多点激励中的控制载荷存在性  

The Existence of Control Load in Multi-points Excitation

作　　者：胡杰[1,2] HU Jie(Institute of System Engineering,CAEP,Mianyang 621999,China;Shock and Vibration of Engineering Materials and Structures Key Laboratory of Sichuan Province,Mianyang 621999,China)

机构地区：[1]中国工程物理研究院总体工程研究所,四川绵阳621999 [2]工程材料与结构冲击振动四川省重点实验室,四川绵阳621999

出　　处：《装备环境工程》2021年第7期112-118,共7页Equipment Environmental Engineering

摘　　要：目的给出多点激励振动试验中控制载荷的存在性判据,建立控制载荷分析的数值模拟方法。方法从控制载荷数量与目标响应数量关系出发,通过传递函数矩阵及其增广矩阵的秩的大小关系比较,对多点激励振动环境试验中控制载荷的存在性进行研究,并针对当前多点激励试验中只控制多个点的幅值而不控制相互之间相位差的现状,对存在性结论进行修正,同时通过理论推导和数值优化算法,建立不同工况下控制载荷的分析方法。结果对于同时控制响应幅值和相位的情况,当传递函数矩阵的秩R_c与其增广矩阵的秩R_z相同且为满秩时,控制载荷存在唯一解;当R_c=R_z但非满秩时,控制载荷不唯一;当R_c<R_z时,控制载荷不存在。对于实际工程应用中一般只控制响应的幅值的情况,当R_c=R_z时,控制载荷不唯一;当R_c<R_z时,在某些频段上控制载荷仍然存在。结论多点激励载荷与响应幅值之间为非线性关系,对于具有工程意义的以少量加载设备实现多个点响应控制的情况,在控制容差范围内,控制载荷在某些频段上仍然存在。The existence criterion of control load in multi-point vibration test is given,and the numerical simulation analysis method of control load is established.Based on the discussion of control load number and target response number,according to the size relation comparison of transfer function matrix with the augmented matrix,the existence of control load in multi-points vibration environment test is studied.Furthermore,aiming at that only the amplitude of multi-points is controlled at present,the existence conclusion is modified because the phase difference is ignored,and the analysis methods of control load under different working conditions are established via theoretical deduction and numerical optimization.For the condition of controlling amplitude and phase simultaneously,if the transfer matrix rank R_c is equal to its augmented matrix rank R_z,both full rank,there is an uniqueness existence of control load;if R_c is equal to R_z,but not full rank,the existence of control load is not unique;if R_c is less than R_z,the control load could not be found.As for the condition of only controlling amplitude of response in practical engineering application,if R_c is equal to R_z,the existence of control load is not unique;if R_c is less than R_z,the control load still exists at some frequency point.The transfer relation between control load and the response amplitude in multi-point excitation is nonlinear;for the state of controlling more points with less load equipment,with engineering significance,the control load still exists in specified frequency range in the limitation of control tolerance.

关 键 词：多点激励 振动 控制载荷 传递函数 唯一性 存在性 

分 类 号：O242[理学—计算数学] O321[理学—数学]