多输入多输出非线性系统的一种函数级数模型

A Functional Series Model of Multi input/Multi output Nonlinear System

提出一种表示多输入多输出非线性多自由度系统的输入与输出关系的函数级数模型，并对模型作了讨论，证明了单输入单输出Ｖｏｌｔｅｒａ级数模型只是本文的一种特殊情况。用这个模型对多自由度多项式刚度非线性振动系统进行分析，得出这一类系统的高阶核和多维频率响应函数。文中模型为具有多输入多输出的非线性系统分析及响应预测与谱分析提供了一种基础工具。

A functional series model to represent the multi input/multi output(MIMO) relationship of nonlinear systems with multi digree of freedom is proposed and analysed. It is proved that the single input/single output(SISO) Volterra series model is a special case of the functional series model. Using this model to analyze the nonlinear polynomial stiffness system with multi degree of freedom, the higher order kernels and a multi demensional frequency response function(MRF) of the system are derived. The model lays foundation for response prediction and spectral analysis for multi input/multi output nonlinear systems.