This work leverages laser vibrometry and the weak form of the sparse identification of nonlinear dynamics (WSINDy) for partial differential equations to learn macroscale governing equations from full-field experimental data. In the experiments, two beam-like specimens, one aluminum and one IDOX/Estane composite, are subjected to shear wave excitation in the low frequency regime and the response is measured in the form of particle velocity on the specimen surface. The WSINDy for PDEs algorithm is applied to the resulting spatio-temporal data to discover the effective dynamics of the specimens from a family of potential PDEs. The discovered PDE is of the recognizable Euler-Bernoulli beam model form, from which the Young's modulus for the two materials are estimated. An ensemble version of the WSINDy algorithm is also used which results in information about the uncertainty in the PDE coefficients and Young's moduli. The discovered PDEs are also simulated with a finite element code to compare against the experimental data with reasonable accuracy. Using full-field experimental data and WSINDy together is a powerful non-destructive approach for learning unknown governing equations and gaining insights about mechanical systems in the dynamic regime.

翻译：本研究结合激光测振技术与非线性动力学稀疏辨识弱形式方法，从全场实验数据中学习宏观控制方程。实验中，对两个梁状试样（一个铝材和一个IDOX/Estane复合材料）施加低频剪切波激励，并以试样表面粒子速度形式测量响应。将适用于偏微分方程的WSINDy算法应用于所得时空数据，从潜在偏微分方程族中发现试样的有效动力学方程。所发现的偏微分方程具有可识别的欧拉-伯努利梁模型形式，据此估算出两种材料的杨氏模量。同时采用集成版WSINDy算法，获得偏微分方程系数与杨氏模量的不确定性信息。通过有限元代码对发现的偏微分方程进行仿真模拟，与实验数据对比显示出合理精度。结合全场实验数据与WSINDy方法，为动态工况下机械系统的未知控制方程学习和机理认知提供了一种强有力的非破坏性研究途径。