结构多位置损伤的线性诊断方法

引入了一阶振型变化率的概念，并且证明了一阶振型变化率具有可叠加性，多位置损伤所引起的一阶振型变化率是各单位置损伤引起的一阶振型变化率的线性叠加．以一阶振型变化率为损伤标识量，将结构的多位置损伤状态等价于各单位置损伤状态的叠加．列出了结构多位置损伤的线性损伤诊断方法的实现步骤．以简支梁和四边固支的正方形板的多位置损伤诊断为算例表明，该方法不仅可准确地判定结构的损伤状态，而且损伤诊断的过程简单．

Linear Detection Method for Multiple Damages in Structures

The definition of variation rate of the first modal was presented. It was proved that the variation rates are superpositionable, so that the variation rate of the first modal caused by multiple damages is obtained by superposition of all variation rates of the first modal caused by all the damages. Therefore, the variation rate of the first modal is taken as the signature for damage detection, and multiple damage state is transformed into superposition of single damage states. The procedure of the proposed method was presented. A simply-supported beam and a square plate fixed at four sides were taken as example. The results show that the method can precisely determine the damage state with a simple procedure.