This study investigates the forced vibration response of a two-row model of an Inlet Guide Vane (IGV) and rotor at resonance speed through numerical simulations. A resonant response prediction method based on equivalent damping balance has been validated, which ensures computational accuracy while reducing response calculation time to only 1% of the traditional transient response method. At resonance speed, unsteady pressure disturbances on the rotor blade surface mainly arise from two sources: IGV wakes and blade vibrations. The unsteady pressure caused by the IGV wakes provides excitation for the system, while the unsteady pressure caused by rotor blade vibrations provides damping. By studying the characteristics of unsteady pressure caused by IGV wakes and vibrations at resonance speed, a method for separating unsteady pressure caused by stator wakes and vibrations has been presented, accurately obtaining aerodynamic damping under multi-row resonance conditions. Compared to the aerodynamic damping obtained from multi-row scenarios without separating unsteady pressures caused by stator wakes and vibrations, and the traditional isolated blade row scheme, the aerodynamic damping considering the effects of multi-row and IGV wakes at resonance speed is smaller. Based on the separated unsteady pressures caused by IGV wakes and vibrations, and combined with the equivalent damping balance method for predicting forced response, a forced response analysis method considering both flow field disturbance excitation and damping effects has been established.

The aeroelastic stability associated with the acoustic wave propagation characteristics of transonic rotor blades was numerically investigated in this study. The influence of the vibration frequency on the aerodynamic damping of the first bending mode was primarily considered at different speeds, including both work and stall points. We found that the state of acoustic wave propagation associated with aeroelastic instability is closely related to rotational speed. At low speeds near stall points, the risk of aeroelastic instability is confined to the upstream cut-off state. However, at high speeds near stall points, aeroelastic instability may occur in both the downstream cut-off state and the acoustic wave propagation state of the upstream cut-off frequency, further expanding the range of the acoustic wave propagation state in which aeroelastic instability can arise. The research findings show that for suction surfaces, aerodynamic work is affected not only by acoustic wave propagation characteristics, but also by shock waves, radial flow, and reflux in the flow field. However, for pressure surfaces, the acoustic wave propagation characteristics play a significant role. When aeroelastic instability occurs, negative damping predominantly arises from the pressure surface. To investigate why lower-order modes are more prone to aeroelastic instability, specific simulations were conducted for the first bending and twisting modes under different operating conditions in the downstream cut-on state. When the vibration frequency significantly exceeds the downstream cut-off frequency, the blade phase is minimally influenced by acoustic wave propagation characteristics, and the rotor is aeroelastically stable in these phases. Simultaneously, there is an approximately linear increase in the unsteady pressure amplitude with increasing vibration frequency, and the aerodynamic work is predominantly influenced by the unsteady pressure amplitude.