关于复模态理论的数学方法、物理概念及其与实模态理论的统一性

本文系统地论述了振动结构参数识别的复模态理论的基本数学方法──状态向量法及拉氏变换法的特点、基本推演过程及基本公式，并论证了这两种方法的一致性；解释了复模态模型的物理意义．说明了ｓ城传递函数与频域传递函数的图象关系；用图解法形象地说明了复振型所反映的振动图象。最后，根据复模态理论推演了转化为实模态情况的条件，并从而导得了实模态模型的所有模态参数公式，论证了复模态理论与实模态理论的统一性。

Some General Concepts of Complex Mode Theory

This paper presents a general review of the fundamental mathematical approaches of the complex mode theory-the state vector method and Laplace transformation, the basic formulas and their derivation. The conceptions of complex mode model and the modal parameters, the correlation between s-domain and frequency domain, and the vibration phenomena of complex mode shape are described. The consistency of these two mathematical approaches is discussed through comparison. The transformation condition from complex mode shape to normal shape is deduced. Based on this condition, all the normal modal parameters and formulas can be derived from the complex mode theory. Therefore, the consistency of complex mode theory and the normal mode theory was proved.