefficient ( \(\mu\) = 0.2), the unstable modes predicted by CMA and TDA show good agreement, and the validity of the results is confirmed. CMA offers higher efficiency, and TDA provides greater accuracy. Next, CMA is applied under constant friction conditions varying from 0 to 0.5 at an interval of 0.1, revealing that increased friction leads to greater instability, while sensitivity analysis reveals that rotational speed has a negligible influence in this method. Furthermore, exponential friction can induce stronger system nonlinearity, which is investigated using TDA. Results show that exponential friction induces higher vibration intensity, and larger initial braking speeds result in greater vibration amplitudes. Overall, CMA consumes fewer computational resources and is better suited for simple scenarios and parametric studies, whereas TDA yields more accurate and intuitive results under complex conditions. Method selection should depend on practical engineering needs and the complexity of the system.