Abstract:

Due to its sensitivity to structural state, strain mode has more advantages than displacement mode in online structural health monitoring and damage identification. Take advantage to the relationship between strain and displacement, apply Least Squares Complex Frequency-domain method (LSCF) into the analysis of structural stress and strain, then establish the frequency domain identification method of structural dynamics parameter based on strain measurement data. Since the strain mode and displacement mode are different expressions of the same physical state, they are similar in mathematical expression. First, establish a parameterized common denominator model with strain as its variable, then on this basis, make the nonlinear least squares problem linearized and obtain the error of the weighted least squares linear equation. Then solve the equation using the algorithm based on the reduction of regular equations and in this way reduce the amount of computation, and avoid redundancy by imposing restriction on the modal parameters. After that, design an experimental system of a free beam structure and use Fiber Bragg Grating strain sensors to measure the structural dynamic strain data, then identify the frequency and damping ratio according to LSCF based on the measured strain data, which fit the results identified by the traditional mothed based on acceleration measurement data well. Besides, the strain mode shapes obtained from the identification are also consistent with the simulation results. Therefore, numerical simulation and the experiment show that the method based on LSCF in this paper can accurately identify the strain modes.

摘要：

由于应变模态对结构状态的敏感性，其在结构在线健康监测和损伤识别方面比位移模态更具优势。利用应变和位移的关系，将最小二乘复频域方法应用到结构应力应变分析中，建立基于应变测量数据的结构动力学参数频域辨识方法。由于应变模态和位移模态是同一种物理状态的不同表达形式，两者在数学表达上有相似性。首先建立以应变为变量的参数化公分母模型，在此基础上将非线性最小二乘问题进行线性化，得到加权线性最小二乘的方程误差。然后采用基于缩减正则方程的算法进行求解，减少计算量，并通过对模型参数施加约束来避免参数冗余。然后，设计并搭建一个自由梁的实验结构系统，利用光纤布拉格光栅应变传感器测量结构动应变数据，根据最小二乘复频域方法，基于应变测量数据辨识得到频率和阻尼比，与传统的基于加速度测量数据的辨识结果相吻合。另外，辨识所得应变模态振型与仿真结果也具有一致性。因此，数值仿真和实验验证表明，文中提出的基于最小二乘复频域方法能够准确辨识结构应变模态。

关键词: 振动与波, 应变模态, 模态参数辨识, 最小二乘复频域法, 模态实验