含分数阶惯容器隔振系统的临界阻尼设计

Critical Damping Design of Vibration Isolation Systems with Fractional Order Inerter

为了研究用含分数阶导数描述的液力惯容器的非线性隔振系统特性,建立无量纲动力学模型。在无阻尼控制时,通过对比力传递率特性指标讨论参数对隔振系统性能的影响。结果表明分数阶惯容器能够反映液力式惯容器的多相特性,既有惯性作用又有一定阻尼作用,相比整数阶惯容器在隔振效果上有一定优势,但同样不能有效抑制非线性效应。在忽略非线性项的前提下,考虑系统含分数导数的特殊情况,详细介绍分数阶临界阻尼设计过程。仿真试验结果表明,所设计临界阻尼可以保证系统在自由振动时单调递减,而且考虑非线性项后,相比整数阶惯容器能够更好抑制非线性效应。

The dimensionless dynamic model is established to analyze the nonlinear vibration isolation system characteristics of the hydraulic inerter with fractional derivatives.In the case of undamped control,the influence of the parameters on the performance of the vibration isolation system is compared and discussed through the specific index of force transmissibility.The results show that the fractional order inerter can reflect the multiphase characteristics of the hydraulic inerter,namely it has both inertia and damping effects.Compared with the integral order inerter,it has some advantages in vibration isolation effect,but it can’t effectively suppress the nonlinear effect either.Considering the special case of the system with fractional derivatives,the design process of fractional order critical damping is introduced in detail.The simulation results show that the designed critical damping can ensure the monotonic decrease of free vibration of the system,and the nonlinear effect can be better suppressed than that of the integer order inerter when the nonlinear term is considered.