Narrow Results

The reduction of the periodicity of phononic crystals (PnCs) usually leads to the decrease of band gap (BG) width. However, a systematic study of the relationship between the unit cell and the supercell in the proposed hybrid stepped PnCs shows that the BG width can be increased in special cases. How the periodicity of PnCs affects the final BG characteristics is important for the design of PnCs with high structural performance. Supercell of PnCs with imperfections from the rotation of the unit cell was used to demonstrate the relationship between the unit cell and the supercell, which was further used for the wave attenuations of the proposed hybrid stepped PnCs. The rotation angle and the number of the rotating scatterers can be controlled for better structural performance for the PnCs. The different changes of the equivalent stiffness corresponding to the starting and the end frequencies lead to the increase of the BG width when the ration angle of the unit cell is $35^{\circ }$ in the supercell composed of zigzag scatterers and cross scatterers. The rotation of the unit cell in the supercell leads to the decrease of the starting frequency.

According to the characteristic of the deformation of helical buckling appeared on sucker rod string (SRS) during down stroke, the influence of the deformation of helical buckling on longitudinal vibration of SRS is considered. Then SRS is dispersed into a spring-mass-damper system and a mechanical model of nonlinear longitudinal vibration for SRS is built. With the mechanical model, a simulation model of nonlinear second order differential equations is derived. The dynamic response under displacement and load excitation is given with Newmark method. The model is verified by comparing it with the experimental data, and good agreement is found. The steady-state response of Sucker Rod Pumping System (SRPS) is analyzed. The simulation results show that the plunger load is increasing and pump pressure is decreasing during down stroke, and the lead time of traveling valve opening is decreasing when the sucker rod buckling is considered, which is important to the fault diagnosis, oil production forecast and energy saving.