The underframe passive inerter-based suspended device, based on the inerter-spring-damper vibration attenuation structure, could improve the dynamic performance of the train body, but its parameters are fixed and cannot meet the dynamic performance requirements under different operating conditions. Therefore, a semi-active inerter-based suspended device based on the linear quadratic regulator (LQR) control strategy is proposed to further enhance the dynamic performance. The rigid-flexible coupling vertical dynamic model of the train body and an underframe semi-active inerter-based suspended device are established. The structural parameters of the semi-active inerter-based suspended device are adjusted using LQR control strategy. Dynamic response of the system is obtained using the virtual excitation method. The dynamic characteristic of the system is evaluated using the Sperling index and compared with those of the passive and semi-active traditional suspended devices as well as the passive inerter-based suspended devices. The vertical vibration acceleration of the train body and Sperling index using the semi-active inerter-based suspended device is the smallest among the four suspended devices, which denotes the advantages of using the inerter and LQR control strategy. The semi-active inerter-based suspended device could decrease the vertical vibration acceleration of the train body and further suppress its elastic vibration in the lower frequency band, more effectively than the other three suspended devices. Overall, the semi-active inerter-based suspended device could significantly reduce elastic vibration of the train body and improve its dynamical performance.

An active inerter-based suspension with acceleration feedback control is proposed in this paper, the time delay generated in the controllers and actuators is considered, which constitutes the time-delayed active inerter-based (TDA-IB) suspension. The dynamic equation of the TDA-IB suspension is established and is a neutral type of delay differential equation (NDDE) in which the time delay exists in the highest-order derivative. The stability analysis is conducted by calculating the number of unstable characteristic roots based on the definite integral stability method, the stable and unstable regions are determined. The effect of time delay and feedback gain on the dynamic performance of the TDA-IB suspension under harmonic, random, and shock excitations is studied in detail and compared with the parallel-connected inerter-based (PC-IB) and traditional suspensions. The results show that the TDA-IB suspension is asymptotically stable for smaller feedback gain and time delay, through increasing the feedback gain, the stable regions shrink, and a smaller time delay could cause the system to become unstable. Furthermore, the time delay could regulate the resonance peak around the unsprung mass natural frequency and generate multiple high-frequency resonance peaks. If the time delay is chosen appropriately and falls into the stable range, the TDA-IB suspension could improve the dynamic performance for the suspension stroke and dynamic tire load while having a deterioration for the vehicle body acceleration compared with the PC-IB and traditional suspensions.

Looseness of high-strength wind turbine bolts is one of the main types of mechanical failure that threaten the quality and safety of wind turbines, and how to non-destructively detect bolt loosening is essential to accurate assessment of operational reliability of wind turbine structures. Therefore, to address the issue of looseness detection of high-strength wind turbine bolts, this paper proposes a non-destructive detection method based on digital image correlation (DIC). Firstly, the mathematical relationships between the inplane displacement component of the bolt’s nut surface, the bolt’s preload force loss and the bolt loosening angle are both deduced theoretically. Then, experimental measurements are respectively conducted with DIC with different small bolt loosening angles. The results show that the bolt loosening angle detection method based on DIC has a detection accuracy of over 95%, and the bolt’s preload force loss evaluated by the deduced relationship has a good agreement with the empirical value. Therefore, the proposed DIC-based bolt loosening angle detection method can meet the requirements of engineering inspection, and can achieve quantitative assessment of preload forces loss of wind turbine bolt.