多自由度系统自然激励技术的统一模型

Unified theoretical model of Natural Excitation Technique(NExT) for multi-degree-of-freedom structural systems

结构运行状态下的模态参数提取是结构健康监测系统需要解决的关键问题之一。自然激励技术的提出为大型复杂工程结构运行状态下的模态参数提取提供了一条新的途径。原始自然激励技术给出了单输入白噪声激励下利用结构位移响应的互相关函数进行模态识别的理论模型,对于多输入情况则缺乏相应的理论模型。本文在单输入理论模型的基础上进一步发展了自然激励技术:推导了多输入独立白噪声激励下多自由度系统结构位移响应的互相关函数的解析公式,并分析了它与单输入情况下互相关函数之间的关系;基于此互相关函数定义了一个新函数,证明它含有结构各阶模态信息,可以表达为一系列衰减正弦函数之和,并且各个组分正弦函数的频率等于各阶模态的有阻尼固有圆频率;提出了以新函数为核心的同时适用于单输入和多输入情况的模态识别算法,建立了自然激励技术的统一模型。

Modal parameter identification （MPI） of structures subjected to highly uncertain natural excitations is crucial for structural health monitoring systems. The natural excitation technique （NEXT） had provided a new approach for MPI of large complicated structures using operating ambient excitations. The original NExT proposed a theoretical model of MPI using the displacement cross-correlation function of structures subjected to single white noise excitation, but there was no proper theoretical model for the multi-input case. The analytical formula of the displacement cross-correlation function is derived for multi-degree-of-freedom structural systems subjected to multiple independent white noise excitations. A new function is defined using this cross-correlation function. It is proved that the new function is the sums of decaying sinusoids which have the same damped frequencies and damping ratios as the modes of the system. Consequently, it has the same form as impulse response function and thus can be used in standard MPI algorithms. Based on the new function,a unified theoretical model of NExT is proposed, which can extract structural modal parameters using displacement responses for the case of either singleinput or multi-input.