关于复模态参数的冗余性

生成仿真传递函数是考核模态识别算法和评估模态分析软件的不可缺少的环节．比较可行的3种计算方案表明:若选择将传递函数表示为复模态参数的展开式，则可以自由设定仿真模态的特性，如密频、大阻尼和复模态；然而，即使采用这种格式也不能随意设置一组复模态振型，因为这种格式的表观参数个数大于物理参数个数；故而，若对应的物理参数有意义，那么复模态参数必须满足一组约束关系．通过分析复模态系统的特征值问题，和复模态参数反演物理参数的方程式，给出了复模态参数间的一组非线性冗余约束．讨论了实模态、无阻尼和不完全模态等特殊情形的冗余约束具体形式与独立参数的个数，值得注意的是，对于实模态系统，冗余约束自动满足．给出冗余约束在传递函数矩阵和一列传递函数上的等价形式．这些结果有助于产生仿真传递函数，实施优化型识别算法，以及评估识别结果；还可用来评价残余模态和识别完整性．

On the Redundancy of Complex Modal Parameters

Generating the simulation transfer function (TF) is indispensable to modal analysis, such as examining modal parameters identification algorithm, and assessing modal analysis software. Comparing 3 feasible algorithms to simulate TF shows that,one of them is preperable,which is expressing the TF as the function of the complex modal parameters(CMPs),because the deliberate behaviors of CMPs can be implemented easily,such as,dense modals,large damping,and complex modal shape,etc.Nonetheless,even this preferable algorithms is elected,the complex modal shapes cannot be specified arbitrarily,because the number of CMPs far more exceeds that in physical coordinate.So for physical realizable system,there are redundant constraints in CMPs.By analyzing the eigenvalue problem of a complex modal system,and the inversion equations from CMPs to physical parameters,the explicit redundancy constraints were presented.For the special cases,such as the real modal,the damping free modal,and non_complete identification,the specific forms of the redundancy constraints were discussed,along with the number of independent parameters.It is worthy of noting that,redundancy constraints are automatically satisfied for the real modal case.Their equivalent forms on the transfer matrix and a column of transfer matrix were also provided. These results are applicable to generate TF, to implement identification by optimization and appreciate the identification results, to evaluate residual modal, and to verify the complementary of identified modal orders.