基于应变分布响应的模态分析理论与应用

 模态分析技术经过近70年的发展已形成较为完整的独特理论和方法，这与模态测试手段的进步息息相关。由于传感技术的限制，既有的模态分析方法主要是基于加速度或速度测量开展的，重点关注位移、速度及加速度频响函数。过去5年间，本课题组研究和开发了用于重大工程结构的分布式应变传感技术，并以分布式动态应变测量为核心开展了包括模态分析理论、模态测试及工程应用在内的研究工作。本文简要介绍分布式动态应变传感技术的基本特点和系统构成，重点阐述基于应变分布响应的模态分析理论、应变频响函数的测试技术及相应的模态参数识别方法。应变模态分析表明，从时频域上看，应变频响是更类似于位移频响而不同于速度或加速度频响的物理量，因此对低频响应更为敏感；基于位移频响函数和基于应变频响函数提取结构固有频率和阻尼比等价有效；基于位移频响函数和基于应变频响函数提取的特征向量之间的相互关系与位移和应变测量之间的映射关系完全相同，即基于应变频响获得的特征向量是直接的应变模态测量。探讨了应变模态在大柔度结构低频测试、动力模型重构、结构损伤识别3方面工程应用中的优势。

Modal Analysis Based on Distributed Strain Measurements: Theory and Application

With the past five years' study by the authors, an advanced distributed strain sensing technique has been developed for the health monitoring of infrastructures. A series of research work including theoretical and experimental modal analyses were conducted based on the dynamic measurements of strain distribution. This paper systematically reviews the work. With a brief introduction of the basic features of the developed dynamic distributed strain sensing techniques in the first place, the strain-response-based modal analysis theory is further presented. Modal testing techniques are then discussed to obtain the macro-strain Frequency Response Function (FRF) and identify the modal parameters, including resonant frequencies, damping ratio, and Modal Macro-Strain Vector (MMSV). In time and frequency domains, the macro-strain FRF is close to a displacement FRF rather than a velocity or acceleration one, so the relation between macro-strain FRF and frequency can provide a more sensitive indicator at low modes, especially, when the resonant frequencies are small. The identified resonant frequency and damping ratio from dynamic strain measurements have the same precision as those from the conventional transducers such as accelerometers and strain gauges. The curves of MMSV versus mode shape share the same mapping relation with the time-series and frequency responses of the measured macro-strain versus displacement responses, which means that MMSV essentially is a direct modal strain measurement. Based on the above findings, the advantages of modal strain over modal displacement in the engineering applications of low-frequency measurements, dynamic model reconstruction and structural damage identification are discussed as well.