Hui Qian

Speed fluctuations introduce pronounced non-stationarity into rotor vibration signals, which makes the accurate extraction of rotational-frequency, amplitude, and phase characteristics considerably more difficult than under steady-speed conditions. To address this problem, a rotor-unbalance characteristic-extraction method is developed for speed-fluctuation conditions. The procedure first evaluates supervised normalized least mean square (NLMS) filtering followed by fixed forward–backward zero-phase filtering for noise suppression without additional phase distortion. The multisynchrosqueezing transform (MSST) is then applied to improve time–frequency energy concentration and track the instantaneous rotational-frequency component of the non-stationary vibration signal. The instantaneous phase is subsequently resampled using the keyphasor signal, and phase tracking regression (PTR) is applied to estimate the rotational-frequency phase under speed fluctuation and keyphasor jitter. Simulation results show that the combined NLMS and zero-phase filtering method achieves the highest output signal-to-noise ratio and the lowest root mean square error among the compared filtering methods. MSST provides better time–frequency energy concentration than the other investigated time–frequency methods, while PTR maintains relatively stable phase-estimation performance under variations in noise level, keyphasor jitter, frequency modulation ratio, and sampling duration. Experiments on the investigated three-disk rotor further show that PTR yields a phase standard deviation of 4.363° across the segmented steady-state measurements, and the vibration amplitudes at all three measurement locations are reduced by more than 70% in both balancing tests at 5000 rpm, demonstrating the effectiveness of the proposed method for the present rotor configuration and tested operating condition.

The bistable structures are widely utilized in energy harvesting, vibration isolation, and morphing applications due to the beneficial effects of negative stiffness. However, the jump phenomena and complex nonlinearity of bistable restoring forces make parameter identification challenging, particularly in high-dimensional systems with localized bistability. To overcome this, paper introduces a novel integrated framework that synergistically combines harmonic balance identification with deep neural networks, capable of identifying bistable nonlinear restoring forces without prior assumption of their analytical form. The proposed approach requires only a limited set of harmonic excitation responses to achieve high-fidelity identification. The linear mass, damping, and stiffness matrices are directly estimated via harmonic coefficient balancing in the frequency domain. For high-dimensional bistable structures, fully connected deep neural networks are constructed to represent each local nonlinear restoring force, enabling scalable and flexible identification beyond conventional parametric methods. Numerical simulations conducted on three typical bistable cases demonstrate that the method accurately identifies system parameters and nonlinear forces under noise levels up to 40 dB. Experimental validations are performed on a bistable nonlinear energy sink with different potential well depths, confirming that the identified model closely matches the measured frequency response, restoring force, and reconstructed random response under band-limited noise. Compared to the pure deep neural networks-based approach, the identification efficiency is improved by a factor of nine. The results verify that the proposed integrated approach offers a generalizable and experimentally feasible solution for identifying complex bistable nonlinear systems.

Traditional modal testing has difficulty accurately identifying the ultralow-frequency modes of flexible structures. Ultralow-frequency excitation and vibration signal acquisition are two main obstacles. Aiming at ultralow-frequency modal identification of flexible structures, a modal testing method based on Digital Image Correlation method and Eigensystem Realization Algorithm is proposed. Considering impulse and shaker excitation are difficult to make generate ultralow-frequency vibration of structures, the initial displacement is applied to the structure for excitation. The ultralow-frequency accelerometer always has a large mass, which will change the dynamics performance of the flexible structure, so a structural vibration response was obtained through the Digital Image Correlation method. After collecting the free-decay vibration signal, the ultralow-frequency mode of the structure was identified by using the Eigensystem Realization Algorithm. Ground modal tests were conducted to verify the proposed method. Firstly, a solar wing structure was adopted, from which it was concluded that the signal acquisition using Digital Image Correlation method had high feasibility and accuracy. Secondly, an ultralow-frequency flexible cantilever beam structure which had the theoretical solution was employed to verify the proposed method and the theoretical fundamental frequency of the structure was 0.185 Hz. Results show that the Digital Image Correlation method can effectively measure the response signal of the ultralow-frequency flexible structure, and obtain the dynamics characteristics.

The vibration characteristics of bolted structures are crucially affected by the pre-tightening torque. An approach for identifying the pre-tightening torque dependent stiffness parameters of bolted joints is proposed in this paper. Firstly, the interface of the bolted joint is characterized by the thin layer element with the isotropic material property, and the parameter value of the property is assigned relative to the distance from the center of the bolt; the influence of the bolt is ignored. Secondly, the model updating method is adopted to identify the parameters of thin layer elements using experimental data, and modal data under different values of pre-tightening torque in the range of 2 N·m~22 N·m are obtained; the torque wrench is used to determine the pre-tightening torque in the modal test. Finally, after identifying the material parameters using partial experimental data on pre-tightening torque range, the empirical equation of the interface parameters with the pre-tightening torque parameter is obtained by curve fitting and the rest of the experimental data are used to verify the accuracy of the fitted empirical equations. It is concluded that this method can obtain all the parameters of the equivalent thin layer elements within a certain range of pre-tightening torque, which can provide a reference for the empirical modeling of bolted structures, improve modeling efficiency and reflect the characteristic performance of real structural dynamics.