失谐周期结构中振动局部化问题的研究进展

ADVANCES OF VIBRATION LOCALIZATION IN DISORDERED PERIODIC STRUCTURES

周期结构在工程中有很多应用实例，其具有频率通带和禁带等特殊力学性质。失谐可使周期结构的力学特性产生本质变化，即失谐周期结构中存在振动局部化现象。局部化破坏了周期结构模态的规则性，在外激励下会使结构某些部位的响应幅值过大，产生能量积聚，甚至导致结构发生疲劳破坏。因此分析失谐周期结构中振动和能量的传播方式与规律具有重要的理论与实际意义，可以为重要子结构的振动控制和减振设计提供理论依据。针对一维直线型周期结构、循环周期结构以及二维周期结构等，综述了其中的振动局部化问题的研究现状，主要集中于力学模型的建立、振动局部化问题的研究内容、分析方法和主要研究结果等，并提出了值得进一步研究的问题。

Periodic structures find many practical applications in engineering. They have special dynamic characters such as frequency passbands and stopbands. Disorder can result in radical changes of their mechanical properties. In disordered periodic structures, one may see vibration localization. Localization destroys the regularities of vibration modes of periodic structures and some parts of the structures may have very large vibration amplitudes under external excitations. This may lead to energy accumulation or even destroy the structures. So it is very important to analyze the propagation characteristics of vibration and energy in disordered periodic structures, which can provide theoretical bases for the vibration control and vibration reduction of substructures. This paper reviews the current development of the investigations on the vibration localization in one-dimensional linear periodic structures, cyclic periodic and two-dimensional periodic structures. The discussion is focused on the establishment of mechanical models, analytical methods and other issues in vibration localization. Finally, some problems for further studies are suggested.