A three-dimensional (3D) detailed numerical model of an immersed tunnel in a horizontally layered site is established in this study. The 3D seismic response of the immersed tunnel in a horizontally layered site subjected to obliquely incident waves is analyzed based on the precise dynamic stiffness matrix of the soil layer and half-space via combined viscous-spring boundary and equivalent node stress methods. The nonlinear effects of external and internal site conditions on the whole model were determined by equivalent linearization algorithm and Mohr–Coulomb model, respectively. The proposed model was then applied to investigate the nonlinear seismic response of an immersed tunnel in the Haihe River subjected to seismic waves of oblique incidence. The dislocation (opening) of pipe joints in the immersed tunnel were analyzed to determine the response characteristics of the shear keys and overall displacement of the tunnel; the dynamic responses of the immersed tunnel subjected to obliquely incident seismic waves markedly differ from those of vertically incident seismic SV waves. The maximum stress value of shear keys and the maximum dislocation of the pipe joint appear as upon critical angle. The overall displacement of the tunnel increases as incident angle increases. Under severe earthquake conditions, both the pipe corners and midspan section of the roof and floor are likely to produce crack. These areas need careful consideration in the seismic design of immersed tunnel structures.

This paper focuses on the design of a flux-biased rotary electromagnetic actuator with compact structure for fast steering mirror (FSM). The actuator has high force density and its torque output shows linear dependence on both excitation current and rotation angle. Benefiting from a new electromagnetic topology, no additional axial force is generated and an armature with small moment of inertia is achieved. To improve modeling accuracy, the actuator is modeled with flux leakage taken into account. In order to achieve an FSM with good performance, a design methodology is presented. The methodology aims to achieve a balance between torque output, torque density and required coil magnetomotive force. By using the design methodology, the actuator which will be used to drive our FSM is achieved. The finite element simulation results validate the design results, along with the concept design, magnetic analysis and torque output model.

A viscous-slip interface model is proposed to simulate the contact state between a tunnel lining structure and the surrounding rock. The boundary integral equation method is adopted to solve the scattering of the plane SV wave by a tunnel lining in an elastic half-space. We place special emphasis on the dynamic stress concentration of the lining and the amplification effect on the surface displacement near the tunnel. Scattered waves in the lining and half-space are constructed using the fictitious wave sources close to the lining surfaces based on Green’s functions of cylindrical expansion and the shear wave source. The magnitudes of the fictitious wave sources are determined by viscous-slip boundary conditions, and then the total response is obtained by superposition of the free and scattered fields. The slip stiffness and viscosity coefficients at the lining-surrounding rock interface have a significant influence on the dynamic stress distribution and the nearby surface displacement response in the tunnel lining. Their influence is controlled by the incident wave frequency and angle. The hoop stress increases gradually in the inner wall of the lining as sliding stiffness increases under a low-frequency incident wave. In the high-frequency resonance frequency band, where incident wave frequency is consistent with the natural frequency of the soil column above the tunnel, the dynamic stress concentration effect is more significant when it is smaller. The dynamic stress concentration factor inside the lining decreases gradually as the viscosity coefficient increases. The spatial distribution and the displacement amplitudes of surface displacement near the tunnel change as incident wave frequency and angle increase. The effective dynamic analysis of the underground structure under an actual strong dynamic load should consider the slip effect at the lining-surrounding rock interface.