第一作者赵晓丹男，博士，教授，1963年7月生

利用分段积分识别阻尼比研究

赵晓丹，徐俊杰，王西富

(江苏大学汽车与交通工程学院，江苏镇江212013)

摘要：提出利用分段积分列方程识别阻尼比方法。用快速傅里叶变换加连续傅里叶变换(Fast Fourier Transform plus Continuous Fourier Transform，FFT-FT)识别响应信号固有频率，并据此构造复指数函数；与响应信号进行两次时间不同的内积运算，控制运算时间为响应信号半周期整数倍；推导衰减系数计算公式，识别阻尼比。该方法具有控制内积运算时间消除负频率项影响特点，不受阻尼大小、采样长度限制，识别精度高，结合迭代运算能识别密集模态阻尼。仿真计算、实验表明，在曲轴阻尼实验中，该方法能准确识别阻尼的微小变化，具有工程实用性。

关键词：分段积分；衰减系数；阻尼比；曲轴

基金项目：江苏大学高级专业人才科研基金资助项目(11JDG096)；江苏高校优势学科建设工程基金资助项目(苏政办发[2011]6号)

收稿日期：2014-05-26修改稿收到日期：2014-09-30

中图分类号:TB123

文献标志码：A

DOI:10.13465/j.cnki.jvs.2015.20.019

Abstract:A method using piecewise integral to identify damping ratios was proposed. The natural frequency was calculated based on a response signal by the application of Fast Fourier Transform plus Continuous Fourier Transform (FFT-FT). A complex exponential function was constructed with the calculated natural frequency, two inner products with different integral time were conducted between the response signal and the constructed exponential function, the operation time of inner products was controlled to be integer times of semi-period of the response signal, and then the formula of attenuation coefficient was derived. As a result, the damping ratio was determined. The feature of the method is that the interference by negative frequency item is eliminated by controlling the operation time of inner products. The method is not restricted by the size of damping ratios and the length of sample, and it has high precision. Damping ratios of closely spaced modes can be also identified by the method combined with iterative algorithm. Digital simulations and experiments show that the method is effective. In crankshaft experiments, small changes of damping ratios were identified. The method is practical in engineering.

Method for damping identification using piecewise integral

ZHAOXiao-dan,XUJun-jie,WANGXi-fu(School of Automobile and Traffic Engineering, Jiangsu University, Zhenjiang 212013, China)

Key words:piecewise integral; attenuation coefficient; damping ratio; crankshaft

阻尼在结构故障诊断、振动实时监控、荷载识别、噪声控制及动力响应等研究中有重要意义[1-2]；但阻尼的识别精度一直不高，受测量方法影响较大，提高阻尼比识别精度成为主要研究目标[3]。测量阻尼主要有时、频域识别方法，时域识别方法包括自由衰减法、ITD法、STD法、ARMA方法衍生及随机减量技术等；频域识别方法最经典的为半功率带宽法；另外有小波变换[4-5]、EMD-HT[6]等方法。小波变换存在端点效应等[7-8]；而EMD-HT方法需用模态经验分解(EMD)，但EMD包络线计算存在过冲、欠冲，数据端点处理困难，存在提取模态不完整及出现虚假模态问题[9]。……