Background <p>Accurately predicting vibration responses in aero-engines remains challenging due to their complex geometric properties and rotational effects. Traditional modal superposition methods usually rely on linear-system assumptions and show limitations in handling non-uniform bearing stiffness and rotation-induced coupling.</p> Methods <p>A dynamic model of the casing–rotor system is proposed based on the finite element method (FEM). A mixed shaft–disk element is developed by employing Euler–Bernoulli (E–B) beam theory and Lagrange’s equations to accurately capture gyroscopic effects and rotational moments. Modal analysis and comparisons with commonly used engineering FE simulations are conducted to validate the proposed parameter-driven reduced-order method.</p> Results <p>The results confirm the effectiveness of the proposed method. The approach significantly improves iterative efficiency while retaining the ability to capture high-frequency modes. It also avoids the computational redundancy associated with global matrix operations in commercial software. Furthermore, the coupled influences of external excitation, bearing parameters, disk position, and mass imbalance on the vibration response are systematically examined.</p> Conclusions <p>The proposed framework enables efficient analysis under complex operating conditions while preserving essential dynamic behaviours, providing a high-fidelity and computationally efficient tool for aero-engine fault diagnosis and structural optimization.</p>