Time-frequency analysis (TFA) technique is an effective approach to capture the changing dynamic in a nonstationary signal. However, the commonly adopted TFA techniques are inadequate in dealing with signals having a strong non-stationary characteristic or multi-component signals having close frequency components. To overcome this shortcoming, a new TFA technique applying a polynomial chirplet transform (PCT) in association with a synchroextracting transform (SET) is proposed in this study. It is shown that the energy concentration of the timefrequency representation (TFR) of a strong frequency modulated signal from a PCT transform can be further enhanced by a SET transform. The technique can also be employed to accurately extract the signal components of a multi-component nonstationary signal with close frequency components by adopting an iterative process. It is found that the TFR calculated from the proposed technique matches well with the ideal TFR which demonstrates the superiority of the current technique in dealing with non-stationary signals having rapidly changing dynamics. Results from the analysis of the experimental data under varying speed conditions confirm the validity of the proposed technique in dealing with non-stationary signals from practical sources.

The operation of an aero-engine involves various non-stationary processes of acceleration and deceleration, with rotational speed varying in response to changing working conditions to meet different power requirements. To investigate the nonlinear dynamic behaviour of cracked blades under variable rotational speed conditions, this study constructed a rotating blade model with edge-penetrating cracks and proposes a component modal synthesis method that accounts for time-varying rotational speed. The nonlinear response behaviours of cracked blades were examined under three distinct operating conditions: spinless, steady speed, and non-constant speed. The findings indicated a competitive relationship between the effects of rotational speed fluctuations and unbalanced excitation on crack nonlinearity. Variations in rotational speed dominated when rotational speed perturbation was minimal; conversely, aerodynamic forces dominated when the effects of rotational speed were pronounced. An increase in rotational speed perturbation enhanced the super-harmonic nonlinearity induced by cracks, elevated the nonlinear damage index (NDI), and accentuated the crack breathing effect. As the perturbation coefficient increased, the super-harmonic nonlinearity of the crack intensified, resulting in a more complex vibration form and phase diagram.

Considering rotation-induced centrifugal stiffening, spin softening, and Coriolis effects, the reduced dynamic model of a rotating blade with a dovetail fixture is established in the ANSYS environment via the fixed-interface method for higher computational efficiency and lower memory consumption. Then some parameters such as rotating speed, friction factor, and stator blade number affecting the nonlinear vibration responses of the system under the combined actions of aerodynamic force, centrifugal force, and gravity are elaborately discussed. The results show that: (1) the contact-induced nonlinearity between the tenon and the mortise mainly results in the frequency multiplications of the aerodynamic excitation frequency; (2) a larger friction factor results in a lower magnitude of contact pressure and a higher resonance frequency, while a larger stator blade number results in a lower magnitude of the uniform and continuous contact pressure distribution; (3) the excitation of the resonant mode caused by the aerodynamic force is primarily characterized by the first-order bending mode of the system.

Considering rotation-induced centrifugal stiffening, spin softening, and Coriolis effects, the three-dimensional finite element model of a rotating blade with a dovetail structure is built through the contact dynamics theory. The fixed-interface component mode synthesis method is then adopted to reduce the model for high computational efficiency and adequate model accuracy. The effects of the number of normal modes on the first-six-order modal characteristics of the model varying with the rotating speed are studied between the reduced and full models. Next, the influence of rotating speed and friction factor on the nonlinear dynamic characteristics of the model under the action of aerodynamic force are elaborately discussed. The results show that: (1) tenon-mortise joint contact-induced nonlinearity under low rotating speeds results in the intermittent interference of contact surfaces and frequency multiplications of aerodynamic excitation frequency in the spectrum cascades, while that under high rotating speeds causes the continuous interface contact and asynchronous excitation at the tenon-mortise joint; (2) the increase of friction factor results in a lower contact pressure distribution and the right shift of the resonance peak (i.e., hard nonlinearity).