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.

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 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.