基于幅频特性曲线簇公共点的智能弹簧减振系统参数设计

研究了无阻尼智能弹簧减振系统的一种参数设计方法.采用等效线性化方法将系统中的干摩擦阻尼等效成黏性阻尼,建立系统的数学模型,推导出无量纲化的振动微分方程,得到系统频响特性的解析解.对系统幅频特性进行了数值分析,结果发现:幅频特性曲线簇通过一个公共点,该公共点随质量比的增大向左偏移,随刚度比的增大向右偏移;系统存在一个最优控制参数值,使系统幅频特性曲线峰值最小,其随质量比的增大而减小,但不受刚度比的影响.根据公共点的性质,得到幅频特性曲线簇公共点对应的频率比、最优控制参数和最小振幅的计算公式.确定系统参数的选用原则与范围,并利用公共点提出智能弹簧减振系统参数设计的方法和步骤.

Parameters design of smart spring vibration suppression system based on common point of amplitude frequency characteristic curve cluster

A design method of system parameters for undamped smart spring vibration suppression system was studied. The dry friction damping of the system was transformed equivalently to viscous damping by equivalent linearization technique, as a result, the mathematical model of the system was established. The dimensionless differential equations of vibration were derived and the analytic solution of frequency response characteristics was obtained. The amplitude frequency characteristics of the system were numerically analyzed. The study results reveal that the amplitude frequency characteristic curve cluster of the system has a common point that will be shifted to the left as the mass ratio increases and to the right as the stiffness ratio increases. There is an optimum value, for the control parameters of system, which could make the peak value of amplitude frequency characteristic curve of the system be minimum. The optimum control parameter will reduce with the increase of the mass ratio, but it is not affected by the stiffness ratio. The formulas of frequency ratio, optimum control parameter and minimum amplitude corresponding to the common point of amplitude frequency characteristic curve cluster were derived. The selection principle and range of system parameters were proposed. The design method and procedures of system parameters of smart spring vibration suppression system were presented.