基于频响函数的复合材料空间分布模量场识别

摘要

Considering the heterogeneity of the macroscopic mechanical properties of fiber braided composites,an identification method for spatial distribution of elastic modulus field of the composite beam structure based on Frequency Response Function (FRF) is proposed.The optimization problem is constructed based on sensitivity analysis.The minimum norm of the difference between the measured and the calculated frequency response of acceleration is taken as the objective function,and the spatial distribution of the elastic modulus of the composite beam is then identified by iterative methods.Numerical simulation of a cantilever beam is conducted to verify the correctness of the identification method,and the modal test is then carried out.The homogeneous elastic modulus obtained from a three-point bending test of the same composite beam is taken as the initial value of the optimization problem.The non-contact measurement approach is adopted to obtain the dynamic displacement response of each measuring point on the beam in the modal test,and the acceleration frequency response function is calculated as input data.Results show that the frequency response functions of each measuring point on the beam calculated by the identified elastic modulus field agree well with the experimental values,and the proposed method is feasible when the measurement dynamic responses are noise contaminated.This method is capable of providing a more accurate elastic modulus field for equivalent modeling of composite materials.%针对纤维编织复合材料宏观力学性能的非均匀特性,提出了基于频响函数(FRF)的复合材料梁空间分布弹性模量场的识别方法.采用基于灵敏度分析的方法构造优化问题,以实测和计算加速度频响残差范数最小为目标函数,进而通过迭代求解识别出复合材料梁弹性模量的空间分布.首先,以悬臂梁模型为研究对象进行数值仿真分析,验证识别方法的正确性.进一步开展复合材料梁模态试验研究,将复合材料三点弯曲试验获取的近似均质化弹性模量作为优化问题的初值;利用非接触测量方法获取模态试验中梁上各测点处的动位移响应,并计算得到各测点的加速度频响函数作为优化问题的输入值.结果表明:采用所提出的识别方法获取的模量场计算得到的梁上各处频响函数与试验获取值吻合,且所提方法在实测动响应存在噪声污染工况下是可行的.该方法能够为复合材料等效建模提供更加准确的弹性模量场.