中文摘要：

针对传统的机械系统固有频率及阻尼比计算方法中，时域方法易造成主观误差，频域方法存在一定精度限制的问题，提出了一种利用指数衰减正弦信号频谱校正算法计算系统阻尼比和固有频率的新方法。该方法首先利用基于汉宁窗的插值频谱校正方法获得频率偏移量和衰减因子，再结合有阻尼自由振动响应与指数衰减正弦信号的相似性关系求取固有频率，进而获得系统阻尼比和有阻尼固有频率，最终计算出无阻尼固有频率。分别使用传统时域方法和本文提出的频域方法对压电悬臂梁的固有频率及阻尼比进行计算，结果表明新方法拥有更高的计算精度和更好的信噪比适应性。与传统的频率拟合方法相比，本文所提方法也更简单，计算效率更高。

英文摘要：

A new algorithm to calculate the system damping ratio and natural frequency using frequency spectrum correction of exponentially decaying sinusoidal signals is proposed to solve the problem that time domain methods are easy to cause subjective errors and there exists the accuracy limit problem in frequency domain methods in traditional methods to calculate natural frequencies and damping ratios of mechanical systems. The interpolation spectrum correcting method based on Hanning-window is used to obtain frequency deviations and damped factors. Then the natural frequency is calculated by combining similarity relations between damping free vibration responses and exponentially decaying sinusoidal signals, and the system damping ratio and damped natural frequency are obtained. The undamped natural frequency is finally calculated. Both a traditional time domain method and the proposed frequency domain method are respectively used to calculate the natural frequency and damping ratio of a piezoelectric cantilever beam. The results show that the proposed algorithm has a higher calculation accuracy and better adaption of signal to noise ratio. Comparisons with the traditional frequency fitting method show that the new algorithm is simpler and its computational efficiency is higher.