The initial and boundary condition,the hydrodynamic force on the cylinder surface and the cylinder response equations with shear flow were derived based on the stream function-vorticity equations in the exponential-polar coordinates attached on the moving cylinder.The whole evolutions of cylinder starting from rest and then undergoing development and vibration steady were calculated and discussed.The development process of separation vortexes,the deformation and shift of drag-lift phase diagram and the variation of cylinder vibration and equilibrium position were described.Moreover,the steady condition of vortex-induced vibration with the shear rate K was investigated.The results show that the symmetrical flow field will be broken due to the background vorticity generated by the shear flow which also causes the increase of upper vortex strength and the decrease of lower vortex strength.The vortex street inclines toward the lower side and the inclination of vortex streets increase with the increasing shear rate K.So does the shift of pressure curves which leads to the increase of absolute value of lift,the amplitude and the shift of cylinder.%将指数极坐标系建立在运动的圆柱上，推导了运动坐标中剪切来流条件下，涡生振荡的涡量－流函数守恒方程、其初始和边界条件、圆柱表面的水动力表达式、圆柱振荡方程。对圆柱从静止开始振荡到发展为稳定振荡状态进行了计算和讨论，描述了脱体涡街的发展过程、升阻力相图的连续变形和漂移、圆柱振荡和平衡位置的变化过程。研究了涡生振荡终态随剪切度K的变化。结果表明：剪切来流给流场加入了背景涡，使圆柱的上涡增强、下涡减弱，流场的对称性被破坏。随着剪切度K的增大，涡街的倾斜程度增大，压力曲线的漂移量增大，由此导致升力的绝对值增大，圆柱的振幅增大且平衡位置向圆柱下侧的漂移也增大。
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