基于摄动法的密频结构可控性

Controllability of Structures with Closely Spaced Natural Frequencies Based on Perturbation Analysis

摘要:

为研究密频结构频率密集度对结构可控性的影响，针对3自由度的密频结构，从结构基本振动方程入手，采用摄动分析方法推导了闭环系统频率、阻尼比和摄动量的相关方程.在速度反馈和状态反馈情况下，讨论了结构频率密集度对结构可控性的影响，并对不确定参数对结构模态阻尼比的影响进行了分析.分析结果表明，对于采用速度反馈、位移反馈的闭环系统，随着结构频率密集度参数的减小，结构的部分模态阻尼比逐渐趋向于零，相应的结构模态趋于不可控.考虑了结构刚度和质量参数不确定性对密频结构可控性的影响，结果表明参数不确定性会影响密频结构不同模态之间的耦合程度，进而改变结构的可控度.

Abstract:

An investigation was made into the influence of frequency intensity on the controllability of structures with closelyspaced natural frequencies.The perturbation equations were established for a closedloop system to study the relationship of frequencies,modal damping ratios and perturbation parameters.The analysis focused on a threedegreefreedom structure with closely spaced natural frequencies.The velocity and displacement feedbacks were considered in the calculation.Several cases with velocity feedback and state feedback were considered.And the preciseness of perturbation methods was checked.The calculation results show that the damping ratios of two modes are decreasing with the decreasing of intensity parameter values of the structure with closely spaced natural frequencies,indicating that the controllability of corresponding modes is diminishing.The uncertainties in mass and stiffness matrices were also discussed in this paper.The calculation results show that the degrees of mode coupling will change due to the structural uncertainties and the controllability will be influenced subsequently.