Sadeghi Mohammad, Bazrafkan Mohammad M, Rutner Marcus, Faupel Franz
Department of Materials Science, Faculty of Engineering, Kiel University, Kaiserstraße 2, D-24143 Kiel, Germany.
Institute for Metal and Composite Structures, Hamburg University of Technology, Denickestr. 17, D-21073 Hamburg, Germany.
Micromachines (Basel). 2023 Sep 29;14(10):1878. doi: 10.3390/mi14101878.
A comprehensive understanding of the linear/nonlinear dynamic behavior of wireless microresonators is essential for micro-electromechanical systems (MEMS) design optimization. This study investigates the dynamic behaviour of a magnetoelectric (ME) microresonator, using a finite element method (FEM) and machine learning algorithm. First, the linear/nonlinear behaviour of a fabricated thin-film ME microactuator is assessed in both the time domain and frequency spectrum. Next, a data driven system identification (DDSI) procedure and simulated annealing (SA) method are implemented to reconstruct differential equations from measured datasets. The Duffing equation is employed to replicate the dynamic behavior of the ME microactuator. The Duffing coefficients such as mass, stiffness, damping, force amplitude, and excitation frequency are considered as input parameters. Meanwhile, the microactuator displacement is taken as the output parameter, which is measured experimentally via a laser Doppler vibrometer (LDV) device. To determine the optimal range and step size for input parameters, the sensitivity analysis is conducted using Latin hypercube sampling (LHS). The peak index matching (PIM) and correlation coefficient (CC) are considered assessment criteria for the objective function. The data-driven developed models are subsequently employed to reconstruct/predict mode shapes and the vibration amplitude over the time domain. The effect of driving signal nonlinearity and total harmonic distortion (THD) is explored experimentally under resonance and sub-resonance conditions. The vibration measurements reveal that as excitation levels increase, hysteresis variations become more noticeable, which may result in a higher prediction error in the Duffing array model. The verification test indicates that the first bending mode reconstructs reasonably with a prediction accuracy of about 92 percent. This proof-of-concept study demonstrates that the simulated annealing approach is a promising tool for modeling the dynamic behavior of MEMS systems, making it a strong candidate for real-world applications.
全面了解无线微谐振器的线性/非线性动态行为对于微机电系统（MEMS）设计优化至关重要。本研究采用有限元方法（FEM）和机器学习算法研究了磁电（ME）微谐振器的动态行为。首先，在时域和频谱中评估了制造的薄膜ME微致动器的线性/非线性行为。接下来，实施数据驱动系统识别（DDSI）程序和模拟退火（SA）方法，从测量数据集中重建微分方程。采用达夫方程来复制ME微致动器的动态行为。将质量、刚度、阻尼、力幅和激励频率等达夫系数作为输入参数。同时，将微致动器位移作为输出参数，通过激光多普勒振动计（LDV）设备进行实验测量。为了确定输入参数的最佳范围和步长，使用拉丁超立方采样（LHS）进行灵敏度分析。将峰值指数匹配（PIM）和相关系数（CC）作为目标函数的评估标准。随后，使用数据驱动开发的模型在时域上重建/预测振型和振动幅度。在共振和亚共振条件下，通过实验探索了驱动信号非线性和总谐波失真（THD）的影响。振动测量结果表明，随着激励水平的增加，滞后变化变得更加明显，这可能导致达夫阵列模型中的预测误差更高。验证测试表明，第一弯曲模式的重建效果合理，预测精度约为92%。这项概念验证研究表明，模拟退火方法是一种用于对MEMS系统动态行为进行建模的有前途的工具，使其成为实际应用的有力候选者。
