基于解析模态分解的时变与弱非线性结构密集模态参数识别

Analytical modal decomposition-based time-varying and weakly nonlinear structures' modal parametric identification with closely-spaced modes

对于时变与非线性的结构系统,由于结构模态响应信号的瞬时频率并不等同于结构本身的瞬时频率,因此推导了单自由度与多自由度体系在自由振动和受迫振动下模态响应信号的瞬时频率与结构本身瞬时频率的关系,理论结果表明,对于时变的线性结构和弱非线性结构,模态响应的瞬时频率缓慢变化的部分与结构系统的瞬时频率近似相等。通过对一杜芬系统的数值模拟和对一调整索力变化而使其频率变化的斜拉索自由振动实验,验证了理论结果的正确性。对于具有密集模态的时变与非线性的多自由度体系,提出了把解析模式分解方法扩展到时变与非线性结构的模态分解。该方法通过小波变换选取二分时变截止频率,对结构的时变模态响应进行分离,从而实现多自由度结构时变参数识别。最后,对一具有密集模态的两层框架时变系统受白噪声激励和地震激励进行数值模拟,结果表明,提出的方法能有效的分解时变系统的密集模态响应并能较好的识别出结构系统的瞬时频率。

The instantaneous frequency of modal response signals is not equal to the instantaneous frequency of the structural system for a time-varying and nonlinear structure.Here,the structural instantaneous frequencies were directly derived from the decomposed modal responses for single-DOF and multi-DOF systems under both free and forced vibrations.The theoretical results showed that the slowly varying part of a modal response’s instantaneous frequency is approximately equal to the systems instantaneous frequency for time-varying linear structures and weakly nonlinear structures.The correctness of the theoretical results was validated with a numerical simulation of a Duffing system and a free vibration test of a cable with time-varying tension force and frequency.For a time-varying and nonlinear structure with closely-spaced modes,the analytical modal decomposition method was extended to deal with its modal decomposition.The mathematical model for this new extension was provided and an approach with wavelet transformation was developed for the selection of time-varying bisecting frequencies.Finally,a two-story time-varying structure with closely-spaced modes subjected to both white noise and earthquake excitations was simulated,the results showed that the proposed method can effectively be used to decompose modal responses and accurately identify the instantaneous frequency of time-varying and nonlinear structures.