线性主动结构及模态(Ⅰ)——基本概念及属性

Linear Active Structures and Modes(Ⅰ) ——Basic Concepts and Properties

阐明了主动结构的若干基本概念,归纳了主动结构动力学的主要问题· 对线性主动结构的模态做了注释,注释包括:右和左特征向量的物理意义,右特征向量为振型,左特征向量表征响应的模态分量;伴随结构及互易定理,两个互为伴随主动结构,且有对偶反馈增益矩阵,左和右特征向量互易;主动结构与被动结构的关联用传递函数表示。

Some basic concepts about the active structures were firstly explained , and the main subjects to study in the field of active structure dynamics were synthesized. For the linear active structures, the annotations on the modes were done in detail. The physical meanings of the right and left eigenvectors were explained. The right eigenvectors are the modal shapes and the modal responses of an active structure depend on the left ones. The adjoint structure of an active structure was defined and the reciprocity theorem was interpreted. For two active structures, which are adjoint to each other and with the reciprocal gain-matrices, the right and left eigenvector are reciprocal. The relationship between an active structure and the corresponding passive structure is expressed with the transfer functions, which is employed to resolve the estimation problems.