A MODAL EXCITATION SPECTRUM-BASED FRAMEWORK FOR VIBRATION-ORIENTED OPTIMIZATION OF CYCLICALLY SYMMETRIC BLADED STRUCTURES

The vibration-oriented optimization of cyclically symmetric bladed structures subjected to aerodynamic excitation remains computationally demanding because conventional strategies typically require repeated harmonic response analyses throughout the optimization process. Controlled modifications of blade geometry, mass or stiffness can reduce critical resonant responses; however, the most favourable modification depends on the operating excitation, the structural dynamic characteristics and practical design constraints. This paper presents a computationally efficient optimization framework based on the proposed Modal Excitation Spectrum (MES). Unsteady aerodynamic pressure fields obtained from computational fluid dynamics (CFD) are transformed into equivalent harmonic nodal forces acting on the structural finite element model. These forces are projected onto mass-normalized structural mode shapes to obtain generalized modal forces representing the aerodynamic excitation in the modal domain. The MES describes the distribution of modal excitation over the selected structural modal branches, whose natural frequencies are tracked relative to the prescribed operating-frequency range. The maximum mass-normalized generalized modal force among the selected structural modal branches is employed as the objective function. Consequently, repeated harmonic response analyses are excluded from the optimization loop, thereby reducing the forced-response computation required during optimization. A conventional harmonic response analysis is performed only after convergence to independently verify the vibration response and the maximum equivalent stress over the harmonic phase cycle of the optimized design. The framework permits independent blade design variables and can accommodate geometric, material, mass and stiffness modifications together with engineering constraints such as rotor balance. It therefore admits both uniform tuning changes and blade-specific intentional mistuning without prescribing either type of final configuration. The methodology is demonstrated on a thirteen-bladed turbocharger turbine wheel for a large marine engine. Although the blade-tip variables were independent, the balance-constrained optimization converged to an identical modification of all blade tips. The final harmonic response analysis confirmed a substantial reduction in the maximum equivalent stress over the harmonic phase cycle within the investigated operating-speed interval.