基于牛顿-拉斐森迭代法的带多个柔性电致动器悬臂梁优化设计

IF 2.3 3区 工程技术 Q2 MECHANICS Acta Mechanica Pub Date : 2024-09-16 DOI:10.1007/s00707-024-04085-9
Yiming Li, Chen Chen, Mu Fan
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引用次数: 0

摘要

本研究深入探讨了优化悬臂梁上多个致动器的复杂性,重点是原子力显微镜(AFM)探针产生的非均匀电场引起的挠电效应。多致动器控制在增强挠电效应、大大缓解应力集中和实现精确振动控制方面具有重要的研究价值。多挠性电致动器研究目前面临的挑战是多目标优化,本文采用在凸函数域以鲁棒性著称的牛顿-拉斐森迭代法作为优化框架。通过分析结构参数和挠性电动致动器参数,选择重要的影响因素形成向量空间,确定致动器位置和驱动电压。这些变量构成了优化空间,并被纳入牛顿-拉夫逊一般迭代方程,从而得出迭代矩阵,该矩阵使用 MATLAB 计算。案例研究证实,牛顿-拉夫逊方法能在无外力的情况下有效确定不同模式下的最佳致动器位置和驱动电压,从而显著提高柔电控制效率。此外,该方法还能在外力作用下快速稳定不同模式下的振动。然而,该研究也存在局限性,因为牛顿-拉夫逊法无法有效解决线性空间中的非凸函数优化问题。这项研究推进了对多重致动器优化控制结构动力学的理解,促进了更有效工程解决方案的开发,特别是在微米和纳米结构工程领域实现更精确的致动和控制。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Optimization of cantilever beams with multiple flexoelectric actuators based on Newton–Raphson iteration

This study delves into the complexity of optimizing multiple actuators on a cantilever beam, focusing on the flexoelectric effect caused by the non-uniform electric field generated by an atomic force microscope (AFM) probe. Multiple actuators control has significant research value in enhancing the flexoelectric effect, greatly alleviating stress concentration and achieving precise vibration control. The current challenge in multiple flexoelectric actuators research is multi-objective optimization, addressed here using the Newton–Raphson iterative method, known for its robustness in the convex function domain, as an optimization framework. By analyzing structural parameters and flexoelectric actuator parameters, significant influencing factors are selected to form the vector space, determining actuator positions and driving voltages. These variables constitute the optimization space and are incorporated into the Newton–Raphson general iterative equation to derive the iteration matrix, which is computed using MATLAB. Case studies confirm that the Newton–Raphson method effectively identifies optimal actuator positions and driving voltages at different modes without external force, significantly improving flexoelectric control efficiency. Additionally, it quickly stabilizes vibrations at different modes under external force. However, the study has limitations, as the Newton–Raphson method cannot effectively solve non-convex function optimization in linear space. This research advances the understanding of multiple actuators optimization control structure dynamics and promotes the development of more effective engineering solutions, particularly in achieving more precise actuation and control in the field of micro- and nano-structure engineering.

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来源期刊
Acta Mechanica
Acta Mechanica 物理-力学
CiteScore
4.30
自引率
14.80%
发文量
292
审稿时长
6.9 months
期刊介绍: Since 1965, the international journal Acta Mechanica has been among the leading journals in the field of theoretical and applied mechanics. In addition to the classical fields such as elasticity, plasticity, vibrations, rigid body dynamics, hydrodynamics, and gasdynamics, it also gives special attention to recently developed areas such as non-Newtonian fluid dynamics, micro/nano mechanics, smart materials and structures, and issues at the interface of mechanics and materials. The journal further publishes papers in such related fields as rheology, thermodynamics, and electromagnetic interactions with fluids and solids. In addition, articles in applied mathematics dealing with significant mechanics problems are also welcome.
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