A method for identifying the instantaneous frequency of a linear time-varying structure was proposed. Firstly, the second-order vibration equations can be rewritten one order state-space equations. Secondly, free response signals were decomposed using the Daubechies wavelet scaling functions. Based on the orthogonality of the scaling functions, the state-space equations of the time-varying system were transformed into simple linear equations. Lastly, the varying equivalent state-space system matrices of structures at each moment were determined by solving the linear equations and the instantaneous frequency can be extracted though eigenvalue decomposition of the state space system matrices. A continuous cantilever beam model and a three degrees-of-freedom close modal structure with three kinds of time-varying cases (abruptly, smoothly and periodically) were investigated. Numerical results show that the proposed method is accurate and effective to determine instantaneous frequency of a time-varying structure.

提出了一种识别线性时变结构瞬时频率的方法。先将二阶振动微分方程改写为一阶状态方程;再利用Daubechies小波尺度函数，对结构的自由响应信号进行投影,并基于尺度函数的正交性，将状态方程解耦为线性代数方程组;最后求解方程组确定等效的系统转移矩阵，通过特征值分解识别出系统的瞬时频率。以悬臂梁和三自由度密集模态结构为仿真算例，识别了突变、周期变化和线性变化三种情况下的结构瞬时频率，从而验证了该方法的正确性和有效性。

参数识别, 时变系统, 状态空间, 小波变换