利用分段积分识别阻尼比研究

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。%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.