弹簧振子链系统的振动局域化现象研究

Vibration localization phenomenon of a spring oscillator chain system

非周期系统具有振动局域化效应,结构阻尼也会使系统的振动发生衰减,为研究两种衰减模式的异同,需分析各自衰减因子的产生机理。以弹簧振子链系统为研究对象,从波传递理论角度出发,结合Furstenberg定理,分别给出对地刚度无序和阻尼作用下系统局域化系数的数学表达式。分别建立两种条件下的有限元模型进行频率响应分析,将各振子单元的振动幅值衰减情况与公式推导结果进行对比,验证理论分析的正确性。研究表明,结构无序会产生与阻尼类似的振动衰减效应,但二者的物理机制不同,无序从结构上改变了系统的振动传递性能,而阻尼使能量发生均匀耗散。研究结果有助于理解结构非周期性的局域化效应,可为改善系统的振动传递性能提供参考。

An aperiodic system has vibration localization effect,and structural damping also attenuates the vibration of the system.In order to study similarities and differences of the two attenuation modes,the generation mechanism of each localization factor needs to be analyzed.The mathematical expressions for the localization factor under ground stiffness disorder and damping were given from the perspective of the wave transfer theory and the Furstenberg’s theorem respectively,taking the spring oscillator chain system as the research object.The finite element models under two conditions were established separately for frequency response analysis,and the decay of vibration amplitude of each oscillator unit was compared with theoretical analysis results to verify the correctness of theoretical analysis.It is shown that structure disorder produces similar vibration attenuation effect as damping,but the physical mechanisms are different.Disorder structure changes the vibration transfer performance of the system,while damping causes uniform dissipation of energy.The results contribute to the understanding of localization effect arising from disorder structure and can provide a reference for improving vibration transfer performance.