周期性结构中结构缺陷的影响及模态局部化

利用一个单自由度子结构串连组合结构模型，研究了结构缺陷对周期性 结构动态性能的影响．当结构中任一子结构成员的质量或／和刚度具有缺陷 时，得到了结构振动主模态、结构缺陷参数变化对频谱分布影响的解析表达 式，并给出了模态局部化发生的条件．最后，运用一个数值例子，简论了此类 结构中最关键的参数──相对耦合刚度对缺陷影响的重要性．

Effects of structural imperfections on periodic structures and mode localization

In the literature of structural vibration and dynamics ,the study of the effects of small structural imperfections on the dynamic properties of engineering periodic structures(which may also be called the dynamics of disordered periodic structures) and vibration mode localization phenomena is a typical subject which attracts much attention of researchers on structural dynamics in recent years. The importance of small structural imperfections not only represents an interesting problem in structural vibration analysis but also plays an important role in affecting the dynamics of the structures. The main motivation for these studies lies in a well known fact that ,under appropriate conditions, small imperfections may cause disproportionately large variations in the system' s response from that predicted from the perfect (periodic) model. Obviously, such phenomena are important to structural dynamics, structural control, and sensitivity based structural re-analysis, etc. A mono-coupled periodic structure model which consists of N single DOF substructures (components) is studied. The analytical solution for the mode shapes and the natural frequencies of such structures with single localized defect is obtained in terms of various models and imperfection parameters, which explicitly shows the effects of structural imperfections on the structural spectral distribution and the conditions of strong mode localization occurrence. The well known concepts of wave propagation of periodic structures are used to simplify the analysis and explain the results of modal analysis ,which provide physical insights into the problem. It is shown that the study of this special case of single component containing imperfections provides much information about the effects of structural imperfections, particularly in relation to the relative coupling strength which is shown theoretically and numerically to be a key factor for the imperfection effects.