Ebrahimian Arash, Tang Haimi, Furlong Cosme, Cheng Jeffrey Tao, Maftoon Nima
Department of Systems Design Engineering, University of Waterloo, Waterloo, ON, Canada.
Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA, USA.
Int J Mech Sci. 2021 May 15;198. doi: 10.1016/j.ijmecsci.2021.106390. Epub 2021 Mar 14.
We propose a novel material characterization method to estimate the Young's modulus of thin 2-D structures using non-modal noisy single frequency harmonic vibration data measured with holography. The method uses finite-difference discretization to apply the plate equation to all measured pixels inside the boundary of the vibrating structure and then treats the problem as a Bayesian optimization process to find the value of the Young's modulus by minimizing the Euclidian distance between the measured displacement field and repeatedly calculated displacement field using the plate equation. In order to assess the accuracy of the method, ground truth harmonic displacement magnitude fields of different plates were obtained using analytical solutions and the finite-element method and were used to estimate the Young's moduli. We applied Gaussian and non-Gaussian noise with different intensities to assess the robustness and accuracy of the proposed material characterization method in the presence of noise. We demonstrated that for multiple benchmarks for signal to noise ratio of down to 0 dB, our proposed method had errors of less than 5%. We also quantified the effects of uncertainties in the geometrical and material parameters as well as boundary conditions on the estimated Young's modulus. Furthermore, we studied the effects of the mesh size on the runtime and applied the method to experimental holography vibration measurement data of a copper plate.
我们提出了一种新颖的材料表征方法,用于使用全息术测量的非模态噪声单频谐波振动数据来估计二维薄结构的杨氏模量。该方法使用有限差分离散化将板方程应用于振动结构边界内的所有测量像素,然后将该问题视为贝叶斯优化过程,通过最小化测量位移场与使用板方程反复计算的位移场之间的欧几里得距离来找到杨氏模量的值。为了评估该方法的准确性,使用解析解和有限元方法获得了不同板的真实谐波位移幅值场,并用于估计杨氏模量。我们应用了不同强度的高斯和非高斯噪声,以评估所提出的材料表征方法在存在噪声情况下的鲁棒性和准确性。我们证明,对于低至0 dB的多个信噪比基准,我们提出的方法误差小于5%。我们还量化了几何和材料参数以及边界条件的不确定性对估计杨氏模量的影响。此外,我们研究了网格大小对运行时间的影响,并将该方法应用于铜板的实验全息振动测量数据。