也论复模态振动分析理论的几个问题

ON SEVERAL PROBLEMS OF THE COMPLEX MODAL THEORY OF VIBRATION ANALYSIS

本文首先推证了线性振动系统的复模态特征参数退化为实模态特征参数的过渡方式;其次,基于实模态理论与复模态理论的统一性要求,规定了复特征向量的正规化条件;然后,建立了复特征向量空间中的展开定理的表达式,并证明了其与实特征向量空问中的展开定理的表达式的统一性;最后,阐述了目前对复模态振动现象的特点的一些基本认识,并对复模态振动系统的共振慨念的近似定义提出了建议。

In this paper,we first prove the form of transition from the complex modal eigen parameters to the real moeal ones of linear vibrational system.Secondly, according to the unity between the real and complex modal theories,the norma- lization condition of complex eigenvectors is stipulated.Then,the expression developing a complex vector into a series of the normal complex eigenvectors is set up,and the unity between the expression and that developing a real vector into a series of the normal real eigenvectors is proved Finally,some basic properties of complex modal vibration phenomena are set forth,and a suggestion to the definition of resonance concept of complex modal vibrational system is put forward.