基于贝塞尔不等式原理的密集模态阻尼识别  

Damping identification for closely spaced modes based on Bessel Inequality

作　　者：赵晓丹[1] 韩俊阳 孙黎明 王西富[1] ZHAO Xiaodan;HAN Junyang;SUN Liming;WANG Xifu(School of Automobile and Traffic Engineering,Jiangsu University,Zhenjiang 212013,China;State Key Laboratory of Power System of Tractor,Luoyang Tractor Research Institude Co.,LTD,Luoyang 471039,China)

机构地区：[1]江苏大学汽车与交通工程学院,江苏镇江212013 [2]拖拉机动力系统国家重点实验室,洛阳拖拉机研究所有限公司,河南洛阳471039

出　　处：《振动与冲击》2018年第20期179-184,共6页Journal of Vibration and Shock

基　　金：拖拉机动力系统国家重点实验室开放基金(SKT2016013)

摘　　要：密集模态广泛存在于振动响应信号中,然而密集模态的阻尼识别困难、精度低,密集模态阻尼的识别是目前研究的难点问题。提出一种识别密集模态阻尼的新方法,在密集模态附近建立一组基函数系,使用Gram-Schmidt方法将函数系正交化,通过內积运算,获取测得的振动响应信号在该标准正交系上的投影,采用遗传算法结合拟牛顿法优化搜索投影的最大值,运用贝塞尔不等式原理诊断出振动响应信号中各阶模态的固有频率和衰减系数,识别出各阶模态阻尼比。该方法不受模态密集程度的限制,经过仿真和实验验证,能够准确地诊断出密集模态阻尼比,具有理论和工程应用价值。Closely spaced modes exist in vibration response signals widely.The damping ratio of closely spaced modes can not be identified accurately.It has been a difficult problem to improve identification accuracy of the damping ratio of closely spaced modes.A new method to estimate the damping ratio was presented.A set of basis functions were constructed nearby the closely spaced modes and processed with the Schmidt orthogonalization.The projection of vibration response signals on standard orthogonal basis functions was calculated with the inner product algorithm.The maximum of the projection was searched using a genetic algorithm and quasi-Newton methods.According to Bessel Inequality,the natural frequency and attenuation coefficient of each modal were obtained when the projection achieved the maximum value.The damping ratios could be estimated with the natural frequency and attenuation coefficient of each modal.This method is not restricted by modal density.Digital simulations and experiment show that the damping ratio of closely spaced modes can be identified accurately.This method is valuable practically.

关 键 词：阻尼比 密集模态 贝塞尔不等式 遗传算法 

分 类 号：TB123[理学—工程力学]