The governing equation of a rotating flexible disc under stationary sliders is modelled under consideration of the initial transverse runout of the disc. Natural frequency and stability of the system is studied and checked, and steady-state response is obtained. The effects of system parameters on the steady-state amplitude of the sliders are analysed and resonance induced by the sliders is discovered. The decrease of the number of nodal diameters of the initial transverse runout and slider mass, and the increase of disc damping, slider damping, and natural frequency and friction force at the disc-slider interface, can be used to suppress the amplitude.

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Dropper is an important component of pantograph-catenary system employed in high-speed railway. The cyclic stress in dropper can lead to the fatigue failure during operation. The study of the fatigue life of dropper is the premise to ensure the safe exploitation of the train. The analytic vibration equation of dropper is proposed. Based on the finite difference method and MATLAB numerical calculation program, the vibration process and stress variation of the dropper are simulated. The influence of excitation frequency, vibration amplitude, and applied force on fatigue life of dropper is studied, according to the stress history of the dropper, the Basquin equation, and the Palmgren-Miner linear fatigue cumulative damage criterion. The numerical results show that the logarithm of the fatigue life of dropper shows a linear decreasing trend with the increase in the excitation frequency, vibration amplitude, or applied force.

The proposed boundary condition is more suitable in hemodynamics modeling.

The borehole acoustic reflection imaging logging is a newly developed acoustic logging method that has attracted many interests. These converted and reflected waves for imaging are usually mixed up with borehole guided waves and therefore difficult to be clearly identified. To improve the downhole tool design and develop more sophisticate data processing and interpretation algorithms, studies on precisely numerical modeling of the wave fields in the acoustic reflection imaging logging are necessary and critical. This paper developed a parallelized scheme of 3D finite difference (3DFD) with nonuniform staggered grid and PML absorbing boundary to simulate the acoustic wave fields in isotropic and anisotropic formations. Applications of this scheme to the typical cases of isotropic and anisotropic formations and comparison with the results from published analytical solutions have demonstrated the validation and efficiency of the scheme. Higher accuracy and lower computation cost (3.5 times faster than the conventional schemes) have been achieved with this scheme for modeling such a complex wave fields of 60 dB dynamic range with higher frequency (10 kHz). This simulating program provides a quantitative analytical means for studying acoustic reflection imaging tool and development of the data processing and interpretation methods.acoustic reflection imaging, 3D wave field modeling, non-uniform staggered grid, PML absorb ring boundary, parallel schemeThe borehole acoustic reflection imaging logging is a newly developed acoustic logging method and has attracted many interests in recent years. After its pioneer tool, BARS (borehole acoustic reflection survey) [1] , developed in the last decade, Schlumberger recently introduced a new generation acoustic logging tool, sonic scanner, which was reported to have achieved much better reflected wave field imaging [2] . Tang et al. [3] have recently developed an algorithm for reflected wave imaging from the signal received by conventional tools like XMAC of Baker Hughes. In China, the Logging Service Company of Dagang Oilfield developed a new logging tool of ultra-long spacing with the similar functions as BARS in 2005 1) . These tools radiate wave energy into the surrounding formations as P and S waves. When encountered impedance discontinuity, these waves will be reflected and refracted, as shown in Figure 1, accompanying also the mode conversions between P and S. According to Snell's law, it is easy to see from the geometrical ray paths that the P-P reflections can be received when the transmitter and receiver transducers are all above (or below) the reflective interface, as shown in Figure 2. While the converted waves P-S and S-P can be received if the transmitter and receiver transducers are located above and below the interface separately, as shown in Figure 3. These converted and reflected waves can be utilized to image the position and geometry of the geological structures away from borehole to obtain the information like dips and azimuths of these structures [4,5] . Th...