质量分布对弹簧振子链系统振动传递特性的影响  

Effect of mass distribution on vibration transmission characteristics of spring oscillator chain system

作　　者：赵鹏 纪刚[1] 李宗威 ZHAO Peng;JI Gang;LI Zong-wei(College of Naval Architecture and Ocean Engineering,Naval University of Engineering,Wuhan 430033,China)

机构地区：[1]海军工程大学舰船与海洋学院,湖北武汉430033

出　　处：《舰船科学技术》2023年第1期31-36,共6页Ship Science and Technology

基　　金：国防预研基金资助项目(995 0204010404)。

摘　　要：为研究质量分布形式对一维弹簧振子链系统振动传递特性影响的一般规律,从波传递的角度出发,分析相同质量分布弹簧振子链系统通频带和止频带的产生机理,利用随机矩阵的数学理论来揭示无序质量分布系统的振动传递特性。采用有限元法对相同质量与质量无序的弹簧振子链模型进行频率响应计算,求取各频率下子单元振动幅值的变化情况,将衰减情况与理论分析值进行对比。研究表明,质量的无序分布对弹簧振子链系统的振动传递性能有较大改善,系统将不再存在通频带,振动主要会被局限在激振源附近,局域化因子理论公式能很好地反映振动衰减情况。研究结果有助于理解非周期系统的振动局域化现象,并为多维复杂结构的振动局域化分析提供参考。In order to study the general regularity of mass distribution on vibration transmission characteristics of one-dimensional spring oscillator chain system, the mechanism about passband and stopband of periodic spring oscillator chain system is analyzed from the perspective of wave transmission, and the mathematical theory of random matrix product is used to reveal transmission characteristics of disordered mass distribution system. The finite element method is used to calculate frequency response of spring oscillator chain model with the same mass and mass disorder, and the variation of subunit vibration amplitude at each frequency is obtained to compare with theoretical analysis value. The study shows that disordered distribution of masses has a great improvement on vibration transmission performance and the system will no longer have a passband. Vibration will be mainly confined near the excitation source and the localization factor theoretical formula can respond well to the vibration decay. The results help to understand vibration localization phenomenon of non-periodic systems and provide a reference for the vibration localization analysis of multidimensional complex structures.

关 键 词：弹簧振子链 质量无序 振动传递 局域化因子 

分 类 号：U661.44[交通运输工程—船舶及航道工程]