当结构损伤发生在未布测点的自由度区域时 ,动态扩阶法、模态型减缩法等得到的扩阶模态都不能有效地识别结构的损伤。为了使测试的不完备的模态参数能够用于结构的损伤识别 ,提出了一种新的模态扩阶技术 ,这种技术将未测自由度的模态振型用原始结构的振型与振型的改变量之和表示 ,通过确定振型的改变量从而获得受损结构的完备模态振型。通过数值算例表明 ,该方法所获得的模态振型能够有效地对结构进行损伤识别。

A Method of Modal Expansion for Structural Damage Detection LIU Hui 1 , QU Wei-lian 1, YUAN Run-zhang 2 (1.School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430070,China; 2.State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology,Wuhan 430070,China)Measurements yield only partial mode shapes with respect to the total degrees-of-freedom corresponding to the finite-element model. The common practice to bridge the gap is to expand the measured mode shape to the total degrees-of-freedom of the finite-element model. Unfortunately, the damage detection method based on expansion modal shapes used dynamic expansion method or modal reduction method that can’t bring out right location. In order to use the measured incomplete mode shapes to detect damage,it put forward a new modal expansion method. Unmeasured modal shapes can be represented undamaged structural modal shapes and changes before and after the occurrence of damage in the structure. The complete modal shapes can be obtained by determining the changes before and after the occurrence of damage in the structure. At last, numerical example shows that this approach is effective for detecting structural damage using the optimum and incomplete modal shapes.complete mode; modal expansion; damage detection