干摩擦阻尼叶片周期振动响应的解析计算

SOLVING PERIODIC RESPONSE OF DRY FRICTION DAMPER BLADES USING ANALITICAL METHOD

研究一个描述干摩擦阻尼器叶片振动的质量—弹簧—阻尼器振动系统。阻尼器摩擦力由黏滞模型描述,由接触面滑动或黏滞状态决定。将滞后摩擦力分为四个阶段,从而得到各个阶段上的线性振动系统,给出求干摩擦阻尼叶片周期响应的解析公式。计算表明,阻尼端压力取适当值时,阻尼器会处于最优的摩擦接触状态,获得较好减振效果。同时引入阻尼器处对叶片还起到调频作用,也可以起到使激振频率避开共振频率的作用,减小振动幅值。

To determine the steady state response of a dry friction damper blade excited by a periodic force, an analytical method is developed. The elastic friction element is represented by a connection of a linear spring in series with a Coulomb friction damper. The friction force is described by a hysteretic model, which is determined by the state of motion of the damper, i.e. stick or slip. The method is based on a procedure that uses analytical solution forms for the response within the four intervals where the system possesses a linear vibration characteristic and combines these solutions to form an exact, periodic motion of the system. Numerical simulations show that the resonant vibration of the blade can be well controlled in case the normal pressure applied between damper contacting surfaces is in a suitable value. In addition, introducing the friction damper can also modulate the natural frequency of the blade system, which can avoid the system operated in resonance sometimes and reduce the vibration-amplitude of the blade.