The water resources in southwest China is abundant and the seismicity is strong, so it is necessary to study the dynamic response and safety of hydraulic structures under rare earthquake. Taking a typical radial steel gate as an example, a three-dimensional numerical model considering the interaction between water and gate during the earthquake is established. The accuracy and applicability of the model are verified by comparing with the measured results of the dynamic response of Zipingpu dam during the Wenchuan earthquake. Thereafter, the dynamic displacement and stress, and resonance frequency of the radial gate under the rare earthquake of two wave types are analyzed. The water-structure coupling effect has a great influence on the seismic dynamic response of the radial steel gate. The calculated result of the dynamic response of the gate considering the fluid-structure coupling effect is significantly larger than that of the specification, and the maximum ratio of the two is more than 2.27 times. Under the action of EI wave, the peak value of dynamic stress response is at the bottom of the panel, and the maximum value of resonance frequency (about49.13 Hz) is located in the middle and lower part of the panel. Under the action of far-field wave, the peak area of dynamic displacement response of the gate is basically the same as that under the action of EI wave, while the maximum value of some measuring points is only half of the maximum value under the action of EI wave. However, the resonance frequency is significantly greater than that of EI wave, the maximum value reaches 65.24 Hz, which appears at the top of the gate. The dynamic response of the gate structure caused by two different wave types of earthquakes is not completely consistent. The comprehensive consideration of different wave types is of significance for the structural design and safety evaluation of the radial steel gate in the earthquake-prone areas.

In this study, IGA is introduced into the performance analysis of the expansion water seal for an exact representation of its complex geometrical shape. Firstly, the incremental equilibrium equations used in the large deformation analysis are derived for the IGA discretization model based on the updated Lagrangian formulation. The unknown contact forces are directly involved in the equilibrium equations, which results in a simple expression. Then, through the investigation of the contact conditions, the normal and tangential contact forces are verified to be the solutions of two box-constrained variational inequalities representing the normal and tangential contact conditions, respectively. Furthermore, the incremental equilibrium equations for all components of the water seal system and the variational inequalities for all contacts between the components are assembled together and reformulated as a global variational inequality, which is resolved by using the Extra-gradient method. Ultimately, the new method is applied in the performance comparison of two optional expansion water seals, in which the capability and precision of the proposed method are investigated. Results verify that the proposed method is effective in the numerical simulation of the expansion water seal and has a higher precision than the traditional FEM under the same conditions.

As the novel suspension bearing, Magnetic-Liquid Double Suspension Bearing (MLDSB) is mainly supported by magnetic suspension and supplemented by a liquid hydrostatic bearing. Due to its great bearing capacity and stiffness, rapid response, great active control, and so on, MLDSB is suitable for medium speed heavy loads and has a large carrying capacity and high operating stability. In addition, the radial inertia coupling and gyroscopic coupling between radial 4-DOF control channels can reduce control precision, operation stability, and reliability of MLDSB. Therefore, a mathematical model of radial 4-DOF rotor-dynamics of MLDSB is established in this paper, and the inherent coupling mechanism is explored. Taking inertial coupling, gyroscopic coupling, and external disturbance loads as lumped disturbances, a decoupled controller based on Generalized Extended State Observer (GESO) is established. The influence of the GESO controller on the decoupling and control performance of radial 4-DOF control channels is simulated. The results indicate that the decoupling effect of the GESO controller is great. Under the action of step signal, the steady displacement, maximum displacement, adjustment time, and peak time of the rotor after decoupling are all reduced, among which the steady displacement and maximum displacement are the most obvious. Under the sinusoidal signal, the steady displacement and maximum displacement are reduced by 90%, which can effectively avoid the “gap-impact” fault. Under the pulse signal, the steady displacement, maximum displacement, adjustment time, and peak time are all reduced, among which the maximum displacement is the most obvious. The research in this paper can provide a theoretical reference for the stable support and decoupling control of MLDSB.