A robust reduced order modeling of mistuned bladed disks: free interface reduction and analytical assembly

Bladed disks in turbomachinery are ideally designed as cyclically symmetric structures; however, in practice they are inevitably affected by mistuning arising from manufacturing tolerances, material variability, and service-induced damage. Even small deviations can trigger strong vibration localization and significant amplification of blade responses, making accurate mistuning analysis essential for reliable prediction of dynamic behavior and fatigue life. Although high-fidelity finite element models can capture these effects, their computational cost is often prohibitive, thus motivating the development of reduced-order models (ROMs). Most existing ROMs for mistuned bladed disks are based on fixed-interface formulations, whose retained modal properties depend on boundary conditions and are difficult to identify experimentally. To overcome this limitation, the present work introduces a free-interface-based formulation with explicit analytical assembly. In this work, a novel ROM for mistuned bladed disks is proposed, based on Rubin free-interface reduction method. The proposed framework applies free-interface reduction to the blades, i.e., the only components where mistuning is assumed to be localized. This results in ROMs with a clear physical interpretation, as the reduction basis is formed by free-interface mode shapes that can be identified experimentally without the uncertainties associated with fixture-dependent boundary conditions. An additional contribution is the explicit analytical formulation of both the reduced and assembled matrices, where all matrix partitions are fully expanded and provided in closed form. This yields a comprehensive view of the reduced system and facilitates its evaluation, particularly when computational resources are limited.