This paper proposes a double-vibrator three-component pillared phononic crystal plate and theoretically studies the properties of vibration band gaps of this plate. The band structures and the displacement fields of the eigenmodes are calculated by the finite element method. Comparing the transmission power spectrums of the vibrations in the plate, the flexural vibration gap is proved more useful than the longitudinal vibration gap. The influence of the lattice constant, the height, and diameter of the pillars on the flexural vibration gaps are investigated. A supercell composed of the uni-vibrator and the double-vibrator unit cells is also investigated, and the analysis shows that the starting frequencies of the gaps in this supercell structure depend on the features of its pillars. This research can be used in the low frequency vibration insulation of plate structures.

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The hinge, a key component of deployable space mechanism, has a significant influence on the precision of the whole mechanism. Hysteresis is one of the uncontrollable factors affecting the precision of the hinge. However, much work so far has focused on the equivalent model of hysteresis, which is far from the actual situation. In this paper, the hysteresis model of the general rotary hinge was established via the finite element method (ABAQUS/Standard 6.14-4). The correctness of the model was verified by experiments, and the loss factor was defined to measure the size of hysteresis. The response surface method was then used to establish the response surface of the hysteresis loss factor of the general rotary hinge. Results show that the hinge was optimised. By comparing the response surfaces of the two types of hinges, the modified hinge can effectively reduce hysteresis loss factor. Importantly, the repeatability of the hinge can be effectively improved by reducing hysteresis loss factor through repeatability experiments. Using this method, the response surface of the hinge's hysteresis loss factor can be established accurately, and the hysteresis loss factor can be reduced through optimal design to improve the precision of the hinge. This method can provide reference and guidance for the hinge design of the high-precision deployable mechanism. INDEX TERMS Finite element method, hinge, hysteresis, response surface method.

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