关于超谐波共振问题  

On the superharmonic resonance problems

作　　者：赵杰民[1] 

机构地区：[1]北京联合大学基础部,北京100101

出　　处：《合肥工业大学学报（自然科学版）》2005年第12期1618-1620,共3页Journal of Hefei University of Technology：Natural Science

摘　　要：文章对复杂的带阻尼和一般力的时滞振动问题求得一致有效渐近展开式,给出了共振解简洁实用的近似解析公式;应用该公式,大量工程中的时滞系统共振问题,可方便的得到近似解析解以及振幅、频率、周期和相位等;同时其结果还推广了一些已知结果。In this paper, the problems of superharmonic resonance of time-delay systems are studied. The famous method of multiple scales is successfully extended to the time-delay systems ,which provides great convenience for the study of the systems with time lag. As to the complex forced oscillation problem of a class of time-delay systems with damping and general force, a uniformly valid asymptotic expansion is obtained according to the distinct circumstance of superharmonic resonance, and an approximate analytic formula which is very simple and explicit is also given. By using the formula,the approximate analytic solutions for a great number of resonance problems of time-delay oseillation systems, especially the amplitude, frequency, period and phase can be got conveniently. The conclusions of related literature become simple corollaries of the paper.

关 键 词：振动 超谐波共振 近似解析解 

分 类 号：O32[理学—一般力学与力学基础]